CURL WITH MATH

A More Offensive Game of Curling – Part II

2011-12-27T23:52:00.004-07:00

In Part I we looked at the introduction of a 5-Rock Free Guard Zone (FGZ) rule in the BDO Canadian Open. Feedback from some of the players was positive, though one commented it hurt their head (winner Mike McEwen)...

and a few others appeared dumbfounded...

even Olympic champions, looked, at times perplexed.

Now we’re going to breakdown each of the televised games and see how each team adapted to this rule.

Quarterfinal: Jeff Stoughton versus Kevin Martin

Kevin Martin asks for lead Ben Hebert to put his first stone in the top four foot. Rather than place a corner guard, Stoughton lead Steve Gould hits and rolls to the 12 foot. Martin hits and stays. Now Jeff calls for a corner guard, with Martin unable to remove it on his second’s (Marc Kennedy) first rock. Kevin instead calls for top twelve, cutting off the path around the corner. This strategy (cutting off corner guards) was used to perfection by the underdog Mike Riley rink against Werenich/Savage during the 1984 Brier finals and was likely used often during this event. A mistake by Stoughton on a blank attempt and Martin steals one point.

In the second end, similar beginnings, Martin goes in the house, Stoughton calls a hit, Martin hits and now the corner guard goes up. This delay in putting up the corner now means when second Marc Kennedy puts up a centre guard, Stoughton can hit it. This scenario for leads rocks in the first two ends shows how, when their opponent plays into the rings, the 5-Rock rule allows the team with hammer to avoid stacking rocks into the middle around a centre guard and instead get a corner guard in play. This situation alone has me favoring the 5-Rock rule over 4-Rock. In the traditional 4-Rock FGZ, the team ahead without hammer can put their first rock in the rings. Their opponent puts up a corner guard and they now can place a guard in front of their rock, and it can’t be hit. The cost for a team to place the corner is significant and the opposition didn’t actually need to make a draw around a guard. In the 5-Rock rule a team without hammer does not gain this advantage. In retrospect I wonder if Kevin would reconsider placing his first rock out front rather than in the rings.

After a miss by Kevin on his first, Jeff draws to lay 3 in the house and Martin is looking at this:

Stoughton is Red

Rather than hit, Kevin ponders the freeze to the rock on the tee-line. Watching this, Stoughton’s caught on camera saying to third Jon Mead “yah, go for it”.

I was also surprised by Martin’s call. Though it was thin, it appeared Kevin could easily double the two rocks in the four foot and possibly spin in behind the guard. Even if Kevin gives up a deuce he’s only 1 down. By playing the freeze, Kevin increased the chance for Jeff to score three and even gave some possibility of four. Stoughton ends up scoring three when Kevin’s rock doesn’t curl enough.

In the third end, Martin (now two down with hammer) throws a corner up after Stoughton puts their first rock top four. Lead Steve Gould then places his next rock 2 inches from the house, guarding shot stone. Martin elects not to throw up the second corner and instead tries a corner freeze around the tight centre guard. Hmmm, didn’t he follow what Jeff did in the first two ends?

In the fourth end, the rocks look similar to the previous end, but this time Kevin puts up the second corner guard:

Stoughton is Red

Stoughton’s lead Steve Gould won’t make the highlight reel, but these two REALLY tight guards in the 3rd and 4th end are great shots which had a significant impact on these two ends, or 25% of the game ¹

Despite the crowded beginning, by skips rocks everything has been removed and another blank end.

In the fifth end, Stoughton escapes some potential danger by making a run back and Kevin missing his first draw attempt. Martin is forced to one and scores his only point of the game with hammer (recall Jeff handed him a steal in the first). Thought there was suppose to be more offense?

In the 6th end, down 3-2, Martin places two centre guards (just as he would in the 4-Rock FGZ). After some house cleaning, Stoughton blanks (footnote - the third blank end of the game, and there were only 13 total the whole event!).

After a missed triple on Kevin’s last, Jeff draws for a deuce in the 7th end. Kevin could have tried a hit and roll instead, but the guard was so long I’d expect he knew Jeff could get it from either side even if it was perfect.

Ok, three down, time to grab a beer and change the channel, right? Not with the 5-Rock FGZ. Jeff has Gould attempt a tick on his first shot, but he noses the rock through the rings and it is replaced. On Reid’s first shot he calls to come into the four foot rather than attempt a tick. Nearly every shot from there becomes a team meeting to review the options. I can’t recall a game where a team led by 3 coming home and there were this many huddles to discuss strategy.

Nerve racking for the team that’s built a 3-point lead and perhaps a whole lot of blabbering to just delay the inevitable outcome, but it made for interesting TV.

Semi-final: Jeff Stoughton versus Glenn Howard

Usually if you give up four points in the first end, all of the air goes out of you. The challenge becomes staying focused, knowing in the back of your mind most likely you’ll be shaking hands soon and throwing back pints before the end of the day.

Curling is a game of mistakes and if you make one early, it can be game over before you even started. Glenn is 4 feet heavy on his second shot of the game and now it’s an uphill climb. But with the 5-Rock FGZ, Howard was never really out of it and, most important, the game was entertaining and made for good television.

In the 6th end, Howard is still down four, now 7-3. Stoughton piles three rocks into the four foot while Glenn places two corner guards. Stoughton ends up in a mess after a missed runback by Jon Mead. On his first shot, Jeff gets lucky and catches a skinny double, not the shot he called but an acceptable Plan B. Howard faces this for his first shot:

Howard is Red

He’s four down. Three has to be the play, even at the risk of not scoring a deuce. If Glenn draws to the open side and splits the house, what would Jeff do? He could guard, and Glenn may need to play a difficult double raise, on his opponent’s stone. Playing the scoreboard, it’s more likely Jeff hits an open Howard rock and sits first and third and Glenn needs to hope a double is available to get three, if not he plays the same run back for a deuce. Running short of time, it seemed Team Howard was looking for something else but defaulted on what was perhaps their best option, raising their own stone to remove the Stoughton rock and sit three.

After Stoughton misses his double attempt, Howard gets three and heads to the 7th end one down. After forcing Jeff to one in the 7th end, Howard has some potential to score not only a deuce in the 8th end to tie, but possibly a three for the win. Jeff and Jon both attempt doubles but instead stick to lay two. Jeff makes a double with his last and Glenn has no chance to score his deuce. Game over. The outcome is what we expect from a 4-0 start, but the storyline was very different.

Championship Final: Jeff Stoughton versus Mike McEwen

Three Stoughton games in a row? Ok, I know that Team Stoughton is current Brier and World Champions, but did they really deserve all that TV time? Granted, ladies love a strong sweeping front end that can throw a little weight around (how's the Olympic training program going?).

...but doesn’t CBC think the ladies at home might want to see the young Euro-plumber views of Team Edin

In the final we are treated to the stylish ball-caps and quality whisker rub stubble of the Mike McEwen rink. Provincial rivals in Manitoba, these teams are no doubt going to clash again in their attempt to qualify for the 2012 Brier.

Stoughton starts off calling a center guard by lead Steve Gould. Unsure if he wanted it tighter but note it’s out of the house (unlike Martin’s play into the rings). Mike calls for a tight corner, rather than the come around, but they slip into the rings. Some talk early by the commentators that skips were uncomfortable with the format. Then again, they’re in the final. As I mentioned above, Jeff outsmarted Kevin Martin in their quarterfinal contest. After 13 hit and sticks, Mike hits and rolls out for the blank.

Second end, another centre guard by Stoughton and Mike calls for another corner. Sloppy start as they figure out the ice, Gould comes light then McEwen lead Denni Neufeld raises it into the rings. Sloppy finish too as Mike comes heavy on his first draw but Jeff makes a terrible error in coming light and leaves McEwen a simple draw to the eight foot for a deuce. Jeff could have thrown his draw as much as 8 feet further and forced McEwen to a single. An early Christmas gift.

Third end, Jeff elects to play into the rings rather than throw up a second corner guard. I suspect being the third end he didn’t want to risk the game getting out of hand too early. Eventually he’s forced to one and now is down 2-1.

Fourth end. Some more sloppy play and McEwen is facing more guards than a team one up with hammer needs. Unfortunately, his front end put them there. Third BJ Neufeld cleans up the mess but then gases his last shot through the rings. Stoughton is able to force Mike to a difficult draw for one.

Mid-game break and the 5-rock FGZ rule has had no effect on the game thus far. It has essentially been played out as a 4-Rock FGZ game.

In the 5th end, Jeff uses his extra guard to guard his own guard, which had slid a little too close to the rings. They have a chance to create some offense but second Reid Carruthers slips too deep on his draw attempt. BJ is able to cut-off the corner guard and McEwen sits three. Stoughton third Jon Mead attempts a hit that just clips the McEwen stone. Mead makes a nice come around on his first, Mike draws and Jeff faces this on his first:

Stoughton is Yellow

It looks ugly, but there is still possibility. Jeff makes a soft hit and roll and sits second and fourth, leaving McEwen with this:

Stoughton is Yellow

A difficult shot to run his own back and not leave a chance for Jeff and, ultimately, he does. At this point we expect Jeff to make the double for two and tie things up, but he noses instead and he’s now 1 down without hammer entering the "End Game".

In the sixth, McEwen is able to clear up the guards but his rocks are behind the tee-line and Jon and Jeff are able to maneuver two of their rocks into good positions. There’s a team huddle over Mike’s first shot, facing this:

McEwen is Red

They first discuss picking it out, forcing Jeff to try the same shot again. They reconsider and make what I agree is the much better shot; hit the yellow stone in the four foot on the nose and sit in front of it once it jams on the back red. The result however, is not quite what he hoped and Jeff is left with a hit to sit three. No triple in play and McEwen is forced to a single.

In the seventh end, another miscue by Stoughton on his final draw attempt. Trying to touch the four foot, Jeff is Light by 3 inches; McEwen steals and leads 5-2 going into the last end.

Again, normally time to change the channel but much drama still to come. McEwen’s squad plays the final end well but Jeff has this opportunity with his first:

Stoughton is Yellow

Jeff makes the double to sit three, but his rock rolls towards his other stone and leaves a double for McEwen. No mistake by Mike and it’s game over.

So to re-cap, it was the 5th, 7th and 8th ends where 5-Rock FGZ came into play. Surprisingly, if Jeff had made his draw in the 7th end it would have only been used in the 5th and 7th end.

It did not take long to convince me (and usually it does), this is a rule that should be adopted. Sorry to those players or fans who think it’s “unfair”. It is a minor tweak that will only adjust play in a few ends of each game, but clearly keeps a team that is down two points “in” the game, and keeps me interested to watch. It makes for better TV; what those of us on the couch and behind the glass want to see.

1 Two out of 8 ends = 25%. it’s been a while since we examined any actual math, I don’t want to disappoint my loyal followers. Either of you.^↩

A More Offensive Game of Curling – Part I

2011-12-20T02:46:00.006-07:00

The BDO Canadian Open has come and gone, but we can onlyhope its new version of curling is not forgotten. Mike McEwen and his rink from Winnipeg wonthe event, the cash and the somewhat controversial CTRS (Canadian Team RankingSystem) points,¹which move them further ahead in their quest for an Olympic Trials berth. What the fans won was a possible glimpse intothe future of the sport.

To the best of my limited knowledge, use of a 5-Rock FreeGuard Zone (FGZ) rule in the BDO was the first for a Grand Slam, WCT, CCA, ICF,WCF, or any other sanctioned curling event. This rule prohibits a team from removing an opponent’s rock in the FGZarea (between hog and rings) until the 6^th rock of an end.

I initially felt the 5-rock FGZ rule would have a minimal impact. Looking at outcomes basedon scoreboard, with an albeit small sample size, it appears I was right. 5-Rock FGZ had minimal impact on outcomes,but what it did have was entertainment impact for the fan. For those who missed the televised games, thearchived video can be seen at http://www.cbc.ca/sports/curling/video/. I have only to draw your attention to thefinal end between Howard and Stoughton in the Semi-Finals where, leading by 2,Stoughton needed to make a double on his first stone to ensure a victory. There was some risk during the end of Jeff possiblysurrendering a three to lose. It didn’t happen,but the drama was much higher than that of a 2 up final end in a 4-Rock FGZ game. During Stoughton’s Quarterfinal and Finalgame, where the winning team was up three in the final end, you’d think twicebefore turning the channel. At thislevel of skill, this usually is not the case.

Some players may dislike the 5-Rock FGZ because it doesn’t rewarda team’s good play. Make all your shots,solid play for 7 ends to build up a two point lead, then one critical miss inthe late stages and you could give 3 back and lose. I can empathize with this point of view. A team holding a two point lead without hammerin 4-Rock FGZ wins 85% of the time with two ends to play and 88% with one toplay. A visiting baseball team leadingby two runs in the 9^th inning wins 86% of the time and 89% when athome. Strong play through 8 innings(similar to 7 or 9 ends) is rewarded with a high probability of success. 5-Rock FGZ feels like the team behind isallowed to put a runner at second base before starting the inning. I agree, it seems unfair. But it is fun to watch and I’ll argue theother side.

I wrote years ago about curling as a Battle for Hammer. What I discovered was, the greatplay of forcing a team to one was, statistically speaking, no big deal. In every case (except the last end) in whicha team is tied and forces their opponent to one point, the team (now one downwith hammer) has increased their chances by no more than 4%, and usually 3% orless. Similar numbers for being down twowith hammer versus one down without hammer (0-3.5% difference). This is whycomebacks in curling can be difficult; you eat up ends just trying to get thehammer back, and give up a point to your opponent in the process. Let’s look at a common scenarioin an 8 end game:

First end, you miss a half shot and give up two. Second end take 1. You’re down one without hammer and only 6ends remain. You are able to get a forcein the 3^rd end and now are back to two down. In order to get back into this game, you mustscore two in 4, force one in 5, score two in 6 and force in 7. That gets youtied coming home. To get this result youmust play extremely well. However, evenif you play well but your opponent matches you, this outcome is not likely to occur. This is how down two after the first endagainst the best teams in the world usually leads to a loss. Going back to our baseball comparison, teamsup two runs after the 2^nd inning win 66%. In curling its 74%, and for the top teams its85-90%. Even allowing for a largeportion of these wins coming against weaker teams, when watching a curling gamewe may want to flip the channel after the first end deuce. I wouldn‘t leave a 2-0 baseball game in thesecond inning, though I may grab an extra beer and try to take a nap.

I’m the first to admit one event produces only small samplesizes and we need further games to provide more analysis, but I did compare thenumbers from this weekend’s 5-Rock FGZ BDO event to the previous Grand Slam,the GP World Cup. What did I notice?

Teams score more (duh). 10.4 pts/game versus 9.85. 1.42 pts per end versus 1.31
Less blank ends. Only 36 total blank ends in the BDO (9.3%) versus 61 (15%) in the WCGP.
Teams are forced to one the same amount of time. Teams scored a single point with hammer 35%in the GPWC and 34% in the BDO. For asoften the extra guard provided more opportunity, teams likely had to bail outand score a single at risk of a steal.
Teams don’t score more deuces, but deuces turnedinto threes. Teams with hammer scoredtwo or more 33% of the time, same inboth events. However, deuces occurred25% of the time in the GPWC and 21% during the BDO. Four or more was still a scarce event (2% GPWCincreased to 3% BDO), and threes increased to 9% from 6%. Note that in both cases the increase is 50%and, though the sample size is small, we should expect an increase in scoringfor teams with hammer.
Teams steal more points. Teams stole 1 point 14% and two or more 3.5%(total of 17.5%) in the GPWC and 17% + 5% for 22% steal percentage in theBDO. The 5-Rock rule doesn’t give anyextra advantage from the 4-Rock rule to a team without last rock. One likely reason for the increase is thatteams, knowing they can’t keep the end clean, become more aggressive withouthammer and steal more often. This leadsto the next effect…
Fewer close games. During the GPWC, 19 games decided by one point,9 extra end games and 89% of games went to the 8^th end. Granted, not all one point games are close(some have a team down three score two in the last end), but we can gain somecomparison to the BDO with 13 1-point games, 81% reaching the 8^thend and only 1 extra end game. However,stats can’t tell us that
The 5-Rock games were more exciting.

Itwasn’t just the novelty and it wasn’t my imagination. Giving the team with hammer an extra guard,which is most often used when that team is down, creates more excitement. Period. Two and three down are no longer reasons to change the channel. The trade-off could be more games which don’treach the 8^th end, blow-outs after 5 or 6 ends. However, many close4-Rock FGZ games are, both statistically and in my viewing opinion, not a closeas they appear. I think 5-Rock FGZ wouldbe a rule that improves the game for the fan and would benefit the sport.

Thenext question to examine is, does 5-Rock FGZ change Win Probability? Sample sizes are way too small to give us anyreal insight. For example, teams leadingby one and two in the late ends (6-8) won more often (75%/93%) in the BDO thanin the GPWC (61%/80%). Given the advantageof the extra guard, we’d expect these numbers to be the opposite. When 3 or more down, teams in the BDO wereable to come back, at any time in the game, 3 times out of 72 (4.2%). In theGPWC , teams only led by 3 or more 44 times, but 4 times a team actually cameback (9.1%). More data is clearly neededto provide a proper comparison. Based onwhat we saw in all of the televised games, we could expect to see an increase inwin percentage for teams down one or two with hammer in the late stages, but I willhold-off judgment until we see more data. To get more data, we’ll need to adopt the 5-Rock FGZ rule at more eventsin the future (yes, please!).

So how did teams handle this rule during the event? I’ll dig into the three televised games andtake a look…in Part II.

1 Yes readers, CWM is going to start using footnotes, in order to segue into information which I’m too lazy to thread into the main article. Similar to the process used by the fine writers at Grantland.com. In this case, it should be noted that all teams participating in the BDO had to agree to the 5-rock rule in order to allow CTRS points to be awarded. Perhaps surprising that no one opted out, but I expect any team voting NO would go years without anyone buying them a round of drinks.^↩

Clash of (Curling) Titans

2011-12-12T03:09:00.008-07:00

Sometimes in life, we are surprised. The gift we receive not for a birthday orChristmas, but because someone was thinking of us. The girl we thought never noticed us actuallyflashes a smile back. Adam Sandler makesa movie which is entertaining and aimed at an audience over 14. Most often, however, we are not surprised.The gift only comes at Christmas, and it’s socks or an itchy sweater. The girl is actually smiling at the guystanding behind you. And Adam reaches newlows in his latest Rottentomatoes.com rankings.

The first Canada Curling Olympic Trials spots, given to thewinners of the 2011 ~~CCA~~ Canada Cup, provided little in the way ofsurprises.

Jennifer Jones produces a deuce in the final end of thefinal round robin game to slink into the last play-off spot with a 3-3 record,and then proceeds to dismantle the competition in her next two contests. The Jones rinks’ mediocre play followed by adominating play-off performance is no longer a surprise. The Chelsea Carey team by way of their 5-1record will no doubt be a team of the future, and they will likely learn fromthe poise seen in the Jones rink for that final game. Jennifer has been there before and itshowed. Congratulations and good luck intwo years!

The Men’s Canada Cup final also left no surprises. Martin versus Howard in an epic battle withKevin the victor and Glenn, once again, falling just short. TeamHoward, the Buffalo Bills of curling these past few years, took early advantageof some Martin misses and appeared to be in position to shake their recentpast. But a key deuce in the 5^th end followed by a Howard singlein the 6^th gave Martin control and he held on for the win. A very entertaining game which included manyinteresting moments.

In the first end Glenn elects to draw into the rings andMartin forgoes the corner guard to hit and stick on the nose. Seriously? The end produces a blank and if you just arrived from a tropical islandand were watching the first game of curling in your life you’d wonder what allthe fuss was about. Was Kevin trying toestablish hammer in the “even ends” (a theory which is not supported bystatistics)? Was Glenn expecting Kevinto hit out the first end? Do these twoteams really still get butterflies in a big game and both skips wanted to workthem out by playing it simple? Should Ireally be spending these many words discussing such a boring end? Probably not.

In the second end, Glenn brings his first rock again intothe rings and Kevin throws up the corner guard. Game on. Some great shot makinguntil an uncharacteristic miss by Martin third John Morris on a possible cornerfreeze allows Glenn to jump on the offensive, and he comes heavy. Glenn makes no mistake on his final shot ofthe end however, able to corner freeze perfectly and produce a steal of one.

In the 3^rd end, John Morris is six feet light onhis final shot and we wonder if that is the same stone that was light in thelast end. Glenn makes a great shot andKevin is heavy on his next. The Howard Team gathers to discuss Glenn’s final shot and thirdWayne Middaugh immediately identifies that if Kevin raises the red guardperfectly and catches his red stone in the top eight foot, he can scoretwo.

Martin is Red

This decision on this shot is so riveting that Martin coachJules Owchar pulls out super spy binoculars to see what is happening.

They decide to leave Martin the difficult shot for two andinstead block off the draw. Kevindoesn’t hesitate and immediately calls for the run-back, which he makes. Commentator Russ Howard agreed with hisbrother Glenn’s call, stating that if Kevin can get two out of it he deservesit. So is it the right call?

We can attempt to determine the odds we believe Kevin needsto be successful in order to choose guarding the raise over the draw.

Let’s assume if Glenn doesn’t guard the centre he simplyguards the raise. Kevin still has to make a draw on veryswingy ice to get a piece of the button. Let’s estimate a 90% success rate by Kevin to score one.

Draw

Martin Win % = .9(.39) + .1(.26) = 41%

Let’s assume if Martin plays the raise (as he did) he eithertakes 2 or Howard steals one. Thereappeared a small chance that Howard could steal two but Kevin would need tomake a very poor shot and get unlucky.

Raise

Martin Win % = 41% = x(.57) + (1-x)(.26)

x = .48

Kevin needs to be successful more than 48% of the time tomake Howard want to guard the raise. What would we expect Kevin’s chances in that situation to raise a rock 5feet and hit between ¼ to ½ a rock? Iwould suspect it is close.

The other potential shot was for Glenn to play a soft raisehit on his own rock in the top eight foot, removing the Martin stone, and lyingfirst, third and fourth. I like thisshot as an attempt to remove the raise and block the draw. The risk is that the rocks roll intoa favorable position for Martin. In hindsight (with the advantage of time and slow motion video toexamine), this appears to be the preferred choice, but I don’t fault Glenn forthe original call. His objective is totry and steal, take control of the game, at the risk of a Martin deuce and beingone down with hammer.

It’s the 4^th end of a ten end game and somehowthe sense is we’ve only just gotten started. An eight end game would seem more urgent. Numbers show that Glenn has a 43% chance towin and if in the 4^th end of an 8 End game, it would decrease to40%.

Tied 2-2 in the 5^th and Howard gets into sometrouble. Wayne misses the raise double take-out,leaving his shooter as a center guard. Kevin elects to have third John Morris draw to the side, to sit two.

Martin is Red

There are 6 rocks still to come and Glenn has to decide howhe wants to approach the rest of this end. They discuss a runback but recognize if he makes it perfect they aren’tshot. I don’t like trying to remove thecenter, it may be needed later on. Anotheroption could have been a freeze to the back stone but to be shot they wouldhave to be very precise and would likely leave a simple hit and stick double tolay two. Glenn could also try to draw tothe centre, even perhaps back four foot, in an attempt to move play back to thecentre and create a force or even a possible steal, but at the risk of givingup a big end. They eventually choose tohit the Martin stone and try to roll towards the middle. Wayneunfortunately rolls out of the rings. John makes the draw again, and Glenn chooses to again try a hit and rollon his first but noses. Kevin now isable to play a freeze and make Glenn’s final decision even more difficult.

Martin is Red

Howard decides to play a hit and stick (the roll attemptwould have jammed the Martin stone on the back yellow). Kevin is left with a simple hit and stick forhis deuce and a 4-2 lead. Kevin is now76% likely to win the game. Could Glennhave taken a different approach to the end? If Kevin scores three, Howard drops to an 11% average chance to win andlikely suspects it is lower than this “average” statistic in thissituation. The hit and roll attempt byWayne is attempting to bring play to the centre while also removing a Martinstone as an “in case” scenario (such as, in case we give up more than one itwill not be three). If this is the 5^thend of an 8 end game I don’t believe the decision is nearly as close, he has todraw. A deuce with 3 ends remainingwould drop Glenn to 19%. Even here in aten end game, I would prefer Glenn tries to draw on Wayne’s last or on skips first, to the backfour foot, to bring the play to the middle. Possibly while trying to tap the Howard rock, Martin would leave morerocks in the area which could help Glenn later in the end. The question to be answered is, would yourather accept being 2 down to Kevin Martin with 5 ends to play or aggressivelytry to force or steal at the risk of ending things right now. Howard decided the two was acceptable. Here’s the troubling statistic: Martin is (inhis small sample size) much higher than 76% when leading by two after 5ends. In the range of 95%. Glenn is a much stronger team than theaverage competition and should rightfully consider his chances are better than5% against Kevin is this situation, but by how much?

After not playing aggressive in the 5^th end,Howard goes all out in the 6^th attempting a bounce back deuce. The look on Glenn as he and Wayne discuss theiroptions during third stones tells it all.

Here is what they are facing:

Martin is Red

Howard brings their next rock behind the corner (see below). Martin throws centre guards and Glenn peels with Wayne’s last shot and his skips first. It felt like they could have perhaps played ahit off their own rock partially behind the corner and roll into the four footand disrupt the pile. Kevin realizesthe possibility and guards it on his final stone.

Martin is Red

Glenn is left with an attempt to raise the Martin shot ontothe yellow in the eight foot, attempting to spin it in for two. He instead takes one and the fans, if it werecrowded, may have considered leaving to beat the traffic rush.

In the 7^th end and John Morris makes a double peelon his final stone. Howard, down 4-3without hammer, is facing this before first shot:

Martin is Red

Clearly set on trying to force Martin to a single, they electto hit the back red stone and sit two. They discuss that even if Kevin manages a double, he likely rolls outand they have a chance to come around and still force a single. I didn’t agree with the “roll-out”double. Appeared many ways Kevin would havea double to sit one and likely blank the end. However, the numbers show that a force is only 2% better than a blank(19% if down two with hammer and 17% if one down without with 3 endsremaining). My first impression wasGlenn should have played a guard on their shot stone. It could be the extreme curl made guards lesseffective and Howard’s team felt a steal was not likely. Quickly looking at thenumbers, if Glenn expects Martin to get a deuce 1/3 of the time he throws theguard, he needs to steal greater than 20% of the time to make it the correctcall.

Uncharacteristically, Kevin hitsand rolls out, leaving Howard sitting one. John attempts to have a brief chat with his skip, but it ends abruptlyas Kevin slides away leaving his third in mid sentence, mouth still open. This is what curling needs to increase itsfan base, more coverage of players feuding. Like this recent first end chat between Randy Ferbey and John Morris.

Martin draws for one and Howard is now down two with hammerand 3 ends to go. The 8^thlooks like a possible blank until Kevin makes a great draw out to the wings,corner freezing a stone, and Glenn is forced to take one. His chances go from 15% (blank) to 14%(force).

In the 9^th, Howard is able to put his rocks ingood positions and Martin needs to throw big weight on his final stone to takeone. His shooter hits over 15/16ths ofHoward’s rock in the top 4 and actually spins forward a half rock to beat outanother Howard stone by a measure.

Now two up without hammer, Martin makes an interesting callon his final stone in the 10^th. Kevin’s squad has been able to clear the guards and Glenn is forced todraw around a single Martin stone in the top eight foot.

Kevin could attempt a 6 foot raise to remove the Howardstone and win the game immediately. Heinstead chooses to play a freeze to the back stone. He comes short and leaves Glenn a chance witha double to tie the game and send it to an extra end. I don’t disagree with Kevin’s call. The largeamount of curl should enable them to bury right to the back rock andessentially end the game, but Kevin Martin is known for laser precise hittingand given a chance to end it that way, I’m surprised he didn’t chose thatoption. Ultimately Howard is unable tomake his final shot and Martin wins the Canada Cup and first Canada OlympicTrials spot. Something tells me Glennwill qualify soon enough and perhaps in another 2+ years we can watch theseguys do this all over again.

The Battle for Canada’s Cups – Part 1

2011-12-09T01:55:00.009-07:00

Thank goodness for PVRs (Tivo specifically in my case). If not for pre-scheduling recordings of allthings Curling I would have completely missed this past weekends’ games. This humble little event, historically knownas the ~~CCA~~ Canada Cup, is played each year with a small select group ofteams whom you’ve heard and seen many times before. This year teams squared off not only for afew sheckles but for the right to play against other teams in 728 days, for theright to represent Canadaat the Olympics in 796 days. KevinMartin’s win in this Canada Cup felt a little like Tiger’s big comeback winthis past weekend at the Chevron World Challenge, a silly season exhibitionwhere only 18 players contended. Was itsurprising to fans that some of our best curling teams this season were notcompeting? Notably absent were SherryMiddaugh, leading the Women’s CTRS (aka, Canadian TeamRanking System) and John Epping, ranking third in the Men’s. Wasn’t the CCA going to give teams a break inOlympic qualifying, making it a 2 year effort instead of 3? Yes, you could argue, this Canada Cup is inthe 2011/12 season, but in order to qualify to play in it, you needed tosucceed LAST year. Hence, this firstOlympic spot was only open to teams who started their Olympic Quest the seasonfollowing the last Olympics. I’m gettinga headache.

With all this at stake, it would have been nice to see morecoverage, televised or even via internet. I expect we’ll see extended coverage of the Pre-Trials (like we did in2009), despite the fact the top teams will have already qualified and bewatching in the stands.

So how do you feel about 10 ends? I remember when 8 ends felt short, now itsimply feels normal. Based on previousanalysis: Is curling a battle for hammer?,I supported a theory that an 8 end game is competitively equal to a 10 endgame, given the percentage chance to win based on the scoreboard stays fairlyconstant until 6 ends remain. Essentially, an 8 end game is a 10 end game where the teams are tiedafter two ends. Because we’ve been watching for shorter time, the 8 end gamemay appear to be different, but in effect the teams are likely playing as theywould later in a ten end game, because strategy should be based on ends remaining, not ends played. For example, if a team seems overlyaggressive in the 4^th end of an 8 end game when down two, it’s thesame approach they would take in the 6^th end of a ten endcontest. The debate will continue and Iwill stay on the fence for now….and on to the games.

Haven’t we read this book before? Jeff Stoughton versus GlennHoward with the winner to play Kevin Martin. This scenario occurred at the 2009 Brier and Olympic Trials, and feelslike it happens nearly every major event. So how will the story end this time?

The Glenn Howard rink have hammer in the semifinals by virtueof their win versus Stoughton during the round robin. Why is the Howard rink dressed in basic navy blue instead of lime greenor shocking pink? Oh, I forgot, it’s aCCA event. The teams are all wearingsingle colour form fitting shirts, complete with racing stripes along theshoulders, no doubt to show off the athleticism of men in their mid to late40s.

A wonder the stands aren’t morefull to see this show. If only we couldbring back The Wrench, sporting a tight fitting gem with his Olympic Shape.

In the first end Stoughton lead Steve Gould draws completelyaround a centre guard, peeking over half out the other side, showing the icehas the same swinging intensity of Plato's Retreat. Glenn later uses that swing to make a fantastichit a roll on a stone buried in the four foot to lay two. Jeff faced several key decisions early. On his first shot, Howard sits one behind a corner guard.

Howard is Red

Stoughton could attempt a peel on the outside ofthe rock or a difficult corner freeze, but instead chooses to draw around thecentre. Jeff makes a perfect shot. The large curl however makes Glenn’s shot,though difficult, not impossible and Howard manages to sit two after his firstshot. Rather than risk another draw thatcan be removed for three, Jeff chooses to remove the open Howard rock andsurrender an early deuce. The decisionis sound in that a deuce leaves him with a 27% chance while a three drops theirchances to 14%. In retrospect, Jeff mayhave been better to peel out Howard’s stone, let Glenn attempt a come around,then use the massive curl to take out Glenn’s shot and likely induce a blank orpossibly a force. It appeared no rockwas safe from being removed, but perhaps ice conditions were not identicalacross the sheet. I still like Jeff’saggressive call on his first and Glenn simply made a great shot.

In the second end, Glenn and Wayne are discussing Wayne’s second shot butwe can’t hear them because the TSN commentators are fixated on discussing JonMead cleaning the sliding path. Iunderstand commentating on curling is not easy (I learned it first hand duringthe 2010 Brier working for CurlTV). Ialso realize Jon looks handsome in his tight fitting CCA jersey. But there is enough silence during a game forplenty of playful media banter that when the players are actually discussing ashot, keep quiet!

The 6^th end shows both the incredible action fromthe rocks and ice conditions. JeffStoughton is down 4-2 with hammer and attempts a double on two close Howard stones. After removingboth, his shooter backs up and nearly fires across the house to be removed fromplay. The shooter bites the edge for one.

Howard is Red

Don’t try this shot at your clubat home. Jeff’s chances go from 21% if ablank is successful to 20% when he stays for a single so in effect, his mistakehas no real impact on his chances. Infact, he didn’t need to try the difficult double and roll out at all and wasfortunate not to hit the first rock too thick, roll across the top andsurrender a steal, which would have dropped their chances to 9%. You could argue his accuracy is such thatJeff would not make this mistake often, but why take on the additional riskwith no benefit? During the 2011 BrierStoughton played flawlessly with the exception of a brain fart against BradGushue during the round robin. Leading5-3 he tried a more difficult shot which the odds did not require to be attemptedand surrendered a three in the 8^th end. Check out Jeff's comments on his Friggin' Bonehead Shot

The loss gave Newfoundland hammer in the 1-2 Page Play-offgame which Team Stoughton won with akey steal in 9, on their way to winning their third Brier.

In the 7^th end, leading 4-3 with hammer, Glenn chooses to split the Stoughton centre guardwith his leads first rock. Craig Savillexecutes perfectly, but Howard then chooses the come around on Craig’s nextshot. I'm not certain what Glenn’s thinkingis there. Either he wants to eliminate Stoughtonhaving two guards (but is happy with one) or just realized it was a 10 end game and he had 4 more endsto go. Jeff ends up facing several redrocks and discusses a hit and roll versus a draw, contemplating whether theycould give up a deuce, three or even four.

Stoughton is Yellow

Realizing a deuce puts them 3 down with 3 ends to play (7% chance towin), they correctly choose to draw. Tono one’s surprise however, like several shots before, Glenn is able to removethe fully buried rock and take three, nearly assuring victory. Jeff made a good shot with his final stonebut may have been trying to come deeper, curl across the guard and place itwhere a possible jam would occur. Is itpossible there can be too much curl in curling?

Another rematch.

Glenn Howard again battles Kevin Martin in a final game onthe path to Olympic qualification. Granted, this game is only to qualify for the Trials but it still hasthe intensity and drama you would expect from these two teams. This game was so interesting; I’ve decided tobreak this article into two parts. Joinme tomorrow for Part Deux.

This is not your father's (breakfast) Grand Slam...

2011-11-12T00:00:00.002-07:00

Wouldn’t Denny’s make a great sponsor for these curlingevents?

Welcome to the 2011/12 Curling Season! Ok, I know, it started months ago, back whenmost of us were still on the golf course and it runs until we tee it upagain. Usually curling for me beginswith the first televised event of the Season. This year it was, technically, the internet coverage of the PheasantClassic in Brooks, but as my time was limited in watching, I’ll begin with thisyear’s first Grand Slam, the GP Car and Home World Cup. Or GPC&HWC GS, for short.

Glenn Howard faced Mike McEwen in the Quarterfinals andthough not always a display of great shotmaking, it was an entertaining match.

The 7^th end has TeamHoward up one without last rock. Howardis unable to add pressure and create any 4 foot play while McEwen is able tokeep things clean and sits one back four with two shots remaining.

Howard is Yellow

Howard’s squad spends some time together in the house,discussing alternatives to what would appear to be a hit and stick. However, this would allow McEwen to blank andgive him hammer, and a chance to score two and win in the final end. The situation has become very common when 1up without in the next to last end: be aggressive and attempt to either stealor force your opponent to one, at the risk of giving up two. This exact situation (open rock, back rings)was examined in the early days of Curl With Math (http://curlwithmath.blogspot.com/2007/01/aggressive-play-in-9th-end.html).

My assessment backthen was that you need to surrender a deuce no more than 20% of the time to bethe correct call. What was interestingin the dialogue, other than the fact it took them so long, was the comments “noone has scored a deuce, so they probably won’t get one in the last end”. Even said with a smile by Craig, this commentdoes not base any of the weight in the decision on rational thinking. The “gut” says “we haven’t scored much,neither have they; let’s head to the next end up one”. The problem is, unless ice or rock conditionsare a factor, their chances of scoring two next end is not related to how manydeuces they have scored during the single game or even past several games. This is comparable to a baseball managerdeciding to bring in a relief pitcher against Albert Pujols simply because he’sbatting 0 for 5 against him. His chancesof belting a homer in his sixth appearance against the pitcher are no lesslikely than if he were 5 for 5.

So after much discussion, Howard made what I agree was thecorrect decision. In future, perhapsthis type of call won’t take as much deliberation. Contrast for example with Mike McEwen’sdecision in the next end. One down andfacing this with his final shot:

McEwen is Red

Rather than play a simple draw for one and go to the extraend without last rock, McEwen elected to try a hit on his rock outside of therings, and roll his shooter into the yellow stone, to possibly score two andwin the game.

Mike correctly understood that his chances of stealing in anextra end against Howard are not good. Stats for Grand Slams have shown that teams tied without and one endremaining only win 20% of the time (larger sample size shows closer to25%). See “Statistics for GrandSlams” at the bottom of http://curlwithmath.blogspot.com/2008/11/statistics-for-womens-curling-and-what.htmlfor more details.

Mike Harris commented he felt McEwen would make the shot 20%of the time, which puts it at roughly an even decision. What Mike Harris forgot to factor in was theanalysis of still taking one, even if they miss the deuce. From Mike McEwen’s comments (writing astucker22) in a recent post on curlingzone.com http://dev.curlingzone.com/showthread.php?s=b918da19a44a9ff96b8c96ab365cf9fd&threadid=8894&pagenumber=3&forumid=10&tp=0

“Here's what was going through my head:

#1) VS the best 5 or so teams in the World you have only a 10-20% chance ofstealing depending who you are playing. Yes, it can get as low as 10% vs thebest (seen the stats).

#2) In our minds we make contact on that in off 40-50% of the time .... and weactually stick it for 2 maybe 30% of the time give or take.”

I expect the numbers showing 10% are a small sample size andMike is not giving his team enough credit. I would put them closer to 20% at a steal chance, but still you arelosing 4 times for every 1 victory. Whatwas also interesting in the discussion was clear understanding from the teamthat this was the shot, likely decided before it had come to rest. The time was spent on how to play it, not onwhether to play it. Great call,unfortunately poor result.

Joan McCusker said they “gambled and lost”. Another example of how this phrase gets usedincorrectly. Which do you think is thegreater “gamble”, attempting to win with this shot or taking worse odds in theextra end without last rock?

The final game between Epping and Howard was one I watchedwith speed and determination, using the fast forward setting on my Tivo. Howard successfully used a corner guard inthe first end to score a deuce (despite some great shot making by John andthird Scott Bailey), but Epping bounced back with a deuce to tie (even with only1 free guard!). This game had a morethan normal amount of corner guard play and after a miss by Epping in 4, Howardwas able to use another one and score a three to take a lead he would notrelinquish. Even if Howard only scores adeuce, they should win at least 79% of the time. The three increased their chances to90%. Here is a clear case where possiblythe 5 rock rule could give a team some more hope of winning (2 or 3 down with 4to play), but how much is yet to be determined. The 5^th end was a prime example of Howard able to remove thecorner guard and Epping having to make freezes on open rocks in the house in aneffort to score two (and does), but he never really had any chance to tie witha three. The 6 and 7^th endplayed out just as they will under a 5 rock rule. The downside being that the team withouthammer, when down, gains no additional advantage over today’s rules. Must say I’m more than mildly interested inthe next Slam to see how this type of end will be played. Perhaps we need more variation in the rulesof each event to create additional interest. But please, I beg you, no mixed doubles.

I don’t know if it’s Wayne Middaugh’s influence but this Team Howard is not dressing to match their colourtone (very “spring” and most of them are “winter”). That bright green with yellow trim does notmatch anyone’s complexion. It will,however, ensure they make it safely across the street during the late night hours;cars will easily be able to see them from blocks away.

It won’t be all blogging for me this year. My 7 year old son actually watched theScotties and the Brier last year and decided it looked cool enough to try thisseason. This is surprising given hemostly gravitates to skateboarding, snowboarding, BMX and any other extremesport that gives his mother a nervous breakdown. My boy’s curling enlightenment led me to haulout my dusty curling pants (is there a slicker pair of black slacks that youcan own?) and shoes and join the local club (St. Albert). I’ve put myself on the spare list and have memorized my line of “Sorry,I’m out of town that day” already, so as to ensure no actual rocks will bethrown. Alas, I did agree to help outwith the Sunday Junior program and my body already hates me for it. The good news is that not just my knee isprepared to give out, but most of the muscles, joints, tendons and other itemswhich make up my legs as well.

It is interesting that they call the program “Little Rocks”,but in fact don’t use the actual little rocks; lighter stones which are thrownby little persons, to a house that is shorter than the normal size rink. When a 4 foot kid starts at basketball, dothey play on a 10 foot hoop? Does atee-ball player face an 80 mph fastball in his first trip to the plate? The idea of having 7, 8 and 9 year oldstrying to slide/push/move a 40+ lb rock down the sheet is ludicrous. It’s surprising to me that most of the kidshave not become more discouraged. I hope this interest is maintained but don’tbelieve we are properly setting the stage to bring these young players into thegame.

I was tempted to take my son out of the program when I sawthat they were attempting to play the adult version of the game. I started at 12 and given the physicalbarriers, would suggest there is no need to start anyone before 11 unless thesmaller rocks/rules are used (except perhaps your child eats hormone enhancedchicken and already shaves). He remainsinterested for now and I will support his efforts, with the hope that hiscontinued failure to get a rock that weighs slightly less than he does to thehog line, much less the button (at the other end) will not discourage himenough that he decides to drop curling for more snowboarding.

Is 5 the Magic Number?

2011-11-08T19:34:00.000-07:00

How about that 5-Rock Rule?

The World Curling Tour’s Player’s Association has decided totrial a 5 rock rule at the upcoming Grand Slam event in Kingston, December 14to 18th (which one is it again, Masters or Open?) The rule would make the 4^th rockof the end (thrown by team with hammer) now eligble for “free guard zone”status, unable to be removed by the opposing team until after the 5^throck, most likely the 7th rock of the end. Essentially 4 rock means that 3rocks are safe from removal (if put in the correct location, between house andhogline) and subsequently 5 rock rule means that 4 rocks are now safe fromharm. Confused yet?

Though I applaud the WCT and their PA for doing what manyother athletes would like to do, which is have a direct influence on theirsport (ask the NBA PA how they feel these days), I don’t believe this newversion of Curling will have a significant impact and may in fact result in theopposite desire than is intended. Butperhaps we need to examine what it is trying to do exactly.

Firstly, is there a desire is to create more offense? That comes with some risk. Curling is a game that actually needs lessoffense to ensure a close game, but needs scoring to be exciting. It is a game where being 3 or more down withhammer or 2 (or even one) down without becomes no longer interesting, and progressively so as the ends tickaway. If more offense opportunitycreates higher scores early, teams will then be apt to stay out of trouble, letthe team behind take chances, and capitalize on their risks (when they fail)and end the game even earlier. As boringas it sounds, a classic game of no free guard zone which is blanked for 9 endsand played tied in the 10^th is closer (though clearly not asexciting) as a game where a team cracks three early, gives up a single and thenscore two (and after three ends we are off to the other sheet for coverage,hopefully). Imagine most any boxingmatch with Bernard Hopkins, grappling, pacing, counter punching and ploddingalong until he wins on a decision as opposed to a Haggler vs Hearns with anexplosion of attack until only one stands after a few short rounds. So my position is, more offense is notnecessarily good. Perhaps what we meanto say is…

Do we want to keep games closer? Similar to the original Pole Position on Atari,do we want the cars that are behind to have more speed than those in the leadso we ensure a close race? As I statedabove, even with the 4 rock rule a team can quickly move from a close game to aposition of Dominance with a quick three and then hold their opponent to1. So can a 5 rock rule allow a game tostay closer, allowing for more comebacks?

I traditionally felt 4 rock was the “fairer” rule to the old3 rock, in that some edge was given to the team without hammer (2 rocksprotected, versus 1), to offset the large advantage the team with hammer isgiven. Despite this edge however, teamsstill only win 25% of the time (closer to 20% in Grand Slams) when tied withouthammer and one end to play. So can 5rock change this?

I believe the answer is yes and no. The one situation I like, and an 8 end gameperhaps stresses this situation, is the fact the hammer team is, early in agame, most likely behind. For example, if I start without hammer, thereare three most likely scenarios, assuming two equally matched teams. In order of likely occurrence: my opponentscores 1, my opponent scores 2 or I steal 1. Threes and steals of two or more can obviously occur, but are lesslikely.

In each case there are now 7 ends left in an 8 end game and,though this may seem obvious, the second end is the only time in a game we are 100% assured the team with hammer is behind. The third end is also very likely to have theteam with hammer either tied or behind. Themost likely scenario where we have hammer and the lead in three is to take 2 inthe first then force my opponent to one.

In the case where the team with hammer is behind, the 5^throck must be an advantage. I don’t knowhow much at this point and, some argument could be made that if the play movesto the centre there would be very little impact anyway, but let’s not disputethere must be some gain in protecting one additional rock. In these early situations I support the ruleas a (however slight) gain for the team that is behind and concede it just mighthelp create a closer contest during the early ends.

So what about later in the game? Today, tied in the final end, the team withlast rock has a significant advantage (75 to 80%). 5 rock is not going to help the team withouthammer in that situation. If you are onedown with hammer in the final end, stats show a 40% chance of winning thegame. Here, this rule could bump up thatpercentage but doubtful how much and, frankly, 40% is already competitive andengaging to the viewer. It’s rare that aone point lead in the final end doesn’t create excitement, so why change forthat? Maybe if we are two down withhammer coming home, our chance might increase from 12%, but realistically towhat? Even if you get your deuce to tie(considerably more likely than a three), you are in the same spot tied withouthammer in an extra end, and no advantage with this 5^th rock rule.

Let’s move to next to last end. The 7^th end (or the 9^thend in a 10 end game), has often provided some of the most interesting situationssince curling moved to free guard zone. Take for example the GP Grand Slam Quarterfinals, where Howard, one upagainst McEwen and facing a single opponent stone on the back four foot,considered freezing to try and force a single. What changes with the 5 rock rule? In a tied game, the team with hammer is notgoing to be forced into any different situation than today’s rules. They may elect to more aggressively attempt adeuce, at the consideration that being one up in the last end without hammer isless advantageous, but I doubt the thinking will change drastically. Today, most teams recognize a blank is lesslikely and the team without hammer is forcing the issue to have a score (be ita steal or surrender a single). When ateam with hammer is one down, there becomes even less incentive to score adeuce, as they would have most likely greater than 40% chance if they remainone down with but their chances when tied without hammer doesn’t increase fromthe rules today. O the flip side, theteam one up without in 7 or 9, is just as likely to be aggressive, risking adeuce at the hope of stealing or forcing the opponent to a single. They may be slightly more aggressive, butthis rule doesn’t help them in that regard.

So where does this leave us? If the top curlers want to try it, I support the effort and wish themwell. Though I suspect the impact willbe hardly noticeable, perhaps it will keep a few games from getting lesscompetitive early and make for more dramatic contests. I doubt it.

Now did anyone ask what is wrong with the game as it’splayed now and have we agreed it needs to be changed? That is something I’d be interested to hearmore about and would suggest that simply adding another protected rock will notrepair a game if it simply does not provide enough excitement and drama for itsaudience or its players. For that we mayneed to add some physical contact to the game, though no head shots obviouslyto avoid concussions and excessive fines.

Good luck curlers and here’s to 6, 7 and 8 rock free guardzone (which would of course be 5, 6 and 7 protected rocks) sometime in the nearfuture.

The World is Flat(ened)

2011-01-16T11:21:00.000-07:00

I’m looking for the words to describe the victory by North America in the 2011 version of the ContinentalCup. Premature? Anti-climax? Dominatri…, er, I mean Dominance.

Despite the format of loading more points towards Saturdayand Sunday, the outcome appeared inevitable after Friday night’s sweep by NorthAmerica, heading into Saturday morning Skins with a 90 to 18 lead. By the time John Morris dropped his draw tothe button on the pin for a 9 point skin, the outcome was never in doubt. Thankfully, the Jennifer Jones rink scored adevastating 22 point carry-over, and saved us all from potential questions suchas, to NA: “how will you be able to sleep on such a large lead, won’t you benervous”, to World: Given you are so far behind, do you see an advantagebecause you have nothing to lose?”.

It may take some time for all of this to sink in. Assuming we still remember the event in 3weeks (quick, how many points did North Americascore in the 2007 Continental Cup?), our memories should include:

The great job by the City of St. Albert (and Edmonton). The volunteersand fans who overpaid and ventured out in 10 cm of snowfall (at -34C)showed us a small arena can make an event appear important on television (even ifit probably isn’t). Take note WCT,perhaps a Grand Slam in a smaller venue with full stands would change ourimpressions (including sponsors).
Team North America were almost too impressive,reminding us all that though the game has become an Olympic sport and manygovernments are funding hand chosen players in an effort to usurp Canada, thereis still a long way to go.
The wild Olympic cheering which surprised all of us regularcurling fans cannot and perhaps will not be duplicated. Several efforts were attempted, and with somelevel of success, but the age and soberness of the fans limited their abilityto reach Vancouverdecibel levels.
Skills competition (Singles), though different, shouldnot be a “regular draw”. I sat beside aman and his grandmother. Confused bywhat was happening, she kept asking him why they weren’t curling. Unfortunate for her but Saturday afternoonwas her one chance to take in the Continental Cup and for $30 she got to watcha really neat practice. One volunteer had trouble looking up from her Sudoku duringthis portion of the event. The lack ofexcitement is evident and, even if you’re following the points, there aren’tenough at this stage of the competition to even matter. Every time the announcer called out theresults, it didn’t seem to mean anything. “4 points for NA” lacks excitement when they already have 133.
Staying with the Singles, perhaps they could move it tothe beginning of the competition and make it no charge, in an effort toincrease sales. Possibly a Wednesdaynight event and include a private party with the teams for those who purchasespecial weekend packages.
Only two games over the first two days were close (andone was Mixed Doubles). That’s awhopping 11% of excitement.
John Morris also appeared to be confused by the format. I won’t fault him, few fans can follow iteither. While skipping during Saturdaynight’s Mixed Skins, he repeatedly mentioned they were playing for a“conservative” deuce in the 7^th end. This was incorrect strategy. Ifthey get a deuce, NA gains 6 points. Aconservative end should reduce chance for a steal but increase the possibilityof a carry-over, in which case Team World gets hammer in the final end with apossible 15 skins. If NA gives up a steal, they still have hammer and a chanceat 9 points. I’ll skip the mathformulas, but given where NA was at the time, the preferred approach is to goall out for the deuce in the 7^th end. Likely John was following a reasonable logicof trying to win the game, something this format doesn’t always require.

If you were cheering for Cana…(sorry), North America, then perhaps you are left with fond memories and pleasedwith the outcome of the 2011 Continental Cup. I do believe there is room on the calendar for this event and manyreasons why we should all want it to succeed. Unfortunately, the results this year won’t help that cause. It will be interesting to see the finaltelevision numbers, although the real opportunity is for this event to reachbeyond a Canadian audience and help market the game around the world. Until they are able to host this across thepond in Europe, that may simply not bepossible.

…and isn’t North Americaactually part of “The World”?

Strange.

Live (nearly) from the Continental Cup

2011-01-14T01:00:00.003-07:00

Let me start with the apology, for those who actuallyfollow my regular blog. I have pages ofnotes from the first 3 major events of the year, but have yet to produce a newarticle. I should have some analysis outvery soon, but for this weekend I have other duties. And my feelings are very mixed.

I live in St. Albert and can tricycle to this event. I’ve never been a fan and don’t actuallyrecall ever watching more than a few ends of the “Ryder Cup of Curling” in itsfirst 6 iterations. My parents evenlived in Medicine Hat when it was the host cityand I never bothered to make the trip, despite living in Calgary at the time.

But after dropping in at Performance Arena (aka Servus Place) forthe evening draw opening day, I am trying to feel a little different. I am on a quest to find the appeal of thisevent, despite its obvious (and not so obvious) flaws. The Continental Cup has struggled to gaintraction from fans and sponsors over the years, and oddly I’m (sort of) lookingforward to this weekend. Perhaps I cangain some insight as to why it struggles and possibly examine how it can gainthe international attention that perhaps it could bring to the roaring game. Or at the very least, I can polish off a fewin the Keith’s Patch while my 7 year old plays indoor soccer in the samebuilding this weekend.

Some impressions:

Walking in, playing in my head, or was it out loud, was theold Hockey Night in Canada Theme (apologies to CBC as I know this is no longerthe official name, but I don’t know it as another). Strange.

Fan turnout was ok, lots of chairs appeared empty but therewere many people standing around the top rail. Still, it is a small venue and would be nice to fill the stands. Perhaps $30 a draw and $69 a day is a littlesteep. Or maybe 34 below and TSNcoverage is keeping some at home.

The North American ladies started a cheer during the earlyends. It brought some mild enthusiasmfrom the fans, though it paled to my Olympic memories. Perhaps it was the age difference in thestands or maybe the fact the actual cheer seemed more complicated than theformat for this event.

Someone please tell me why you get 6 points for win (teamcompetition)? What’s wrong with 1? Oh, that’s why…. Mixed doubles is also 6,single matches are 4 and Skins are, ahem, 20, 30 or 55 points! I’m the numbers guy on this blog but damnedif I have been able to figure out how this thing works without a detailedprogram and a financial calculator at my disposal. If I can’t follow easily, how can the averagefan who heads home to a VCR still flashing 12:00? I’ve mentioned before the average age of the curling fan continues to rise and every effort should be made to make the formatof this event as simple as possible for the senior crowd. It is not.

What is “simple” about the structure is the fact a losingteam can make a valiant comeback on Sunday and win. In fact, with 400 points up for grabs, a NAor World team can be shut out for the first 2 days and still have a fightingchance on the weekend to win. Iunderstand why the points are heavily back-ended (260 of the 400 are “Skins”points, battled for during 4 of 5 weekend draws). When you want to attract sponsors and gaintraction with a new event, it is imperative to keep the fan interested to thebitter end. As a fair method todetermine the winner, or a way of simplifying things, this approach failsmiserably. Golf’s Ryder Cup had no faninterest for nearly 60 years. Each matchwas worth one point, no more or less than any other. If a team played very badly the first day(usually Great Britain)they lost, often by a landslide. Onlyonce the European teams began to win did the event take off and become what itis today. The Continental Cup does not,I suspect, have the luxury of waiting 60 years. It has created a structure as an attempt to build drama for the finalday/draws and I believe with the exception of 1 year, has succeeded. Yet I still struggle to find its appeal.

The players appear to enjoy this event and that meanssomething. The cameras need to try andcapture as much of this as possible. Inoticed Blake MacDonald give Kevin Martin a big high five after the gold medalsquad scored a three. Granted, Kevinlooked less coordinated than Tiger after his chip-in at the 16^thduring the 2005 Masters, but exciting nonetheless.

There is some controversy apparently on the restriction ofthe famous Norwaytrousers. Can anyone tell me one goodreason why those flashy Olympic pants that became a hit in Vancouverwould be disallowed or not embraced by all of team Europe?I will provide more details as my investigation continues, but I expect thiscould be responsible for 10% drop off in attendance, if not more.

I got a chance to speak with TeamNA coaches Rick Lang and Neil Harrison. Perhaps two of the nicest guys in the history of curling. I forgot to ask them about their strategy inthis type of format. Actually, I forgotto ask them if they understand how the scoring system works. Hope they figure it out by Sunday….

Strategy appears interesting as it relates to singles andmixed doubles. Mixed Doubles lacks the loud screams of "hurry hard" you hear in a regular game, but does give you an opportunity to nap during the afternoon. And for the life of me, I can’t watch aplayer jump up from their slide and run ahead to sweep the rock withoutrecalling my days long ago in Winnipeg, practicing against my teammates…. whenI was 13! It looks and feels strange. With that many players on both sides, can’tthey allow one sweeper?

Some of you may have seen the TSN camera crew spot me in thecrowd during the 5^th end of the evening draw. It was fortunate for Randy Ferbey to be sitting next to me and gain some additional airtime, including a plugfor his local St Albertsports bar, “The Rink”.

Oh, and current results are North America leading 42 to 12. Does it mean anything to you either?

Curling Season started?

2010-10-20T22:53:00.000-06:00

Greetings to all CWM readers and welcome to the 2010-11 Season. Must admit that my interest in Curling and related studies is currently nil. Many things have been occupying my time over the summer/fall and have not had the time I would like to work on some of the many ideas that have been rolling around my brain. A large part of my reading over the summer was dedicated to Sabermetrics and wondering how baseball (and other sports) use statistical analysis and what would be beneficial if applied to Curling. There is plenty. However, in some aspects we lack the correct type or amount of data necessary to do what could, in my opinion, lead to altering our view of the modern 4-rock game and possibly change the way it is played.

So, before I dig into any new articles this year, here are a few thoughts on what we could measure.

1. Shot Percentages: CurlingZone has come a long way in trying to change this and make it more beneficial (6 pt ratings, shot categories, etc) but this should become universal for all events.
2. Rock tracking device: If we can put a sensor into a rock for hogline violation, it would be very simple I expect to also do the following. Place a sensor (perhaps use the same one) in the centre of the rock. Have a sensor in the button. This would allow us to track EVERY SINGLE SHOT. I cannot begin to describe what this could provide for data and analysis. An aside, it could also solve the problem of draw for hammer when both teams cover the button.
3. Ice conditions: Like "ballpark" effects, could be useful if events tracked the ice conditions and that data was kept. For example, knowing the 2005 Brier had 14.5 sec ice and 2.5 ft of curl might be useful. This would likely help when anomolies occur (slow and/or straight ice) but have less use otherwise.

Some ideas that are currently percolating:
- How important is a three ender?
- Is holding a team to one (Force Efficiency or FE) more important than scoring two?
- How often do top teams/players make: run-backs, hit and rolls, draw around guards, etc and how does that play into strategy.
- Effect of the corner guards and centre guards on scoring.
- Comparison of agressive and conservative teams/strategies
- Exploiting the competition
- Why good teams often close out their opponent with an early two point lead

And many others. Unfortunately, much of these questions would be better explored with data as I mentioned above (like tracking EVERY SHOT in a database), but we have to start somewhere.

As always SEND ME YOUR IDEAS, I'm open to examining any thought on the roaring game, strategy related or otherwise.

Of course I'll continue to question in game calls that I see during the Grand Slams, The Brier and other televised events. I may even chime in on the ridiculousness of the Continental Cup and provide my suggestions on how to make it successful. And at some point this season, if the debate of 8 versus 10 ends rages on, I may have to dedicate an entire article to examining which is better for the game and fair to the competition. The answer may not be the same.

On Baseball thoughts, the other night I watched Game 4 of the ALCS. Giradi (Manager of the Yankees) walked Murphy with 2 outs in the 6th inning and a runner on second, up 3-2. Molina then went deep for a three run homer and the Texas Rangers never looked back. I hope even non-math folks will ponder the question of why you put the go-ahead run on, in the 6th, with 2 outs.

For light reading on why this is a bad idea, check out "The Book" http://www.insidethebook.com/
, it's an in-depth read. Also recommend "Mathlectics" - http://waynewinston.com/wordpress/?page_id=13

And for anyone that understands the concept of "regression toward the mean", you will know why I was VERY hesitant to cheer the return of Brett Favre to the Vikings this season. So far, the numbers are supporting this phenomenon. Now when will Kevin Martin regress towards the mean, or has he just set a new bar for his own "average" play? Will be interesting to watch it unfold this year.

Brier Notes and Blanking the 7th End

2010-03-25T01:02:00.003-06:00

A great Brier. I had a wonderful time working for CurlTV, playing part-time fill-in host. Paul Flemming, local Haligonian and four time Brier rep from Nova Scotia, including runner-up in 2005, was good enough to join me in the booth for nearly the entire week. Despite our complete lack of professional training and minimal or no experience broadcasting, we’d like to think we did ok. Paul’s father Don joined us for a few ends one game, as did Paul’s teammate Shawn Adams. Naturally I had to ask both Paul and Shawn about the famous 2005 final, where Ferbey chose to remove his own rock and, not only captured his 6th Brier, but launched this very blog you are reading. It was that very game that made me think “why would he do that and….is it statistically the right decision?” For the answer, click to http://curlwithmath.blogspot.com/2006/12/ferbey-vs-dacey-brier-final-part-1.html

Incidentally, Shawn and Paul both thought Ferbey’s call was crazy, kind of like throwing your second last rock away in the final end.

Thanks again to Paul and his family for hosting a great lobster dinner mid-week. Also thanks to CurlTV for allowing me to blabber semi-coherently over the web. After 10 days of being immersed in the Brier, should be no surprise it’s taken me over a week of decompression to get back to my thoughts on what transpired….

Is it better to have loved and lost than to have never loved at all? Is it better to have been to 9, yes, that’s right, 9 Brier finals, even if you only win 3? Would you rather go home early or finish 19-3 in an effort to wear the Maple Leaf in 2010, only to come up empty because two of those losses were final games?

Of course, 3 Brier wins is solace only for Glenn Howard after what must feel a disappointing year. This squad of Glenn, Rich, Brent and Craig has one Brier and World Championship win in 2007. They have been one of the two or three best teams on the planet for the last 5 years, and this year came ever so close not once, but twice, of challenging the rest of the world one more time. I hope they will be back.

The week was disappointing at first, both the attendance and the play was below our expectations. Into the middle of the week, high hopes for colossal clashes between the Big 4 came up short, with no dramatic last shot finishes and, with the exception of perhaps a few ends here and there, average shot-making and little excitement. Then, Thursday came along and we were treated to a Northern Ontario team that showed us all they were for real with a morning draw victory over Gushue. Manitoba then won a nail-biter in the afternoon against the surprising rookies from Quebec, keeping their hopes alive. In the end, Stoughton could only hope for a Gushue miscue in the evening draw to qualify for a tie-breaker. No mistake by Newfoundland and the Buffalo continues its Brier drought, worst in history (11 years). It was, however, the Thursday night game between Ontario and Alberta that foreshadowed what the weekend might have in store. We were fortunate to cover the game on CurlTV and it was clear to me that night that these were the two teams who belonged in the final. When Alberta lost in the last end, on a final draw to the four by Howard, it didn’t seem fitting they would head to a 3-4 game, after beating all the top teams and giving Ontario its toughest test of the week. The play-off games were, with the exception of the Saturday night semi-final, fantastic. As disappointing as this Brier was early on, we were treated to one of the best weekends at a Brier since moving to a play-off format in 1980. The final is already being mentioned with Dacey-Ferbey (2004) and Hackner-Ryan (1985) as perhaps the best ever since the inaugural Labatt’s sponsored event some 30 years ago. Certainly there are others which have been memorable: Stoughton-Martin in 1996 and Martin-Peters in 1997 come to mind, and though I don’t remember it all (I was 9 when it happened), I’d expect Burtnyk-Hackner in ’81 (in Halifax) is not easily forgotten.

Now on to some analysis:

1. Quebec (Serge Reid) vs BC (Jeff Richard)

The BC team impressed early in the week. Jeff Richard had won extra end victories in the provincial semi and final to get out of BC and then took Manitoba to an extra and Glenn Howard to last rock. If not for two half shots by Jeff, Ontario could have had an early loss instead of sweeping the round robin. Quebec was also an early surprise; Brier rookies just like their opposing skip. This game was a turning point for both and some interesting decisions during the End game (final 3 ends) could have influenced the outcome.

9th End: BC is down 6-5 with hammer. Third’s first shot and they sit one and have a centre guard.

BC is yellow

Time out, as Jeff’s first inclination is to peel. His thinking is he’d rather blank than score two. If you’ve read my blog before you know two is better than a blank, roughly 60% Winning Probability (WP) for the team 1 up without hammer. However, if BC is held to one at the risk of trying to score two, that is not a desired outcome. The team discusses their chance at 3, assuming Quebec will hit the open rock if they play a come around. More on that in a second.

With one end remaining:
Tied without hammer WP=.25
One up without hammer WP=.6
Two up without hammer WP=.88

Essential question for BC is: Do we try for 3, maybe get 2, but risk being held to 1?

If they do blank, BC’s WP = .40. Let’s suggest they get one 40% of the time, get 2 50% and get 3 only 10%.

.25(.4) + .6(.5) + .88(.1) = .49

Nearly 10% higher than a blank and that assumes being held to one 4 in 10 times. There is also some chance of a steal, which we haven’t taken into account, but in my mind the aggressive play is preferred. The interesting question may have been, if BC draws around the centre into the four foot, should Quebec hit the open stone or draw around the centre and freeze? Alas, that didn’t happen – a missed peel and a possible force looked eminent. Serge had the opportunity to force BC to one with an open hit on his final shot:

Quebec instead elects to try a guard and, leaving the shot stone partially open, surrenders a deuce. I don’t mind the call in some cases, a force is great (.75) but a steal is also fantastic (.88). Two things would lead me to not try the guard here however. The rock was only biting top four foot and, given the draw weight we’d seen from Jeff, I’d expect he makes that draw 80% of the time, if not more, so you are going to likely surrender one anyway. The significant amount of curl, especially around the centre line, made throwing the “perfect” guard somewhat difficult. Also, if it was too long, the large swing would allow Jeff to get a piece of it and possibly score two, even if only a sliver was open. BC gets the deuce they didn’t want.

In the 10th End, BC attempts a guard on Jeff’s last and, as with Serge’s in the 9th, it’s not placed where they want it and a draw for 2 gives Quebec the win. Both teams were 2-2 at this stage and afterwards BC dropped two more fall to 2-5 and Quebec went to 5-2 and kept them in contention until Thursday.

2. NL (Brad Gushue) vs NO (Brad Jacobs)

It is the 6th End. Gushue has just tied it up last end with a deuce and they are about to start third stones. Brad faces this:

NL is red

He elects to have third Mark Nichols play a draw around the corner guard and sit third shot. This is an interesting call. I’m not certain what Brad’s thought process is here. Worse case scenario, the 5th end break took too long and Brad forgot he doesn’t have hammer. More likely, he is expecting NO to hit the open rocks, allowing NL to hit and stay and eventually force a single. NL could have hit the open yellow, though would be difficult to stay. They could have chosen to hit their own and drive it on to the NO rock, though both NL rocks likely spin to the back tee behind the corner. They also could have played a tight centre guard, even into the rings. Peeling the corner may appear conservative, but it is another choice in this scenario. Not an easy decision here and an indication of how dangerous corner guards can be when you do not have last rock and are unable to plug up the centre and force play into the four foot.

The draw stays half open, NO hits and rolls into the two rocks in the four foot, now sitting second and third.

Brad chooses a freeze to the two rocks in the four foot. Now we are really wondering if he knows he doesn’t have hammer. Mark actually makes a perfect shot. Brad then also makes a good shot. Jacobs makes a thin double and rolls out with his first, Brad is left with a difficult hit. He elects to play it soft and leaves a draw for three to NO where a bigger weight hit may have removed both NO rocks.

It appeared as they were starting thirds rocks, play was already in favour of NO, having no center guards and a corner. I like NL playing the end for a blank and not trying to create a force in a difficult situation. A strange end that I’m certain Brad will want to review and analyze if it could have been played differently to avoid giving up the big end.

3. ON (Glenn Howard) vs AB (Kevin Koe) - Round Robin (Draw 17)

Fantastic game which, shot for shot, was the best of the week (in my opinion). Doubles and nearly triples by both squads. Alberta gets down 2 in the second but bounces back with a 3 in the third and it was back and forth all the way until the 7th and 8th…

Scenario in the 7th End which occurred again in the 7th end of the final, though the hammer was reversed. Howard is up 5-4 without hammer. Ontario lead Craig Savil puts his first rock in the rings and Alberta, rather than placing a corner guard, hits and stays in an attempt to play the end out as a blank. Blank is successful and Koe goes to the 8th end one down with hammer. What was interesting is Ontario at this point was 4-5 minutes behind Alberta and by Koe playing the end this way it allowed Howard to bank time for the later ends. It also sounded as though Koe and third Blake MacDonald were concerned about their time and felt the quick blank would be helpful to them. I think it would have done more harm to their opponent, but the thinking also prevails that a blank here gives AB hammer in the 8th and 10th ends (assuming no steals or further blank ends). In the final, Howard chooses the same tactic. AB gets a 3 to go up 4-3 in the 6th end and places lead Nolan Thiessen’s first rock in the rings. Ontario hits and the blank is on once again.

What does the math say about this strategy?

Down one with hammer and 4 ends remain, WP = .404

Down one with hammer and 3 ends remain, WP = .390

It appears that playing for a blank is not supported by these numbers. Certainly not a large mistake (1.4%) but no advantage is gained other than clock management. Let’s look at it another way:

Most likely outcomes if we chose to play aggressive with hammer instead of playing the blank: take 1, take 2 or a steal.

Take 1:

After 7th end, tied without hammer and 3 ends remain = .359

After 8th end, tied without hammer and 2 ends remain, WP = .329

Take 2:

After 7th end, one up without hammer and 3 ends remain, WP = .610

After 8th end, one up without hammer and 2 ends remain, WP = .634

Steal 1:

After 7th end, down 2 with hammer and 3 ends remain, WP = .193

After 8th end, down 2 with hammer and 2 ends remain, WP = .150

Astute readers will notice that a steal is bad in both cases; our opponent is in Dominant position. The opposite is true if we take 3 and go 2 up, in either the 7th or 8th end.

An advantage is gained by scoring a deuce in the 8th versus the 7th end (2.4%), however a 3% drop if we are held to a single point.

Given that the numbers don’t appear to warrant this call, why do it? The thinking is, 3 ends leave me “two hammers to one” and I will likely have hammer in the last end. The result is you can limit the number of times your dangerous opponent will have hammer and give yourself the last shot at the end of regulation. This theory is supported by the confidence and the importance skips place on the hammer, especially towards the end of the game. Intuitively this thinking makes sense, but is not yet supported by statistical analysis. Further work is needed to examine this area if we are to defend what appears to be logical thinking, but currently is not supported by the numbers.

What about the decision by the team without hammer to throw the rock into the rings? If you know your opponent is going to blank, why let them? If you support the “two hammers to one” argument, then you should place a centre guard without last rock. By not doing so you are supporting your opponent’s strategy and giving them a perceived advantage. Though it should be noted, the stats don’t indicate any real advantage.

So what do I think? It is an interesting decision which is not likely a mistake either way.

8th EndAn exciting end that unfortunately for Koe ends in a Howard steal and becomes a critical shift in the game, going from Close to a Dominant position for Howard. On Kevin’s first rock he faces this:

ON is yellow

Kevin elects to try a run back on the tight Ontario guard in the top twelve foot. Nearly makes it but leaves Howard sitting one. An alternative play was a difficult hit and roll through the tight port that Glenn had just come through with his first shot. The second option could leave them sitting two but leaves the Ontario rock in front and a miss could be disastrous. Kevin’s thinking is logical, and he does open up the in-turn side of the house. Ontario attempts to draw around to the button and rubs second shot belonging to Alberta. Fortunate for Glenn that they miss the sweeping, get a rub, but the shot sits in a perfect spot and Kevin has virtually no shot to score. An example of how curling can surprise you. The shot played by AB to open things up was intended to ensure Kevin would have a shot; ironically Glenn misses and still leaves Koe nothing.

Stat note: During the 1-2 game between Ontario and Northern Ontario, Linda mentions the team scoring a deuce in the first end wins 70% of the time. I believe these were numbers taken from the last 10 Briers. Our stats, which incorporate a much larger sample size indicate WP = 73% for men and WP = 72% for women’s teams in this position.

All of this and I haven’t even gotten to the weekend games yet! Page Play-off analysis will have to wait for another time.

Congratulations again to Team Koe and good luck in Italy at the Worlds.

Olympics, Scotties…and Brier Preview

2010-03-06T11:27:00.002-07:00

We’ve been overloaded with curling these past weeks with the Scotties, Provincial Mens, and the Olympics all taking place since my last major article. I’m going to attempt some analysis of various situations that have taken place over these many games, and try to provide some preview for this weeks Tim Horton’s Brier in Halifax where yours truly will be sitting in for Luke Coley in the CurlTV broadcast booth. Luke had commitments with both the Olympics and now the Paralympic Games, and someone at CurlTV was crazy enough to give me the online microphone for the entire Brier. My apologies in advance.

Now on to the article:

Scotties

Tie-breaker: Krista McCarville (Ontario) vs Jill Thurston (Manitoba)
The score is 0-0 in the 2nd End, last rock of the end belongs to Ontario. Krista faces the following with her last shot:

The immediate question the team debates is whether to draw for a single or play the run back for 2 or possibly 3. What’s the math on her decision? With 8 ends remaining, winning probabilities are as follows:

1 down with hammer, WP = .44
1 up without hammer, WP = .56
2 up without hammer, WP = .7
3 up without hammer, WP = .84

When they make the run-back, let’s assume they are able to score a deuce ¾ of the time and score 3 the remaining 25%. Let’s also assume if Krista attempts to draw for one she misses 10% of the time.

.44(.1)+.56(.9) = x(.7(.75) + .84(.25)) + (1-x)(.44)

Solving for x = 36.5%
Krista needs to be confident she will make a multiple score well over 1/3 of the time for this to be the correct call.

A simple way to estimate this on the ice might be as follows:
If I draw I’m between 44 and 55%, say 52%.
When I make the run-back, I usually score 2 with is 70% but sometimes score 3 which is 84%, lets, say 74%. If I make a run back 1/3 the time then my winning percentage is approx. 30% + 25% = 55%.

It's not exact but does provide simple way to make these decisions in real time during a game, even the skip isn't a math professor or poker player.

Ultimately, they decide on the run back and Krista executes a spectacular shot, scoring 3 and cruises ahead to victory.

Alberta Mens Provincial Final: Kevin Koe vs. Randy Ferbey
Team Ferbey loses their third Provincial final in a row. Close early, but steals in the 5th and 6th ends put Koe up by three. In the 7th end, Randy chose to draw for a single rather than blank. Winning probability with 3 ends remaining is as follows:

3 down with hammer, WP = .07
2 down without hammer, WP = .06

Numbers indicate this is not a bad decision, either scenario is close.

Olympics

1. Sweden (Niklas Edin) vs. Great Britain (David Murdoch)

Sweden is up two in the 9th end and Murdoch has the hammer, In an attempt to blank the end, he hits and sticks for a single. Announcers Russ Howard and Cathy Gauthier both state the blank is preferred, however, if you’ve read the “Extra-End” portion from my article from here:
http://curlwithmath.blogspot.com/2009/12/ferbey-vs-dacey-brier-final-part-2.html
...you may recall that Kevin Martin intentionally took one in the same scenario against Kevin Koe in the 2007 Alberta Provincial Final. That article is several years old and more recent statistics still hold true.

Winning probability with one end remaining:
Two down with hammer, WP = .117
One down without hammer, WP = .107

I only hope the scorekeeper didn’t deduct too many points from Murdoch’s “miss” on his blank attempt. This is another example of how shooting percentages never tell the whole story.

2. The Final: Canada (Cheryl Bernard) vs. Sweden (Annette Norberg)
Firstly, a fantastic showing by Team Bernard all week. They represented Canada well and played their hearts out. It was afinal game that could have gone to either team. The focus in days since has been discussion on missed shots, but it should be remembered for some of the great shots made throughout the game as well as the entire week. For example, in the 2nd end, Bernard makes a nice corner freeze on her first when Sweden had them under pressure. In the 5th, Cheryl makes a great shot to freeze on top of the Sweden stone and nearly gets shot. Norberg then makes a great draw to the button for two. In the 6th, Cheryl makes a great draw on her first, Norberg then makes a spectacular run back and sits shot buried on top of the button. Cheryl then calmly makes the soft hit for a single. In the 7th, Cheryl makes a great shot to sit two behind the centre guard and, after Norberg misses, is able to steal a huge two points and make the game close.

4th end Bernard chooses to hit the Sweden rock in the four foot and play her corner guard on leads second rock, allowing the opponent to attempt a peel with second’s first rock. The peel is missed (nose hit). I don’t mind the strategy during the early game, encouraging Sweden to not play a centre guard. This is a strategy that would be very questionable in the Mens game but has some validity in the Womens where the chance of a missed peel is higher.

7th End. On Norberg’s last rock, she chose to draw tap Bernard’s shot rock sitting half open in the back button.

She alternately could have chosen to blast it out and give Canada a single, retaining hammer in the 8th and be tied. If she is too tight they likely push the Canada stone top four out instead, though perhaps some small chance it jams on the Swedish stone at the side of the rings. The winning probabilities for Team Sweden with 3 ends remaining are as follows:

Up 2 without hammer, WP = 79%
Tied with hammer, WP = 61%
Down one without hammer, WP = 40%

I like the call, but she made a bad miss by not at least having tee-line weight to at least cut down Canada to a single.

8th End. Bernard calls for a peel on the Swedish corner guard with second’s final stone. This appears to be a conservative call and she could have opted instead to maintain the pressure by playing a tight centre guard or drawing around the Canada stones staggered at the top of the house. They now bring a possible blank into play. I really like this play but uncertain if Cheryl understood the mathematical reasons. Statistics for Womens has an interesting situation at this stage:

It is more advantageous to be one up without hammer than tied with hammer when two ends remain. Cheryl’s WP = 61.5% tied with hammer and 62.5% if one up without hammer, starting the 9th end. This situation does not occur in the Mens game. Some of you might suggest these numbers are very close and 1% is not a significant advantage. That is partially true, but what it does indicate is Canada does not have to take risks in this end in order to force a single by Sweden. Why risk your opponent possibly scoring two or three when it is unnecessary? Better to keep the play simple and ensure Norberg is held to either a single or a blank. So should Cheryl simply throw her last stone away, allowing Norberg to blank? It’s not inconceivable, though it would have appeared very strange to most observers. Depending on ice conditions and other factors, if she had made that call I would not have been too critical and would possibly applaud her. However, it is still advantageous to put pressure on your opponent, rather than concede the blank. As we saw, this did provide a critical steal at that stage in the game.

What about Norberg? On third’s first she chooses to hit the Canada stone just biting at the side of the rings, rather than play aggressively for a deuce. She could prefer to play for her deuce, knowing that if she’s held to a single her WP doesn’t change (in fact it goes up!). However, the risk of a possible steal needs to be evaluated. I’d prefer a draw here but likely Norberg is not aware of the numbers and wants to avoid being held to a single.

3. The Final: Canada (Kevin Martin) vs Norway (Thomas Ulsrud)
Nothing really to say here. Job well done by Team Canada and a well deserved victory. The semi-final appeared to have more tension early on but no real fear of an upset against Kevin Martin. Kevin has reached the pinnacle of his curling career and it will be interesting to see where he goes from here. He is still young (for a curler) and he’s always been committed to the game as a career, unlike most of his contemporaries, so would be surprising if he slows down at all.

Brier Preview
The Olympic Trial teams had built up a considerable record against each other over the previous years. The Brier does not provide us the same statistical detail in order to analyze probability of outcomes. What do we have?

We know Stoughton, Howard, Gushue and Koe have fought often, so let’s take a look at those results:

These numbers are interesting, but as always they only tell us part of the story:
• Gushue is 3-3 in last six vs Koe
• Gushue is 3-3 in last 6 versus Stoughton, but 0-3 in last 3. Gushue did win a significant game in Halifax against Stoughton in 2006, if you remember the 2006 Olympic Trials.
• Gushue is 2-4 against Howard since 08-09 season, including a big semi-final win at the Swiss Chalet National this past January.
• Stoughton is 2-7 in last 9 against Howard. One of those was a victory in the 2009 Brier semi-final.
• Koe’s lone victory over Howard was the 2007 Players Championship. Since then Glenn has won 4 in a row, all but one were close games including an extra end win in the Olympic Trials.
• Stoughton has won 4 in a row over Koe. Koe had won 3 in a row prior to that. Prior to that, 3 in a row for Stoughton, and prior to that 4 in a row for Koe!

I see these four teams a very close throughout the week. Gushue’s disappointment at the Pre-Trials is either forgotten or is motivating them to an impressive season, including a a Grand Slam win only 2 months ago. Is it perhaps their time?

Stoughton has looked very strong all year and is looking for redemption after their defeat to Howard in the Trials semi-final. Manitoba hasn’t won since 1999, and Alberta is catching up with 24 Brier wins, trailing the Buffaloes by only 2. Perhaps a transplanted Albertan, Kevin Park, will increase that margin to 3? I expect after seeing Martin win gold, he’d like nothing better than to return to the World stage where playing third for K-Mart he lost the final 19 years ago in Winnipeg.

Alberta’s Kevin Koe is poised and ready. They certainly know they can beat anyone here and are likely feeling as if it is their time. Third Blake MacDonald and Carter Rycroft are returning to the Brier, but Kevin himself is a rookie skip. The atmosphere in Edmonton during the Trials would have prepared them for this event so I don’t expect to see any nerves in front of the Halifax crowd this week.

Finally, Glenn Howard. Team Howard must have had mixed feelings watching Martin’s team stroll into the Brier opening banquet last night to a round of applause. Kevin gave a nice speech, but I wonder if Ontario was listening? The loss in the finals of the Olympic Trials surely still lingers, but this week provides a chance at redemption. This is also a team that likely should have had two Brier wins, after the upset in 2006 and a victory here will put them in the same conversation with Ferbey and Martin as top Brier teams of the decade. Unless of course 2010 is part of the next decade, in which case they will have a head start on the next ten years.

Predictions? Only that it’s unlikely anyone other than these top four teams gets a direct spot in the play-offs. New Brunswick and Saskatchewan are possible surprises, and could sneak into a tie-breaker. The rest is unknown. The Brier is where names are made and possibly there are a few to be made here this week. But in the end, one of these four will take the Macdonald Brier Tankard.

For the record: One down with hammer in the last end

2010-02-21T12:49:00.003-07:00

My apologies, but I have been too busy to craft a new article yet. There is much to examine, with the Olympics currently underway, Scotties finished up and Provincial Championships all completed. I also have plans to compare individual teams or groups of teams to baseline analysis. Trying to use an approach similar to WPA (win Probability Added) in Baseball, but this will take some time.

In the meantime, I was struck by a recent thread on Curlingzone.com related to Scotalnd...er, um...I mean Great Britain against Canada last night in their Olympic Round Robin game.

In the game, GB was one up without hammer starting the 9th end. GB (Team Murdoch) attempted to throw a centre guard but inadvertantly came into the rings and Canada (Team Martin) subsequently blanked the end and had hammer, one down, in the final end.

One poster mentioned that the NBC commentating duo of Colleen Jones and Don Duguid stated that it is preferred to be one down with hammer in the last end. Anyone who reads this blog regularly will know this is absolutely not true. The first question a viewer might then ask Don and Colleen is:

Why didn't Murdoch throw his last rock away, leaving Martin a draw for two in the 9th end? And then why wouldn't Martin then peel his own rock out of the house in order to be one down in the last end?

Let's be clear for anyone who might still be uncertain:
Over a very large sample size of competitive games, encompassing Mens and Womens: Worlds, Olympics, Canada Olympic Trials, World Curling Tour, Grand Slams, Provincials and Canadian Championships, the number consistantly comes out to a 40% chance to win if one down with hammer in the last end.

The result of these numbers is that, mathematically, the best end to be one up without hammer is the second last end. WP = 65%, nearly Control (which I calculate to be 66% to 80%, see my previous article here: http://curlwithmath.blogspot.com/2008/11/statistics-for-womens-curling-and-what.html).

The reason for this advantage is, the team without hammer can play the end aggressively, trying to force the opponent to take one (WP=75%) or possibly even steal (WP=88%), and the primary risk is surrendering a deuce and still having a 40% chance in the final end.

Murdoch's mistake last night was allowing the 9th end to play out as a blank. Perhaps they could have considered playing a centre guard on their second shot, even if facing a Martin stone in the rings. Also, Murdoch could have considered drawing to the back eight foot on skips first shot. then, if Martin nose hits, he would have the option to attempt a freeze to the Martin stone and possibly force Canada to a single.

Notes from the BDO Grand Slam

2010-01-29T01:33:00.007-07:00

A good weekend for Ontario Juniors taking home both the Mens and Womens national titles. You had to feel for the Manitoba skip watching in agony as his last rock just shaved past the Ontario stone. To make matters worse, the missed shot meant I lost a “Provincial” bet with Steven Lobel. Steve, your frozen Bison steaks will be in the mail next week. At least I have Alberta going against Ontario in the Brier for 10 in a row this year.

A non-curling stat I heard a lot these past few weeks was “92% of teams with +2 turnovers win play-offs game in the NFL”. I was hopeful the Minnesota Vikings would be one of the 8% and head to the Superbowl, but alas, it was not to be. Perhaps next year…

On to some Curling thoughts from the BDO.

1. Glenn Howard vs Pat Simmons

In the 5th end, Simmons is up 3-2 with hammer. It is Glenn’s last rock.

Howard is yellow

This is the last end of the Middle Game (middle three ends) and they are about to start the End Game (final three ends).

CBC announcer Mike Harris says Glenn can’t afford to leave the Simmons rock in play. Can he?

Hitting: Glenn is most likely going to give up a single to Pat. There is some chance he could make a hit and roll, in which case Pat will most likely try a double and then there is some chance he could miss or jam and Howard steals. Let’s estimate that Glenn makes a good hit and roll 20% of the time and Pat misses 25% when that happens, leaving the chance of a steal as 5%. There is also some slight chance of a blank, but we’ll assume those odds as negligible.

WP = (.2)(.95) + (.35)(.05) = 21%

Guard: If Howard elects to play a guard, he brings a deuce into play.

WP = .07x + .2y + .35z

Where x is the odds of a deuce, y is odds for a single and z is odds for a steal.

The Howard stone was just back tee-line and likely a single will occur often. Let’s estimate a single is 60% and odds of a deuce or steal are each 20%. WP = 20%. If we estimate the odds of a deuce to be lower, say 10% and set z =30%, WP = 23%.

What at first appeared to be a simple decision now appears to be very close and, depending on our assessment of the situation, perhaps in favour of throwing a guard. I personally preferred the hit, due to ice conditions and the Howard stone being behind the tee-line. If the rock is top button and/or the ice is straighter with less finish, I would prefer the guard in that situation.

6th End, Glenn is now trailing by 2 with the hammer and faces this with his first rock:

Richard Hart drew to the Open side with his last rock and Simmons hit and rolled just out of the rings. Glenn’s first instinct was to replace that stone and play the end out for a deuce and be tied up playing the 6th end without hammer. The Howard front end then talked him and Richard out of the shot, and they elected to play a freeze on their shot stone frozen to the Simmons rock in the four foot. Glenn asks “what are the odds of us getting 3? Brent responds with “zero if we go open”. Glenn then comments “we’re getting a guaranteed two if I go open”.

I disagree that the open side gives them a “guaranteed deuce”. There is some margin for error and if they don’t come deep enough Pat may have a possible hit and roll into the four to make Glenn’s last more difficult. The margin for error on the freeze is slightly higher and the result showed having 6 inches too much weight left Simmons a chance to get out of the end.

If Howard scores two, WP=33% or 2-1 (on the border of Close and Control, per my past article here http://curlwithmath.blogspot.com/2008/11/statistics-for-womens-curling-and-what.html. If Howard makes a great shot, Pat still has a possible chance of running his rock in the top twelve into the Howard rocks and killing one, holding them to deuce. If Howard does score three, their WP = 67%, flipping the odds against Pat Simmons to 2-1 against. If Glenn is forced to one (the actual outcome) their chances drop to 14%.

WP = .14x + .33y + .67z = .33

The actual outcome that occurred was, I believe, the least likely. Glenn made the surprising mistake of being heavy. If he is light, even third shot, a deuce for Howard remains the most likely outcome. A little heavier and there may not have been a chance for the double by Pat, leaving a deuce possible. Glenn’s rock happened to land in the worst possible spot and I’d suspect this would happen perhaps 10% of the time. If we assume x=.1, how often does Howard need to score three to make this the correct call?

z = .05 or 5%

If we estimate the chance of scoring a single as 20%, then z doubles to 10% and it becomes a questionable call.

I like the call but not the execution. It was a shot which had very little margin for error and probably would result in a deuce anyway. If this is the 7th end, there is no question it is the correct call. Because it’s the 6th end there is some argument to taking the nearly “sure” deuce and 2-1 odds instead of risking 14%.

2. Kevin Martin vs Mike McEwen – Quarterfinal

In the 4th End, Martin is up 4-2 and McEwen has the hammer. John Morris hits the open BJ Neufeld stone in the 12 foot. On Neufeld’s next rock, thirds last for the McEwen team, they choose to hit and roll rather than draw. Martin then has an open hit when the roll is not made. Mike Harris points out that McEwen may then be unable to play behind the guard based if Kevin hits on the nose. As it turns out, Kevin rolls to the four foot and Mike has to hit.

Martin is Red

At this stage in the Middle Game, Mike has a 21% WP (Win Percentage) if the end is blanked and 38% WP if he can score two. Even if Mike is forced to 1, the WP = 21%. This stat clearly shows that there is no need to play for a blank as an option, there is no advantage to do so. If we add the fact they are playing Kevin Martin, the odds may be more in favour of attempting a deuce. Martin historically is 49-7 (87.5%) when 2 up without hammer and 4 ends to play. Mike could consider that Kevin’s numbers have come against teams weaker than his own. That is a factor he needs weigh against the baseline statistics to then estimate his teams’ likely chance of winning in this situation.

In any case, I prefer the draw on third’s last rock when it was available. Perhaps others might disagree.

After the blank in the 4th End, Mike has another draw opportunity in the 5th End and chooses instead to attempt a hit and roll on Neufeld’s first.

Mike Harris mentions that, especially on this ice, the draw is much higher percentage shot. I would agree.

In the 7th End, McEwen is behind 6-3 with hammer but after a jam on Kevin’s run-back attempt, is looking at scoring 3 and possibly even 4. Mike makes a draw around the corner guard to sit four and Kevin, as expected, attempts a double on the two open McEwen stones. Martin surprisingly noses the top rock leaving yellow sitting two.

Mike Harris states there is a double for four if he wants to attempt it. He does and misses, scoring only two. If McEwen simply draws for three, WP = 25%. Per earlier analysis, Mike may believe it to be even less, given his competition. If he is able to score 4, they would be 1 up without hammer playing the final end and WP = 60%. Interestingly, Martin is 12-20 or 37.5% when down 1 with hammer in the final end; very much in line with the average. Needless to say, the triple does not have to be made often for this to be the correct call. The miss, however, needs to be thick to get three and as is often the case. I’ll spare the reader the formula, but even if McEwen makes the same mistake 30% of the time and only gets the double 10%, it is still a break even decision.

3. Kevin Martin vs Thomas Ulsrud – Semi-Final.

In the 4th End, a surprising call by Kevin. Tied 2-2 with hammer, he is about to throw skip’s first rock.

Martin is yellow

To the surprise of many, including me, Mike, Joan and likely Ulsrud, Kevin elects to draw to the back four foot with the out-turn, rather than play a double. Harris comments that perhaps Kevin doesn’t feel the double is an easy shot. Martin may have also believed the top red likely jams on his own yellow and, with the swing in the ice and long guard, Ulsrud could be left with a possible hit to lay two. An interesting call which could have backfired if his rock was not placed perfectly. As it happened, Kevin and John then discussed the outcome and Kevin appeared to be more focused on the risk of Ulsrud tapping while John saw the possible chap and roll into the centre which would make it difficult for Martin to score. Was Kevin possibly so focused on one outcome that he missed seeing the other risks in his call? Unfortunately for Thomas, his final shot racked on the top red and left a draw for three.

4. Kevin Martin vs Glenn Howard – Final.

Mike Harris mentions during lead rocks that if Kevin Martin gets a deuce in the first end they are tough to beat. Are they ever! Kevin Martin is 80-6 (93%) since 2003 when up two without hammer and 7 ends remain. Glenn can at least take solace in the fact the last time Martin lost in this scenario was the BDO Final last year when his squad was able to overcome an 0-2 deficit against Martin.

In the 1st End, Glenn, without hammer, is faced with some options on his last shot.

Martin is yellow

Glenn elects to try and hit and roll in front of the yellow stone in the back eight foot. This would force Kevin to try a delicate hit for two or possible he may draw for one if the shot is perfect. Surprising that Glenn does not choose to play a soft hit and try to flop behind the centre guard, Joan mentions this is her preferred call. Another option is to simply try the thin double. I’m not sold on the shot that was called and prefer either the hit and roll inside (if it’s possible) or a freeze. The rock is right on the pin hole and a freeze will leave no draw for two. Depending on the location, Kevin may have a big weight double to remove his own shot stone, keep his shooter, and score two.

It’s possible Glenn was not entirely certain of ice and weight, being the first end. However, the hit and roll had, I suspect, had a similar margin for error if not more than the other options. Given Kevin’s record when 2 up and 7 more ends to play, I believe Howard would be better suited to look at all options, even those that may appear too aggressive for the first end of a game, even a Grand Slam final.

Further to this theory, when down 2-1 without hammer in the 3rd End, Richard Hart misses on a run-back on his first and John Morris splits the rings.

Rather than call a hit on Richard’s last, Glenn could have attempted a freeze and tried to escape the end. They instead try to roll to centre, to possibly set up a later attempt at a double on skips rocks. I believe the freeze was a better play, given the situation and score. Three down with 5 ends remaining WP=11% as an average and Kevin’s team is 67-3. On Glenn’s last shot he also elects to play a hit when a freeze may have been the more statistically correct call.

Incidentally, Glenn Howard is 87-12 when leading by 2 without hammer and 7 ends remain. No slouch either.

Some points in defense of Howard:

25-23 (52.1%) when 2 down with hammer and 7 ends to play
5-14 (26.3%) when down 3 with hammer and 5 ends remain.

The question a team needs to ask is; given my strength vs the average team and my opponents strength versus the average team, and understanding these are small sample sizes, what will my outcome be against this opponent? This answer involves adjusting the WP based on your team's ability and the strength of your opponent. More on this in a future article.

Enough for tonight, I’m heading to sleep. Sweet dreams math fans. Mine are filled with nightmares of Favre throwing yet another play-off ending interception…..then I wake up and realize it wasn’t a dream.

The National…To tick or not to tick…BC Scotties 8th End

2010-01-13T01:46:00.005-07:00

Greetings and Happy New Year to all. Many items to dig into this month so let’s get right to it….

1. Grand Slam - Swiss Chalet National

Semi-Final: Brad Gushue vs. Glenn Howard
A rematch of the 2007 Brier final. That game included an interesting decision by Gushue which I analyzed here
http://curlwithmath.blogspot.com/2007/10/blackbook-of-curling-200708-reprints.html

One of the more interesting decisions in this rematch was the 1st End. Tied (naturally) without hammer, Gushue was faced with an option on his first rock to be aggressive and attempt a steal but instead chose to peel out the Howard stone protecting his rock in the four foot. This shot call forced Howard to a single rather than giving Gushue a chance at a possible steal.

Gushue is Red

Down 1 with hammer and 7 ends remaining WP = 47%.
Down 2 with hammer and 7 ends remaining WP = 26%

Assuming the most Howard will take is two, how often does he need to estimate a deuce occurs for the Gushue call to be correct?

We will assume that if Gushue peels Howard will always take 1. Chance of a blank is assumed negligible.

Variables:
x = Gushue steal
y = Howard scores 1
z = Howard scores 2

.47 = .53x + .47y +.26z

Simply looking at the equation, if x =0 than the correct decision is to peel. Let’s choose x as 25%.

.47= (.25)(.53)+(1-z-.25)(.47)+z(.26)

Solving for z = 7%

Would appear the decision which at first seemed conservative is very prudent, given the estimates we have chosen. Hard to believe that with the Gushue rock behind the button that Howard will fail to prevent a steal at least 75% with two rocks to come. Even if Howard never scores a deuce and Gushue steals 50% of the time, he only increases his WP from 47% to 50%.

Finals: Brad Gushue vs. Randy Ferbey

3rd End
Game is tied, Ferbey has hammer. Gushue places a centre guard with the first stone. Marcel places his stone in a high position, biting the eight foot. Gushue elects to play a runback on his own rock, which he is entitled to do under the 4-rock Free Guard Zone rules. Not a play we see very often. Teams commonly play a corner freeze regardless of the placement of this stone. I think this type of play could be used more often.

What is interesting is, tied with 6 ends remaining, a team chooses to place a guard without hammer – while two ends previously they commonly put it in the rings.

This leads to a question a poster on CurlingZone asked: “If you have hammer in the first end of an eight end game and your opponent places a rock in the rings, should you hit with desire to blank the end and have hammer in the second?”

The odds do not change from 8 ends to 7 ends remaining. Beginning eac end, probable outcome for Tied with hammer WP= 61%, one down with hammer WP=43% and down two with hammer WP=26%. These ends are considered the Early Game, which I explained in this past article:
http://curlwithmath.blogspot.com/2008/10/is-curling-battle-for-hammer.html

Possible reasons for choosing this play:

If your opponent is stronger you may want to shorten the game.
You want to conserve time by playing a quick end early
You are unfamiliar with ice and/or rocks

There may be other considerations I haven’t addressed. I prefer aggressive play as outlined in a previous article:
http://curlwithmath.blogspot.com/2007/11/curling-myths-how-do-we-calculate-truth.html

However, taking into account other considerations could lead a team to the decision to play an open end for a blank. As always, understanding the numbers is a first step but situational analysis must always be considered as well.

4th End
Ferbey is up 2-1 without hammer. It is Nedohin’s last rock of the end.

After much discussion, the Ferbey rink decided to play a freeze to shot stone in the four foot, forcing Gushue to make a difficult shot for multiple score or possibly even steal. Dave makes a great shot but not quite perfect and Gushue is left with a run back for three, which he makes.

Gushue is Red

At one stage, the Ferbey team discussed hitting the half open Gushue rock in the eight foot, conceding a deuce. Randy mentioned he was unsure of the ice, though I ‘m surprised given it’s the 4th end and the final game of the event. The question I had is, if they could be assured of conceding a deuce, how often does Dave’s rock need to be perfect to make the shot call they attempted?

When 1 down with hammer and 4 ends remaining WP = 41%

If Ferbey attempts the freeze, 4 outcomes are possible: steal, Gushue takes one, two or three. This leaves a lot of possible outcomes to examine.

WP = .79s + .62x + .41y + .21z

Let’s examine extreme case where Gushue scores three 60% of the time, deuce 20% and 10% forced to one and 10% a steal.
WP = 35%
If z becomes 30% and a deuce (y) becomes 50%, WP = 41%.

It’s very likely if Nedohin’s shot curls 2-3 inches more the play for three is not even possible. I’d suggest Ferbey’s estimation of David placing the rock perfectly would lead him to believe giving up three is not likely higher than 30% and is certainly not 50%.

What we don’t know is, if Dave’s rock had been short, leaving Gushue sitting one, would Gushue simply draw for two anyway, rather than attempt the hit for three?

7th End
Tied without hammer, Ferbey has a long off centre guard and a Gushue stone in the wings. It is Nedohin’s first shot.

Gushue is Red

They could choose to play around the guard and attempt to steal or force Gushue to one at the risk of a possible deuce. They instead choose to hit and increase the likelihood of a blank, which occurs, and then need to steal in the final end to win (WP=25%).

Compare this decision with their choice to risk a difficult double for two to go one up against Howard in the Olympic Trials, rather than take a single and be tied without coming home.
http://curlwithmath.blogspot.com/2009/12/canada-olympic-trials-aka-roar-of-rings.html

Here they take a very different approach. Perhaps it was their competition, thinking the chance at a steal was better than in the previous situation. Instead it could have been the ice conditions and the length of the guard led Ferbey to believe a deuce was simply too likely. In either case, a somewhat surprising call given Ferbey’s aggressive nature. Looking at the numbers, assuming a draw attempt will result in no blank, if we assume Ferbey never steals, he will need to successfully force a single by Gushue at least 45% of the time to make it the correct decision.

2. Tied with hammer “To tick or not to tick”
I recently read Russ Howard’s book “Curl to Win”. In it, he discusses the situation of tied with hammer in the final end. His preferred strategy is to play both leads rocks into the top of the rings, allowing your opponent to place two centre guards.

I noticed this weekend that both Gushue (against Ferbey in the final) and Koe (against Murdoch in the quarterfinal) adhered to this philosophy. Ferbey, in his round robin game against Gushue chose the alternate strategy of playing tick shots to remove both guards. Interestingly, Russ’ brother Glenn used the tick strategy during the Olympic Trials against Koe.

Both Gushue and Koe won their games, but both had tense finishes in which their opponent had chances to perhaps pull out a victory.

I can appreciate Russ’ approach, but prefer the tick strategy for a few reasons, one of which he mentions in his book.

If the first tick is missed, you can choose to draw around on your next shot. I believe a well placed rock has nearly as much benefit as placing two stones, and still provides an option to make the tick shot.
At this level, teams should be able to succeed at the tick shot. It would surprise that top teams would not be extremely proficient at making the tick shot a high percentage of the time.
If you could walk down to the end of the sheet and place the stones, what would you do?. The obvious answer is open the front of the rings by moving the guards. So if you can’t move the rocks correctly by throwing them, practice until you can.
More rocks give the team behind more options. This is a general concept that does not clearly translate to all situations, and does not have sufficient data to defend, but may have some validity in these scenarios.

I suspect over time the tick will become the more common play, but for now the “draw twice” strategy appears to have some followers.

3. BC Scotties - Kelly Scott vs. Kelly Law
Several posts on CurlingZone related to Kelly Scott’s decision to draw for a single point in the eighth end of the BC Provincial final. Rather than blank and start the 9th end 2 up with hammer, Scott chose to be three up without and two ends remaining.

The numbers actually indicate the decision is equal, a team’s WP =7% whether they are down three with or two without hammer. I would support either decision as it was made based on any number of other factors such as ice conditions or opponent.

To those posters who state that Scott made a horrible decision and it almost cost her the game due the outcome which almost occurred in the 9th end: you are wrong. Basing how a single end plays out and what occurs is irrelevant to how a decision is reached beforehand. Even if you argued Kelly made a wrong decision that her competition and/or conditions should have led her to blank, it simply is not a big enough “mistake” in that case to have a substantial impact. For example, if she was 100% wrong (and she wasn’t), Law’s chances only increase to 14%, still a Dominant position for Scott.

Congratulations to all the Scotties Provincial Winners. Also, congratulations once again to the Lobel Team http://teamlobel.wordpress.com/ for gaining a third straight trip to the Provincials in Ontario.

Until next time, remember to keep your numbers in mind before placing your broom.

Canada Olympic Trials: AKA Roar of the Rings

2009-12-16T02:12:00.011-07:00

It was an enjoyable week for fans in Edmonton, but not necessarily for 14 of the teams participating. Four years of hard work, practice, travel, and time away from family and jobs, all culminated into one intense week of curling. Ultimately only 8 remaining players (ok, 10 if you include the 5th man/woman) experienced the thrill of victory. The remaining squads are left to wonder what could have been.
Speaking of the 5th position, will the CCA approve of the current extra teammates? Will the teams keep them or toss them aside? Does it really matter? Not for me to ponder I’d prefer to look at specific games and some of the decisions made throughout the week.

1. Randy Ferbey vs. Glenn Howard
Ferbey was 9-7 against Howard going into this game and needed a win to ensure their game against Koe Thursday night would have play-off implications.

5th End: Russ Howard (commentating for TSN) questions Ferbey’s decision to come into the rings on David’s last shot. A valid point and Randy’s squad is fortunate to get away with only giving up a single.

Ferbey is Red

At this stage, Ferbey is up 4-2, Howard has last rock. If the freeze attempt by Nedohin is perfect, Howard is likely forced to one. He could attempt a difficult double raise but more likely may try a delicate draw to the edge of the button avoiding the corner guard on the in-turn. Most likely Howard gets one and Ferbey is up 4-3 with hammer and 5 ends to play. In this situation his Winning Percentage (WP) is 80%.

If Ferbey instead throws a guard, he could cut-off Howard’s in-turn draw and make it difficult for him to get two. Glenn would have to play an out turn and try to catch half of the four foot. If we assume Glen makes his deuce 100% of the time, game is tied and Ferbey’s WP = 61%. If Glen gets three or four, which was possible given where David’s rock ended up, Howard’s WP is either 60% or 75%. Ultimately Ferbey is trying to gain Dominant position (80% or greater) rather than stay in a close game (<66%) at the risk of putting Howard in Control (>66%<80%).

I’ll spare everyone the formula (let me know if you’re interested), but Dave needs to make this corner freeze roughly ½ the time for the call to be correct.

9th End: Alan Cameron may have misquoted me slightly in his article: (http://communities.canada.com/calgaryherald/blogs/curling/archive/2009/12/12/numbers-favour-martin-in-final.aspx). What perhaps I meant to say was “if you agree with Randy’s assessment of David’s chance to make that shot (4 or 5 out of 10) then it is the correct call”. Alternately, if you agree with Russ Howard’s assessment of Dave’s chances as 10%, then it is not. How often does he need to make the shot to make it the correct call?

If Ferbey takes one, WP = 25%. Taking stats exclusively from Grand Slam events show this number is closer to 20%. This is the only significant difference in numbers we see from Grand Slams versus all events. We’ll use 25% for now.

.25 = .6x +.12y +.01z +.25s

Where
x = estimate the double is made for two
y = estimate Howard steals 1
z = estimate Howard steals 2
s = Ferbey takes 1

And x + y + z + s = 1

Let’s chose z as 10% and s as 5%.

.25 = .6x + .12(1-x-.001-.0125) + .01(.1) +.25(.05)

Solving for x = .246 or approx 25%.

If we assume s is 0 and z is 20% it only increases to 27%. Giving up a single or a steal of two to Howard has minimal difference in the probable outcome.

If we also think our chances of stealing in the 10th end is less than 25%, we are even more inclined to try the double. If we think we will only steal 20% (similar to Grand Slam numbers) then x = 14% or 16%. This is still above Russ Howard’s estimate, but well within range of Randy’s.

2. Kevin Koe vs. Glenn Howard
In the 9th End, Koe, trailing 5-4, is faced with a similar decision as Ferbey was in the previous example. Rather than draw for his single, Koe elects to play a soft out-turn take-out around the guard in front of the rings. It’s an attempt to score two but a miss results in a steal. No steal of two here, and perhaps some small chance his draw for one would be missed (needed full four foot). The hit he played could also possibly result in a single, but very difficult given that they were pushing shot stone towards the button. I’ll leave the calculations up to the reader, but appears their chances for two needed to be close to Nedohin’s in order for it to be the correct call.

Koe is Red
3. Koe vs. Gunnlaugson

Easily the most entertaining 7-2 game I’ve seen in a long time.

3rd End: Koe is up 1 without hammer. There is a single tight corner guard way out on the wing. Koe attempts a draw around on his first rock and comes light, leaving two stones staggered. Jason decides “because it’s the 3rd end” to draw to the open. The end is blanked. This is simply a case of over thinking a philosophy which I’ve heard before about “scoring in the even ends”. I even discussed some of this in my article from February 2009. In it, I discuss the 5th and 8th ends. Notice the 5th end is an odd numbered end; however in that article I argued preference to have the hammer.

Gunnlaugson is Red

A score here by Jason and a Koe score in the 4th gives Gunner hammer back in the 5th. An example: If Jason scores 2 here and then forces Koe to one in the 4th he is tied with hammer entering the middle game (5th end) and has 61% WP (Close Game). If Jason scores two in the 5th, his WP = 75%. If he waits to the 4th and holds Koe in the 5th, his WP = 62%. If he then scores two in the 6th, his WP increases to 79%. Interestingly enough, this is a .04 difference and shows Gunnlaugson does gain if scoring a deuce in the 4th instead of the 3rd. However, both are still in what I define as Control and not a Dominant position. And the overriding factor is, there are too many “IFs”.

All we specifically know at this stage is the chances at the end of the 3rd end: Blank WP = 43%

Jason scores two WP = 61%

Gunnlaugson takes one WP = 39%

Koe steals, Jason’s WP = 26%

In order for the call for two to be correct:

WP = .61x + .39y + .26z

Where

x is a deuce for Jason

y is a single for Jason

z is a steal for Koe

We can likely assume the chance Koe steals is very small. Jason would only need to bite the eight foot to take one. Let’s assume z=0

WP = .43 = .61x +.39(1-x)

Solving for x = 18%.

Bringing a possible steal into play, we could estimate Jason needs to make his deuce more than 20% of the time to make the attempt at a deuce correct.

These WPs are also based on average numbers and I’ve stated before that the more ends remaining, the greater disparity from the average for teams of unequal strength we can expect. We can assume that Koe is a stronger team; however we can still compare the values and determine which decision leads to a better outcome.

The only possible argument to be made is that with fewer ends remaining, the result will be closer – but it is only one end less so it is not significant enough to sway our decision. For example, if you are a weaker team and win the toss, my theory would indicate your best chance may be to blank 9 ends and then be tied with hammer in the final end. This eliminates the chance your opponent will can use their superior skill during the many ends available to score multiple points. With free-guard zone however, this is simply not possible. At any stage your opponent can force you into a non-blanked end.

5th End: I’d nominate the 5th end in this game with the 9th end in Howard vs. Middaugh for “Best Ends” of the week. See image which shows the rock placement before Jason’s first stone.

Gunnlaugson is Red

There were multiple calls which could be argued several ways and all opinions could likely be supported. One thought I’d like to bring up was Jason’s comments heard on CurlTV of a “big end” vs a deuce. Should they position for a “big end” or try for the deuce?

At this stage, Gunnlaugson is two down with hammer. Here are various WPs at end of the 5th, based on possible outcomes from this end:

Koe steals, Jason’s WP = 11%

Single WP=20%

Deuce WP = 39%

Three WP = 61%

Four WP = 75%

I won’t even begin to analyze the possibilities based on rock position, etc. Have fun if you like. In general, I like Gunnlaugson playing for a big end based on the fact that he expects his opponent is stronger and the positioning of the rocks are such you may be able to take some risk and put the game back to Close or with a 4, take Control. If I’m the stronger team I would be more inclined to take my deuce and use my skill to create opportunities in the last half of the game. Unfortunately, Jason wasn’t able to make the big shot or place the rocks correctly to get the big end. Hats off to Kevin Koe who made a brilliant shot on his last to take away most of Gunnlaugson’s options.

4. Kevin Koe vs Kevin Martin

Martin is up 6-5 with hammer in the 9th End. On John Morris last rock Kevin Martin elects to keep the centre guard and play into the rings (see image). Why doesn’t Martin peel the guard here? If Kevin takes one or blanks, he leaves Koe with an 11-12% chance to win. If Koe steals it goes up to 20-25%. If Koe steals 2, as unlikely as it would appear, Koe now wins 60%.

Koe is Red

Kevin’s thinking could be:

“If I peel twice, Koe will hit on his last rock. I’ll face three and have to play a double and likely give up a steal. If I play into the rings now, I at least give myself some chance to score and it is doubtful Koe could steal 2, which is my primary risk”.

During the CurlTV broadcast I questioned the call, preferring to peel. In retrospect, you can make a good argument for both decisions.

5. Glenn Howard vs. Wayne Middaugh

Wayne had a tough week. His first three games were Ferbey, Howard then Martin. He needed to come out of those three with at least a win but never got any momentum. The Howard game was a close one which could have gone the other way.

9th End: The 9th end was (along with Gunnlaugson vs. Koe 5th end) my vote for most exciting end of the event. It lasts nearly 25 minutes!

Check it out at http://www.tsn.ca/curling and link to Video.

The view of the house before Wayne throws his last rock...

Howard is Red

Howard is up 5-4 with hammer and elects to leave the long guard. This gets them into some trouble and they nearly give up a steal of two. See analysis above in Koe vs. Martin and think if a similar decision comes into play for Glenn at some point in the end.

6. Glenn Howard vs. Kevin Martin, Round Robin

Clearly the best game of the week. Unfortunate the final didn’t live up to the re-match we’d have wanted.

8th End: Martin is tied 5-5 without hammer and elects to play his first rock in the rings rather than play a centre guard. I wrote about this in several previous articles, including January 2009. Kevin is still the only top skip I’ve seen make this play.

Howard is Red

Martin’s final shot in this end was the shot of the week. Facing a 2 or possible three by Howard, Kevin makes a fantastic hit and roll, corner freezing to his own stone. Howard still has a raise for a multiple score but it is much more difficult and he is held to one instead of the game being possibly over. Because it’s tied in the 8th end, Kevin knows that whether Howard scores a two or a three it has little bearing on the outcome, they will likely lose the game.

What is interesting in this scenario is both the ability to visualize the shot and the dynamic between John and Kevin. At first Kevin didn’t like the out-turn. John was able to maneuver the conversation and ease Kevin into the decision, without challenging him. It is generally accepted that you don’t want your skip playing a shot he or she is not comfortable playing. This discussion captured parts of the game that are critical to success and can’t be simply analyzed by numbers.

Further to this, I’d suggest Curling is made up of 4 key areas:

1. Physical Skills

a. Throwing the rock

b. Sweeping

2. Mental Skills

a. Reading ice and rocks

b. Communication

i. Calling line

ii. Judging weight

3. Strategy

a. Calling the game

4. Psychology

a. Emotional control

b. Team chemistry

My blog focuses almost exclusively on Item 3. This is an example of item 4. In these cases, teammates become like a caddy who is discussing which club to play on an important shot. It’s not always about which club is correct but about how the caddy interacts and builds confidence in the golfer. These areas are ranked by what I would consider level of importance, although top teams are generally strong in all areas.

If you’d like to review video from any of these games or others, check out http://www.curltv.com/ or http://www.tsn.ca/curling and click on Video.

Have a Safe and Happy Holidays!

Canada Olympic Trials Preview – and Coming Soon to CurlTV…

2009-12-02T16:32:00.000-07:00

Yes readers, yours truly, the Curl with Math guy (perhaps a better moniker would help my marketing efforts), will be joining Luke Coley in the broadcast booth for several draws during the Roar of the Rings! Actually, I prefer the name “Olympic Trials”, as it more clearly states what is actually going on. ROTR seems to be a screenwriter’s pitch to Warner Brothers for a new movie…. “Lion King meets Lord of the Rings….and we’ll film it in Edmonton; parts of it look just like Mordor and the locals look like Hobbits”.

Let’s begin our Preview show…

Men’s Teams
The “Big Four” are Martin, Howard, Ferbey and Stoughton. No slight to Middaugh, who is a two time Brier champion or Koe who is an original 4 qualifier, but those four teams have the most wins, best records and greatest success against the field going back many years. It would not be a surprise if any of these teams won, and the numbers will show us why.

The Favorites

Kevin Martin is 76-35 (68%) since start of the 06/07 season against this field and is 41-19 (also 68%) against the rest of the Big Four.
Howard is 13-13 against Martin and 7-8 since 06/07. However, they are also .500 against the others in the Big Four, 31-31 overall and 17-17 since 06/07.
Martin has outscored all Trials teams by nearly a point per game. Howard and Ferbey are around a half point.
Martin is 22-18 against Stoughton historically but 11-2 since the 2007 Brier.
Provincial Rivals – both Favorites have been dominant:

Martin is 20-7 against Ferbey since 06/07 and 27-10 overall.
Howard is 12-5 since 06/07 (70%) and 25-14 historical numbers against his ex-teammate, Wayne Middaugh.

Contenders

Ferbey is only 16-29 (36%) since 06/07 against other Big Four teams but minus Martin, they are 9-9 against Stoughton and Howard since then and 21-17 overall against those two teams.
Stoughton is 80-74 against the entire Field but has beaten Gunnlaugson (including Carruthers) 10 times. Jeff is 37-46 overall against the other Big Four teams including a mere 13-22 (37.1%) since 06/07.

Challengers

As a top 4 qualifier Koe has a (somewhat) easier start, not facing Howard, Martin or Ferbey until their final three games. Their opening game is against Simmons, against whom they are 11-0. They are 7-6 vs Stoughton but against Howard, Martin and Ferbey they are 18-41 overall and 18-37 since 06/07.
Middaugh plays Martin well (11-12 and 4-4 in last 3 years) but Howard (see above) and Ferbey (4-11) both seem to have his number. Middaugh is 7-0 vs Carruthers/Gunnlaugson.

Underdogs

Simmons, is he an underdog? Numbers indicate yes. They have only won 32% against this field and haven’t shown to be any stronger since 2006. They are 5-1 against Middaugh in the last few years and…if they can finally win against Koe…
Gunnlaugson has no chance, mathematically. But then again, Gushue probably didn’t have much chance last time either, even Stoughton said so…. With their small sample size, we don’t have much to analyze. Including Carruthers, Daley Peters and Gunnlaugson as skipping the squad is 12-37 against this field. However, Gunner is 3-5 as a skip and has beaten Howard, Koe and Stoughton. If only he’d picked up a veteran to play front end….

Play-off Bound?
Let’s examine chances of outcomes. These are based on handicapping analysis I have done. I will spare you the details of the numbers, other than to say if you’d like to bet on any games, please let me know.

Martin has 7% chance and Howard a 4% chance to go undefeated.
At least 5 Wins – Howard is around 54%, Martin near 65%. Next closest is Ferbey at 32%.
At least 4 Wins – Howard is 80% likely, Martin 86%, Ferbey 62%, Stoughton 58%
Koe is 49% likely to get to 4 wins, Middaugh is 45% and Simmons 16%
Gunnlaugson is calculated at approximately 7% chance at 4 Wins. As I stated earlier, this is based on small sample size and with other skips, so if someone offers you better than even money that Gunner will win 2, then it is a good bet. Of course, he still might go Winless (12% chance).

Women’s Teams
The Women’s Trials teams have the Big Two but also 3 others who are very close. Jones and Lawton then Scott , Bernard and Kleibrink. Let’s call them the Top 5.

It would not be a surprise if any one of these five finished as the winner. It should be noted, the sample size (or numbers of games played) amongst these teams is far smaller than those for the Men’s. This leads to more variability in probable outcomes. But let’s still take a look…

The Favorites

Jones is 39-23 (63%) and 29-21 against the other top 5 teams. She is 8-1 against Bernard, 4-0 against McCarville but 6-9 against Scott.
Lawton is 38-25 against this field including 27-19 (59%) against the other top 5. They are 9-3 against Scott and 0-3 against McCarville
Heads up Jones edges Lawton 6-5.

Contenders

Scott is 33-30 against the other Top 5 and 12-5 against Bernard. Interestingly, she’s only 2-5 against Holland.
Kleibrink is only 41% against the other Top 5 and, though 10-9 against Scott they are 7-3 in the last 10 meetings.
Bernard is 40% against the other Top 5. Strong against her Calgary opponents: 8-4 against Kleibrink and 6-0 against Webster.

Challengers

McCarville’s numbers are close to Kleibrink, Scott and Bernard. They are 46% against this field while the others are 48-50%. However, her sample size is much smaller and we can expect her success at this level of competition is not on par, so we will put her in this category (so that we have someone!).

Underdogs

Webster played well at the Pre-Trials, qualifying in A, but historically they are 10-24 against this field. It’s not likely, but if given the right odds, some would say it’s good to bet a streak.
Holland is 16-27 against these teams but is 5-2 versus Scott. Being the last qualifier they have a tough start but who knows….

Play-off Bound?

Jones has a 6% chance and Lawton a 4% to go undefeated.
At least 5 Wins – Jones is 59%, Lawton is 50%. Next closest is Scott at 25%.
At least 4 Wins – Jones is 84%, Lawton is 78%, Scott and Bernard 53%, and Kleibrink (50%).
McCarville has a 47% expectation for 4 wins and Holland is 25% likely.
Webster is 11% likely to get 4 wins and 9% likely to be Winless.

Predictions
So now that we’ve looked at the records, who do I like? The correct answer is always whoever gives me the best odds, but if we aren’t taking Gunner at +380 to beat Stoughton, then I suppose I’ll go with my gut (and not my wallet)…

Howard, Martin, Ferbey all get in the play-offs. 2006 was an anomaly and these guys are all more prepared and playing better against the field coming in than they did in 2006. I think one or two others may also be in tie breakers, likely Stoughton and possibly Middaugh – but he needs a good start. Koe has a chance to get on a roll with some early wins but will need to hold on. Simmons had a good Pre-Trials but they may get called for too many men on the ice. I think if Gunner goes 0-7 its possible to have a 6-way tie at 4-3. Wouldn’t that be something?

Women’s? I don’t watch/study this game as much and think anything is possible. Many of these teams have the big game experience and should be able to play to their potential despite the magnitude of the event. The qualifying format through a Pre-Trials likely helped teams like Webster and McCarville in this regard and make them possibly more dangerous than some would suspect.

Play-off predictions?
I’ll wait until Thursday.

Note: the accuracy of these records is the responsibility of CurlingZone. We may be out by a game or so, but we have to start somewhere. If anyone has numbers which contradict these, please e-mail Dallas or Gerry @ CurlingZone.com.

Another note: These numbers don’t rank the value of a win based on the importance of the game. For example, a win or loss could come in the Brier or in the opening round of a WCT cashspiel. We could try to add this to our analysis, but I do have a day job and I don’t know how much more value it gives us.

And yet another note….

PLEASE, PLEASE, PLEASE…will PinnacleSports or some other betting web site offer the Canada Olympic Trials? Four years ago some great gambling opportunities and the Brier last year was a potential gold mine. And finally, this year, I do all the prep, analyze the records, am prepared to lay down my money….and no where to put it. Guess we’ll have to wait for Vancouver….

Two other Math notes this month…

There should be no surprise that I agreed with Bill Belichek’s call on 4th and 2 versus the Colts a few weeks ago. For anyone wanting math analysis in Football, check out http://www.advancednflstats.com/ and their coverage of that controversial decision at http://www.advancednflstats.com/2009/11/belichicks-4th-down-decision-vs-colts.html. Of interesting note is how talking heads (of which I will be one next week) try to attempt to support their belief regardless of the actual numbers. Tony Dungy said that Bill “should have gone with the percentages” and punted. Actually Tony, percentages say the opposite. The following weekend on ESPN Sports Reporters, Mitch Albom of the fine quaff and author of such books as Tuesday’s with Morrie, Five People You Meet in heaven, and other books which can be made into an ABC Hallmark movie of the week, said “No, it’s one of those things that if it works it’s the right call. It didn’t work and every single number out there that you can crunch says it was the bad call.” What?
Troy Aikman this past weekend mentioned, while commentating on my Vikings, that coach Brad Childress should be concerned that Favre has only thrown 3 interceptions this year and he is likely due for a bad game where he will throw 4 or 5. We hear nonsense like this all the time in baseball when the announcer says “he’s 0 for his last 5 at bats, he’s due for a hit here”. These examples are similar to stating that if a coin comes up heads 9 times then it is more likely to come up tails on the 10th attempt. I hope my readers have figured out that is not the case.

If you happen to be at the Trials in Edmonton and read my articles, whether you agree, disagree or really don’t care, please come say hello. I’ll be the person in the CurlTV booth most likely to be fired.

Notes from the Pre-Trials (AKA “Road to the Roar”)

2009-11-15T01:14:00.007-07:00

I’m struggling with this event called the Road to the Roar or more aptly named Pre-Trials. It reminds me of the NFL deciding to increase playoff teams from 10 to 12 in order to generate more games (and more revenue) on opening “Wild-card” weekend. It’s not that the entertainment isn’t there, but why not just have 16 teams at the Trials in December? Money must have something to do with it. Or perhaps the 400 or so people in the stands in Prince George demanded their opportunity to shine in the spotlight.

Some random thoughts and analysis….

1. TSN please show me the first stones of the end! Not doing so makes it hard to understand what strategy is being played. I couldn’t tell if Gunnlaugson had some strange calls or they just missed shots. In 7th end Gunnlaugson is up one without hammer (5-4) and plays a centre guard, rather than in rings. Perhaps he read my article from February 2009 where I stated “If we are one up in the 4th or 7th, we should force our opponent into scoring, even at the risk of a deuce, in order to have hammer in following end.”

2. Linda Moore, please think about what you say related to hammer in the 10th end. You are the “stats” announcer, relaying all of the appropriate shooting percentages for the fans, but you fail to recognize the basic premise of statistics related to the final end of a game. During the 9th end of the C Final between Gunnlaugson and McEwen, you said “that hammer is still the advantage in that last end”. No, the advantage is to be one up without hammer vs one down with. You then state “There’s lots of things that Jason could do but I don’t think it’s wise, I think he’s going to wait till the 10th as well and there lots of things you can do in the 10th end…he can do the job without the hammer”. So which is it, advantage with hammer or not? The correct strategy is to play for a steal at the risk of a deuce, and if you force your opponent to one you increase your chances to win from 60% to over 75%. I didn’t see if Jason intended to play their first rock in the rings because, per note 1 above , TSN didn’t show it! I don’t like the 9th playing out the way it did for Jason. Much better for him to be aggressive in this situation.

3. Simmons vs Stoughton, A Final. Interesting choice by Simmons to hit and roll in the 8th end. It appeared he could have played a draw and sit shot stone frozen to the Stoughton rock behind the button. Possible he was concerned by lack of curl or afraid of leaving the angle raise or other shot for a big end.

Stoughton is Red

This is an important point in the game. Simmons is two up and holding Stoughton to one is a huge advantage. Simmons chances of winning goes from 67% (tied with hammer and just barely Control) to 86% (and Dominant Control) if he holds Stoughton to a single instead of the two he surrendered. Even if Stoughton makes a circus shot and takes three, Simmons still has 37% chance to win. I prefer the draw for these reasons and if he comes short he still leaves a very difficult shot for two.

4. Yes Mike McEwen, you should have played the double in the 8th end against Jason Gunnlaugson in the C Final. Your margin for error was substantially smaller with the hit and stick you attempted. Also, you left your opponent a chance, the other option did not. Kevin Martin would have removed both those stones before you got in the hack. I suspect in years to come you will also.

McEwen is Red

5. The B Final, 8th end. Simmons is up 5 to 4, McEwen has hammer. Simmons plays the run-back again on his last shot.

McEwen is Red

He could have chosen to draw instead. A successful run back likely forces Mike to one anyway. It appeared an out-turn draw to the face of the stone could provide the same outcome with more margin for error. However, the amount of curl may have weighed in on the decision. Let’s take a look at Pat’s thinking:

Draw: Let’s expect Pat makes a reasonable attempt to draw to the face of Mike’s stone but Mike makes his draw 50% of the time.

W = .5(.67) + .5(.37) = 52%

Run-back: How often does Pat need to make the shot for it to be the correct call?

W = .52 = x(.67) + (1-x)(.37)

Note we assume Mike always scores two – in the actual game his rock caught debris and he did not, but that is assumed to be minimal for our analysis and then can be factored into our decision later.

We can see that if x (Pat’s chance of the run-back) is greater than 50% then it is the correct call. If we assume Mike makes the draw 60%, then x = .4 and Pat only needs to make the runback 40% for it to be the correct call. Further examples show it as a linear equation in that Pat needs to make his shot more often than Mike misses a draw for it to be the correct call. The readers can decide if Pat made the “correct” choice.

6. Same game, 9th end, Simmons plays a corner guard? Interesting call (unless of course he was light). Stating that he prefers to score multiple points at risk of a steal, rather than leave a possible blank open.

7. Same game, same end. McEwen’s first stone, he plays a run-back of the centre guard to Simmons rock in the top four. Giving up a deuce here is not good (less than 12% to win). Mike must hold Simmons to one or possibly steal.

McEwen is Red

I like keeping the centre guard in this situation, if only to keep the middle protected. At this late stage, he may have felt there was no good placement in the rings and he may be correct, but see how this decision drives the next decision? Even if he makes the shot (which he did, but was unfortunate the jam) Pat still can make another strong come around (which he did) and put himself in good position for two.

On Mike’s last I’d almost prefer a draw to either freeze or the back four foot.

McEwen is Red

As difficult as the shot is, the run-back needs to be a double. The issue here is, a deuce or a three have nearly the same outcome: you are very unlikely to win the game. The interesting analysis here is, Mike deciding to run-back on his first was already setting himself up for another run-back on his second. In essence, by calling it once, Mike is saying “I will make this shot twice” In making that decision, might be wise to determine your odds for making a run-back (ahem) back-to-back. If your chances are 90% of making one, then two in a row is (.9)x(.9) = .81 or 81%. If you only figure 80%, then you drop to 64% to make two in a row.

8. I grew up a rink rat at the Assiniboine Memorial in the mid 80s, watching Kerry Burtnyk. One of the classiest champions curling has ever seen. Kerry’s loss to Gunnlaugson was heart wrenching. His last rock in 10 needed only to roll an inch, it did not. Then a draw to the full eight turned into a burned rock, ending Kerry’s chances at an Olympic medal. I was hoping to see Burtnyk in Edmonton, but it is not to be. We can only hope he makes another run or two at a Brier bid (a la Werenich in 1995 and 1997).

9. Back to McEwen vs Gunnlagson, C Final. In the 8th end, up 6-5, Mike appeared to be in good position, sitting first and second on BJs first rock. They called time out, thought for a while, then peeled a corner guard.

McEwen is Red

I was unclear to their thinking here, other than it seemed like the best idea at the time. It didn’t appear to have much impact on the end. Alternatively, they could have chose a more aggressive play, either draw to open side or play some type of tight guard or draw. The rock they were concerned about (top yellow) did come back to haunt them later in the end. Mike commented they would have to make “a lot of good shots to get two” and, as often happens at this level, they did. The best part of their decision was avoiding 3, so we can’t fault them for that. And as I said above, if Mike had just played the double on his last….

10. Interesting choice by Jason to play a centre guard when one up in the last end without hammer. Mike doesn’t bite (perhaps Jason wanted him to?) and choses to play a corner guard rather than draw to centre.

Good luck to all in the “Actual” Trials, which I suppose we could now call the “Pre-Olympics”. Final thought…..is it too late for some young team to pick up Russ Howard?

New Season Begins and World Cup Final: Koe vs. Howard

2009-10-30T16:44:00.000-06:00

Well, the new Curling Season is here and though I’m disappointed in the end to golf season I am anxious for the Olympic Trials. The Olympics themselves, sadly, I’ve never had much interest in. Why is it every four years I’m suppose to get excited about sports which I’ve never cared to watch during the past 1460 days since the last Olympiad? I never tuned in to CBC for skiing during the World Championships in 2008, so why now? If not for Curling, Hockey, and perhaps women’s’ short track speed skating (it’s like a cat fight on skates!), I’d likely pass on the entire thing completely. And don’t even get me started on the Summer Games – days on end of coverage from multiple networks, journalists, etc – and the only thing worth watching is 9.7 seconds of men running and a couple of laps in a pool (which took slightly longer). Better to watch the highlights on the internet after it’s all over.

In any event, we’re back into the “sweep” of things and need to begin.

1. Shorty Jenkins: Martin vs. Matchett
Gerry Geurts of CurlingZone relayed this shot call to me and he may have not remembered exactly right, but the analysis should still be interesting. In the semi-finals at the recent Shorty Jenkins event, Kevin Martin was one down playing the 7th, with hammer, against Dale Matchett. Matchett had a rock in the outside rings, perhaps biting eight foot, and there was a slightly off-centre guard. Martin, on his first stone, chose to play for his deuce by drawing around the guard. Remember, this is an 8 end game and only the final end remains. Kevin is forgoing an attempt at a blank, attempting to take two, with an increased risk of being held to one or even giving up a steal.

The chance of winning up one without hammer coming home is roughly 60%. If held to one, Martin’s chances drop to 25%. The difference in outcome between a successful two or held to one is greater here than at any point during a game. Let’s look at each option:

Draw: Assuming the draw takes away any chance of a blank, let’s determine how often Kevin must get a deuce to make this a correct call.

W = d(.6) + s(.25)

Where d = chance of a deuce and s = chance we are held to one. Assuming these are the only likely outcomes (blank and steal of two not likely), we solve for s= 1-d

W = .6d + .25(1-d).

To complete this calculation, we need to compare against the scenario if Kevin hits the stone.

If Kevin hits the open stone, Matchett either hits the Martin stone (trying to roll behind the guard I expect) or simply draws around the guard attempting to force Martin to a single point.

What likely entered Kevin’s thought process “if I hit and stick, Dale will draw around the guard and now I may be forced to one. My chances are better at two if I force the play now.”

When guessing what an opponent may do, we can estimate what the chance is they will make a certain play and evaluate further. For example, let’s start to analyze what happens if Kevin hits open stone.

Assumptions:

Martin will always hit and stick successfully.
If hit and roll succeeds, Martin always draws for one successfully (assuming the roll puts the rock in the back rings).
If hit and roll doesn’t succeed, a blank always occurs.

Let’s first examine what happens if Matchett draws or hits:

Where:
x = Odds of winning if tied without hammer = 25%

y = Odds of winning one down with hammer = 40%

z = Odds of winning if two down with hammer = 12%

Hit: Estimate a roll successful 25% of the time.

W (Martin) = x(.25) + y(.75) = .363

Draw: Estimate with a draw Matchett steals 20%, Martin takes one 60% and he gets a deuce 20%…

W (Martin) = x(.6) + (1-y)(.2) + z(.2) = .294

Matchett should draw (based on our estimates are correct) – but perhaps he will only draw half the time. Then we weigh the chance of winning as:

W (Martin) = .5(.363) + .5(.194) = .33%

Therefore, using this in our original equation:

.33= .6d + .25(1-d) solving for d = .23

Therefore, Martin only has to get his deuce 23% of the time in order for the decision to be correct. Note that if Matchett always plays the draw, then Martin needs to make a deuce even less often (12.5%):

.294 = .6d + .25(1-d) solving for d=.125

2. Masters Final: Koe vs. Howard
It was an entertaining game last Sunday with Howard winning yet another Grand Slam. This was clearly one that could have gone the other way. An early steal of two had Glenn and his squad battling back. There were some timely misses by the Koe rink, but also some interesting decisions which may have provided them better opportunity to clinch a victory rather than being a bridesmaid for yet another Grand Slam final.

Some observations….

Second End:
Matt Hames in his Curling News blog suggests Koe could have played the in-turn draw instead of leaving Howard an opening for one…
http://curlnews.blogspot.com/2009/10/world-cup-sweeping-rant.html

I would tend to agree. At this stage he’s 2 up and if he does make a poor shot, at worse Howards gets a deuce and Koe’s odds are at 61% tied with 6 ends remaining. A steal would have put the Koe rink at odds of 89% chance to win. That is a chance you want to take during the Early Game, IMHO.

Third End:
Blake throws two draws. One appears 20 feet heavier than the next (according to the assessment by announcer Mike Harris). The sweepers are surprised and there is some discussion that his stones aren’t matched. How can teams at this level not have properly matched stones in a final of this type of event? Situation seemed very strange.

Fourth End:
Koe appears to be sitting third stone in the top eight foot, Howard is first, second and fourth. Kevin calls a hit on his own stone (driving it onto 4th rock), rolling across the house to then double the Howard stone. If successful, Howard would have a shot to hit and stick and sit two. Koe then would have had a double to force Howard to one. I thought the correct call on his first was the one he played on his final stone. Double the 1st and 2nd rocks and roll behind his other rock. If successful, Howard would be left with a choice to either draw around Koe’s top stone or attempt a difficult hit which appeared to be unlikely to allow him to sit two.

Sixth End:

Howard places a centre guard. Please see my articles from January 2009 and March 2009 for the analysis of why this not the “correct” call. I wonder if it was an intentional decision on the part of Howard to choose an alternate strategy, or if he is unaware of the analysis.

Interesting call on Howard’s first. Rather than hit the open stone, he plays into the centre and leaves a (albeit) long run back double for Koe to lie two. This is not a good position to give up a deuce, Howard’s odds of winning would drop to

15% if Koe pulls out the miracle. The flip side is, a steal of one for Howard puts the odds at him winning to 63%. Howard’s call into the rings on his last was clearly an intent to tempt Koe into a big weight shot rather than a draw. He could have instead placed a guard, leaving him a draw – but Koe may have hit no matter what the result. Also, a poor guard could have left a soft double with the inturn and a possible deuce for Koe.

Seventh End:
Blake’s second shot, after much debate, Koe’s team agrees to play a run back. In their position the centre guard is a critical stone to help plug up the four foot in an attempt to force Howard to one. The risk of a deuce is worth the attempt to steal or force a single. Playing the run back was an attempt to take a three out of play – which ultimately succeeded. However, if Blake plays a freeze, Howard may again play a draw, but more likely remove the guard and give Kevin a chance to clear the house on his first shot – or have the option to guard again. If Howard draws, then the play is into the middle with a centre guard and likely a good position for Koe to force a single. Continually attempting run backs is generally counter-intuitive to what a team one up without in the second last end wants to do: force the play to the centre and force the opponent to a single and have a 75% or better chance in the last end – with a risk of giving up a deuce and having a 40% chance coming home. The small chance to steal one, leaving Howard a 12% to win, also supports a draw strategy. In Koe’s defense, playing to avoid a three was perhaps his motive and they were comfortable with that style. It is a case where the risk of a three is minute compared to the great advantage of forcing one or stealing – but sometimes it’s difficult for a team to want to take additional risk if they feel it could take them out of the game. Let’s attempt to analyze the shot call. This involves VERY rough estimates of final outcomes, but allows us to examine how to reach a decision.

Draw:
Koe steals = .1
Howard scores one = .4
Howard scores two = .3
Howard scores three = .2

W (Koe) = 53%

Koe chose the hit, which ultimately resulted in two. Let’s estimate what outcomes may have been most likely:

Hit:
Blank = .1
Koe steals = 0
Howard scores one = .3
Howard scores two = .6
Howard scores three = 0

W (Koe) = 53%.

If Howard scores a deuce more than 60%, then Koe wins less than 53%. The decision appears close. Ultimately, it depends on Koe’s estimation of Howard’s chance at scoring 3 and ensuring that Howard never scores 3 when they attempt the run-backs. I would prefer the draw but it is closer than I had first thought.

Eighth End:
Blake’s first rock, they attempt to come around Howard’s stones staggered in front of the rings. An alternate play would be to double those top stones out and sit 2nd and 3rd shot. By playing to the middle it left a greater chance of only a single and increased chance of a steal. This is the style of play I suggested earlier Koe could have chosen in the 7th, but here the opposite is perhaps true and opening up the play may have increased his chance at a deuce and provided a greater chance at a single if he needed a draw on his last.

A good game and one where a few more made shots on the part of Koe’s rink could have changed the outcome. Whether the decisions we’ve examined here may have had any difference is up to the reader to determine.

Until next month, Happy Halloween!

Team Martin Can’t Hold Down the Haggis

2009-04-17T01:31:00.000-06:00

What is it that makes sports entertaining? Is it watching the thrill in victory, or the agony of defeat? Do we admire and respect our sports figures for their immense talent and skill, something we do not possess, or for their ability to face the challenge and, sometimes, fail to over come it. Golf, baseball and, similarly curling, present a case for the latter. Do we remember Greg Norman for his heroic achievements at the British Open, or for his complete collapse at the 1996 Masters. The answer is pretty clear. By showing us the same frailty in their inability to overcome the tension of the moment, we see these stars are human. We share the same nervous anxiety when we stumble giving a presentation to a large audience, three-putt from ten feet for a $5 Nassau, or babble incoherently when asking the pretty girl to go on a date.

We still marvel at the feats of Tiger Woods or Michael Jordan, who may lose to an opponent who bests them on a certain day, but never seem to “choke” when the opportunity for greatness is at hand. Jack Nicklaus was the Greatest, but Arnold Palmer and his collapses in the US Open, Masters and PGA, along with his wins, make him “The King”. Something to me is very appealing in experiencing these moments of sport. Moments with a Greg Norman, Jean Van De Velde, Kenny Perry and, yes, a Kevin Martin.

Kevin Martin does not have the records in world competition that anyone would expect from (arguably) the greatest pure curler this country has produced. Kevin Martin beats EVERYONE. Regardless of his team, Kevin has been at the top of Men’s Curling for almost twenty years. He simply Wins. Against every team, at every event….except on the World stage. Is it something more than poor ice, off-days or random chance?

In watching Team Canada’s struggles against Scotland in each game they played, I was trying to determine if it was more Scotland playing great or Canada flat. It was clear Scotland took Canada off their game and disrupted their rhythm. Unlike other games the past two seasons, Kevin never appeared to have a clear sense of his strategy or an ability to dictate the flow of play in each game. In the finals, they looked to have this solved, but the final end proved otherwise.

Most of the discussion in future years, over a cold one at the local rink, will be the call to throw first skip stone away. This shot does appear bizarre and I prefer the option to drive the top yellow stone into the pile – but this is more an opinion versus a fact. Kevin made a very difficult choice, one he must have known would be scrutinized for the remainder of his life and beyond. However, on his last shot, he had two possible options, both likely better than 50%, to win the World Championship. I believe a different choice could have left him a better chance or possibly made Murdoch’s last more difficult, bringing the chance of a hand shake before the final rock. However, several options, such as a guard or a slightly missed hit, could also have left Kevin with less than 50% chance to win. It is my opinion Kevin could do better choosing an alternate shot call. It is a fact that with second’s first stone in this situation: peel the guards. Why does Kevin Martin call Marc Kennedy to play a soft hit and roll into the four foot, when two centre guards sit covering the four foot, in the final end, when tied with hammer? I suspect two things may have led to this critical mistake:

Martin “felt” a need to play a more aggressive end. This could be similar to the Brier final in 1997 against Vic Peters, played during the 3-rock free-guard zone era. I can’t recall the specifics, but the final score was 10-8 and Martin had an option to play a conservative final end, but instead chose to be aggressive.

Kevin strategically “choked”. After months of curling, against the best teams in the world, and the hours of practice and preparation, the culmination of a season comes down to the final end. Similar to Kenny Perry, seeing a two stroke lead with two holes the play, he begins to picture the win. The fatigue combined with the enormity of the moment, leads to a mental breakdown at a critical point. Instead of focusing energies on the job at hand: the shot, the putt or the pitch – just as they would normally - the curler, golfer or ballplayer starts to see themselves winning. In an interview with Scott Hoch during the recent CBS Masters telecast, referring to the missed 2 foot putt from 20 years previous, Scott stated he saw himself in the green jacket and could not focus on what he needed to do, get the ball into the hole. Kenny Perry said in his Saturday press conference, when asked what it would feel like to win, that he wasn’t going to answer the question – he needed to stay in the moment. He did for 70 holes, and then his crisp draws turned into evil hooks and his right hand got twitchy. These golfers have both won many tournaments, just as Kevin has, but when the title that they REALLY want to win, The Masters, was close at hand, they got out of their routine, out of tempo and performed well below their ability.

I obviously can’t say if the latter was the case. Kevin has been in similar pressure situations many times and shown the ability to overcome these nerves. From my vantage point, and my analysis of the three games played, something with team Martin just didn’t seem right when matched against Scotland. They did not look like the same team that plowed through Canada’s best all year. It seemed to be more than simply shot making. I expect Team Martin will prepare, focus and do all they can to ensure next time to execute to their peak ability and with clear thinking, when the “moment” happens again.

Some other notes from the recent Mens’ World Championships:

Thanks to TSN for the extreme close up of the antique measuring device (and the CCA logo) being used for a World Championship. At a critical point in the game, the Swiss were held to a single when their second rock was deemed “tied” with Norway’s. The gaps in the measuring device were similar to those dial kitchen timers from the 60s. Can’t these enormous prices for tickets go to support some digital devices? If not, at least get someone to “sharpie” some extra lines on the dial so this fiasco doesn’t happen again.
No thanks to TSN for constantly missing the leads rocks. Fine, if you need to come back late in the early ends, but in the final end of the final game we missed the first 3 rocks of the end. That’s 18.75% of the end. And the tick attempt in a tied game is perhaps the second most critical shot of the end (other than skips last). Makes it even harder for me to analyze calls if I don’t know what was played. Ray did fill us in on occasion, which is helpful.
In the 3-4 Game, Norway chose not to play a corner guard when one down with hammer and Switzerland came into the rings in the 7th end. They played out for a blank. My February article examined the interesting position in the 8th end, where a blank or taking one is essentially the same, but what about the 7th end? In the 7th, Norway has a 40% chance to win when one down with hammer. After they blank, their chance in the 8th is 38%. If they play aggressive and are held to one, they are 35% playing 8th. If this happens in 8, they are 34% starting the 9th end. Doesn’t appear to be a poor decision. What does 3 do? If Norway takes 3 in the 7th, they are in Control with 79% chance. A three in the 8th moves them into Dominant Control and 85% chance to win. I like to stay aggressive, and might prefer to play a corner – but there appears to be some reasoning behind their decision.
Another example of strange events for Team Canada. In the 1-2 game, Martin is down one without playing the 8th end. John’s rock doesn’t quite move the Scotland stone far enough, and they lay second. On Kevin’s first shot, they elect to guard. I’d suggest this is a position where greater risk could be taken. Kevin may have thought he’d have something on his next shot – but let’s assume he knew he would not and he is playing out the end to force Scotland to one. Two down with and two ends remaining,. Martin will win 15% of the time. If you’re wondering if Kevin’s numbers are better than our average statistics, they’re not. The Martin team is statistically in line with these numbers. If you add in the small chance Scotland manages a deuce in the end, the 15% is actually high. I would have preferred Kevin to play aggressively for a steal, even at the risk of a big end. He needs to steal 44% of the time to make the risk statistically correct. Clearly he felt his chances weren’t that high – or possibly that he’d have a chance with his last shot. Strange that they were unable to see what Scotland’s shot would leave them – similar to the 10th end in the finals.
In the 10th end when tied – tick, tick, peel, peel and then, when in doubt, peel some more. Then draw for the win. Anything else, in my opinion, increases your risk of losing. Did you notice that Marc made both his shots called and his Scotland counterpart missed his – and they lost.
Thanks to Scotland for great play and great strategy (long guards, attempting to minimize run-back opportunities for Canada).
And thanks for the drama. In the words of Jim Nantz “ It was a World Finals unlike any other”. Amen.

Brier Notes: Martin’s Math Test

2009-03-17T01:34:00.000-06:00

During his round robin game with Ontario, Kevin Martin says to TSN: “It’s a real Math Test out there!” Could he perhaps be a fan of this blog? Does he have his own computer programs to analyze data? What goes on in his mind during a game and will he share it with us some day?

Kevin in my opinion appears to make more correct decisions, and in a quicker and more decisive manner, than any other skip. It doesn’t hurt that he and his team have missed very few shots in the last two years either.

I had a great time at the Brier, if only for one afternoon and at the patch later that evening. I’ve finally reviewed all of the Tivo recordings I made from the event, and have started to gather some random thoughts and ideas. I may yet come back to a specific situation again, but for now, below are some non-sensible ramblings.

1. “It’s a Math Test out there”. Says Kevin Martin to Cathy Gautier of TSN at the 5th end break of his round robin game with Ontario. Simply one of the finest games I’ve seen in years, perhaps only rivaled by their rematch in the 1-2 game. Condolences to Steve Lobel. That makes it 9 years in a row in our “My Home Province vs Your Home Province Bet”. I’m looking foreword to eating some of those Toronto Pork Chops.

An interesting situation developed in the 9th end. Ontario leads 5-4 and Alberta has the hammer. Forgive me if I’ve stated this before, this is the best time in the game to be one up without. Howard will aggressively attempt to steal (90% chance to win) or force Martin to a single (74% chance to win), at the risk of giving up a deuce, where they still have a 38% chance to comeback and win in the 10th end. Martin is sitting one, with a Howard stone covering it in the rings. Howard begins placing centre guards and Martin is peeling these guards. For some observers, this could appear a strange situation. Why is Ontario guarding when their opponent is sitting one and they are up one? With 7 stones remaining, John Morris is about to throw a peel, when he heads down to the other end to discuss with Kevin and they instead decide to draw into the rings. Howard actually avoids giving up three, but surrenders a deuce. He is unable to score his deuce in the 10th end and Alberta wins.

I did not like Howard’s decision to play a guard on Richard’s first stone and, regardless of outcome, Martin’s decision to draw seemed correct. How might we analyze this situation mathematically?

Let’s assume a peel will result in either a blank or Martin being forced to one. I suspect if that Ontario would have tried a soft hit and roll to split the rings and lie two with Richard’s next shot. This would have forced Alberta to make a double in order to blank. We’ll estimate a blank 80% of the time – i.e. where the rocks were lined up, given three chances, Martin will clear the rings 4 in 5 tries.

W = (1-.74)(.2) + (.38)(.8) = 35.8%

With a come around, there are several rocks to come and difficult for us to determine outcome. Clearly, a blank will not occur, we need to estimate what the odds are Martin is able to score two (let’s assume no three is scored) versus a steal or held to one. We need to come up with Variables, which are estimates of an outcome.

X = Howard steals one
Y = Martin takes one
Z = Martin takes two

W = x(1-.9) + y(1-.74) + z(1-.38)

Initially, let’s assume Howard doesn’t steal. Set W to .358 and y=(1-z) and solve for Z

.358 = (1-z)(.26) + z(.62)

Z = .281

Assuming Howard does not steal, we need to expect a deuce 28% of the time, in order for the draw to be the correct call. Factoring for a possible steal, let’s suggest that at least 1/3rd of the time we need to score two. Is that the case given Martin’s team, a guard and shot stone? I suspect it is, but that is up to Martin to decide. Adding in even a slight chance for three, and 90% chance to win, it is very favorable to take the risk now. Thinking ahead, Martin would consider Howard’s likely call on Richard’s last stone and his chances of blanking when that occurs.

What should Howard do? Perhaps placing the guard off-centre on the other side of the four foot and giving themselves an open shot at their stone may have provided more options for them. Depending where John’s stone landed, Rich would have a potential double or at least a hit to lie 2nd and 3rd with rocks in good position above the four foot. I am more inclined to have Rich hit and roll to lie two and take the chance Martin is unable to double them out for a blank. Worst case is you are 1 up coming home and 62% likely to win. I expect Glenn, like many teams, expect Martin to score his deuce more often than 40% - and this could weigh in his decision to play the 9th more aggressively than he may have given another opponent. I will continue to argue the case that Martin has no more than a slight advantage over 38% against a team of Howard’s ability. Our study of Grand Slam events supports this argument – but it remains an argument where some will always side against the numbers. Good luck to those who choose luck as the basis for their strategy.

2. Further evidence that Kevin Martin either reads my articles, studies the math himself, or has the best instinct in the game. On not one but two occasions, Martin chose to bring his first rock into the rings when tied with hammer and without last rock in the 8th end. Martin did this against both Gushue and in the 1-2 game against Howard. Incidentally, in the 1-2 game he placed a centre just the end before in the 7th, when tied without hammer. This decision was discussed in my January article.

3. It is the 1-2 game, 7th end. Howard is tied with hammer. On Kennedy’s last rock, Howard has a single corner in play and Kevin yells down “play for a blank? I don’t know”. They decide to play a tight centre guard and Howard continues his conservative play in the end by peeling. Martin then has John draw around the corner on his first rock. In this situation, Howard can go from a 65% chance if he blanks to an 80% chance by scoring two. A steal puts him at 38%; take one they are 62%. If, however, he blanks, the outcome in 8 of two is 85% compared to 66%. I’m not certain I agree with Glenn’s approach in 7 at that stage. Coming around the centre would have forced the end, increasing a chance for multiple score. The added risk of a steal is not as bad in this end (7th) as it would be in the next. I’d like to examine this end further, but it’s late and I’m tired. Perhaps another day…

4. The 3-4 game with Manitoba versus Stoughton. Linda comments in the 8th end that Gushue wants to force Stoughton to 1, he doesn’t need a steal. Granted he does not HAVE to steal but to imply he is not playing for a steal is foolish. If Stoughton takes one, Gushue has a 15% statistical chance to win. If he can steal, his chance increases to 34%. In the 9th end, Stoughton chooses to play a run back from outside the rings on his first rock. Linda states he “has to”. I don’t agree has to. In fact, he could play a draw on his first stone. He could have put his rocks in a position where Brad would likely guard again and steal a single, putting Stoughton 1 down in 10 with last rock. The draw could protect Manitoba from what nearly occurred, a steal of two. In the 10th end, Stoughton made a fantastic shot. But with more time, Gushue may have examined the option of coming into the rings for second shot. An option which, though not eliminating the outcome, may have made Stoughton’s shot either more difficult or only to tie. They both came close to running out of time, something I can’t remember seeing at a game of that level in a very long time.

Scotties Decision by Team Canada and Middle Game Strategy

2009-02-17T01:39:00.000-07:00

Jennifer Jones’ Team Canada rink made some interesting decisions in their round robin game against Ontario at the 2009 Scott Tournament of Hearts (Scotties). During the 6th end, Team Canada (TC), one down without hammer, could have chosen a more aggressive route during the latter part of the end. Instead of drawing around their opponent’s stones in front of the rings, they instead chose to hit the Ontario stone towards the back of the rings and play out the end as a blank. Was this the correct decision? Recall:

Notice that if the end is blanked, TC has a 24% chance. At the beginning of the 6th they had a 22%. In fact, their odds get slightly better if the end is blanked.

If they play aggressive and steal, they increase their chances to 40%. Holding Ontario to one is 22%. In fact, a blank appears to be 2% better than actually forcing Ontario to a single point! It appears the risk of attempting a steal at this stage is not necessary.

What about in the next end? If it had been the 7th instead of 6th end, the decision is very different. Now, entering the 8th end when 1 down without hammer, the odds are only 18%. Holding Ontario to a single gives a 21% chance. A steal in 7 instead of 6 still leaves them 40% - no change. It would be more tempting to play the final rocks aggressively if it were the 7th end. If the 7th were to be blanked and TC is one down without hammer playing 8, it is imperative to either score a steal or force opponent to a single. When entering the final two ends 1 down without hammer, a teams chance drops to 16% - but more importantly, a steal in 9 gains less. A steal in 8 would produce a tie and a 39% chance, but a steal in the 9th to tie the game is only 30%.

The 5th and 8th Ends
Recall my previous article on Early, Middle and End Game. The Early Game is the first 4 (or 2) ends. At this stage, most top teams will play aggressive attempting to take control or dominant control as soon as possible. In the End Game (final 3 ends), teams will play the scoreboard more closely, attempting to be tied with hammer or two up without hammer in the final end of a close game. So what is Middle Game Strategy?

Middle Game is the 5th through 7th ends in a ten end game (or 3-5th in an 8 end game). Recalling my previous description, statistical changes start to appear in the middle game. Trends appear for each situation (tied with hammer, 1 up without, etc). So what are some considerations when determining our Middle Game Strategy?

The first decision is whether to continue aggressive play. This is usually the case early in each end, but as the end develops a team will choose shot calls based more on scoreboard and ends remaining before the End game. So to start discussion on Middle Game strategy, let’s start by examining which scenarios are more favorable in the End Game.

I will use a 10 end game from now on, the reduce complication. To transfer this analysis to an 8 end game, just subtract 2.

In the 9th End, one down with hammer is a disadvantage greater than any other point in the game. In fact, only the scenarios starting the 9th and 6th ends have tied without hammer the same (less than 1%) as one down with hammer. In all other cases, one down with hammer is preferred position. If we have the hammer in a close game the ends previous (5th and 8th), it allows us to take some additional risk with less penalty for being forced to a single point. Recall a Close game is one in which a team is down one with hammer anytime or tied prior to final two ends.

One down with hammer:
In the 5th and 8th ends we can aggressively play for two or three and if we are forced to one, our chances are actually the same as if we had blanked the end. If we instead are one down with hammer in other ends, if our aggression results in being held to one, we are worse than if we blanked the end.

One up without hammer:
Conversely, forcing our opponent to one in this situation (5th or 8th end) gains no advantage over blanking the end. The risk of playing aggressive to force our opponent to one, which may result in a deuce, provides no advantage – a steal is required to gain any advantage. Stealing in the 5th puts us at a 76% winning probability (Control). Stealing in the 8th an 85% chance (Dominant Control). Blanking 5 and then stealing in the 6th in fact gives us now an 80% chance. I’d suggest a sensible play is to tempt our opponent into blanking the 5th end and force our position without hammer in the next end. Blanking the 8th was discussed in our last article and is more open to debate.

Tied without hammer:
If we force our opponent to a single, we again gain no advantage to blanking. However, a steal is a significant advantage over our current position. For the 5th end, in our previous example (one up without) a steal takes us from a 61% chance to 76%. If we are tied and steal, we move from 39% to 61%. Using our analysis from the last article, switching from 39 to 61 is 50% better, whereas 61 to 76 is only 25% better. For the 8th end we go from 34 to 65 (91% better). It would appear we are more inclined to attempt to steal in this scenario. However, stealing is always difficult and we risk our opponent making a multiple score. We are forced to be more aggressive because of our position but being one down with hammer gives us an ability to be aggressive without the same risk.

Tied with hammer:
Being forced to one in the 5th or 8th end is no mathematically disadvantage. In all other ends, being held to one is a disadvantage over a blank. Again, per situation one down, we can be very aggressive at the risk of being held to one. However, as pointed out above, a steal is very bad for us in this position. In fact, a steal is very bad for us every time in this position. It is most critical in the 9th where we drop from 74% to 38%.

In every case, having hammer appears to be a greater advantage in this position. We can be aggressive without any risk of being “held to a single” as it is virtually no different mathematically from a blank.

So…what is our finding? In a close game, we’d prefer to have hammer in the 5th and 8th ends. We may in fact make decisions in the ends previous which will force this situation. For example, if we are tied playing the 4th with hammer and have an opportunity to blank, we are more inclined to take this route. If we are one up in the 4th or 7th, we should force our opponent into scoring, even at the risk of a deuce, in order to have hammer in following end. Eight end games become interesting because the advantage exists in the 3rd end. A team may even choose to tempt a blank if they are without hammer in the first end, to force their opponent to score in the second end, in order to have hammer in the third. This seems drastic and I’d suggest the advantage is not significant enough to “drop an end”. But further analysis might disprove my initial thinking.

Some readers may have noticed that there are two ends between the 5th and 8th. This means, without a blank or a steal, if we have hammer in one of these ends, our opponent has hammer in the other end. For example, say having hammer in the 5th when one down results in a deuce. We are now one up. If our opponent is held to one and then we are held to one, we are now one up without in the 8th end. However, if our opponent ties us in the 6th and we instead manage a blank in the 7th, we are now tied in the 8th with hammer.

I would not suggest this analysis should be a factor in how a team begins play in and end. The modern game does not allow a team to force a blank end at will. However, as an end develops we may be more inclined to “bail out” of certain ends in order to better position us in ends where we have greater advantage with hammer in a close game.

End Game Strategy: BDO Quarterfinal – Howard versus Burtnyk

2009-01-17T01:51:00.000-07:00

There were several decisions made during the 6th and 7th ends of the 2009 BDO Quarterfinal between Glenn Howard and local favorite Kerry Burtnyk. This month I will attempt to breakdown some of the decisions and determine how math could be applied to each scenario or shot call to support or contradict the final decision.

The 6th End: Centre Guard
At this stage, the game is tied 4 -4 and Howard has the hammer. The 6th end is, per my definition, the beginning of the “End Game” (see November 2008 article). Statistics indicate that Burtnyk at the beginning of the 6th end (in an 8 end game) has a 35% chance to win. (Math whizzes may have already guessed Howard has a 65% chance).

Let’s begin by reviewing the probabilities that Burtnyk will win, based on various outcomes of the 6th end (percentage chance to win with two ends remaining):

With two ends remaining:
Tied without hammer (Howard blanks 6th) = 34%
Down one with hammer (Howard takes 1 in 6th) = 35%
Down two with hammer (Howard takes two in 6th) = 15%
Up one without hammer (Burtnyk steals in 6th) = 65%

The numbers indicate that holding Howard to a single, in the 6th end, is in fact not much different than a blank. This is NOT the case if Howard is forced to one in the 7th, the difference is 25% (if Howard maintains hammer) to 38% (if he is forced to one).

A steal, however, is a great advantage in the 6th (65%). In fact, it is the most mathematically advantageous point in the game in which to be up one without. At all other times, chances are 61% or less.

Let’s ask a few questions:
Should Burtnyk play a centre guard or place the first stone in the four-foot?

In the game, Garth Smith placed the first stone in front of the rings. I would suggest this is the incorrect call…and here is why…

If Burtnyk places the first rock in the rings, should Howard play for a blank or attempt to score a deuce?

Howard now has to determine if he will play a corner guard, using hammer aggressively in an attempt to score two (or more) or instead play out a blank. We’ve seen above a blank is identical to a single point. In fact, if Howard plays out for a blank and noses his final stone, there is statistically no difference!

There are few skips at this level that would not prefer to force the issue while they have hammer with 3 ends remaining. The key reason: a deuce results in a high probability of winning. Two up without hammer during the End Game is as follows:

Two Up without hammer wins:
1 End remaining = 90%
2 Ends remaining = 85%
3 Ends remaining = 80%
4 Ends = 80%
All earlier ends = 74-75%

Howard’s only reason to wait to the next end is for a 5% advantage – IF he is able to score a deuce. Is the difference of 85 to 90% enough to make up for the risk of sacrificing an end with hammer? I don’t believe it is, and here is why. Recall my article from Dec 2008 describing a game as Close or one team being in Control or Dominant. A deuce in the 6th or 7th end results in a Dominant position for Howard.

For those who understand how chip values change in a Poker tournament, a similar analysis can be used here. In a poker tournament, as you collect chips, each additional chip’s “value” is less than those previously acquired. For those interested in understanding this better, read David Sklansky’s “Tournament Poker for Advanced Players”.

Each percentage point in probability of winning becomes less important, the higher your chances are. The difference between having a 50% chance versus 55% is more important that 85% to 90%. Another way to examine this is the advantage in the first scenario is 10% better, but in the latter it is only 5.8%. Some readers may also note the contrary is true. A team that is behind sees a greater benefit from small percentage changes. The advantage of a 15% chance over a 10% probability is 50% better!

If Howard blanks the 6th and either team scores one in the 7th, the game remains “Close”. He has essentially given up an opportunity to take a Dominant position; with very little risk of Burtnyk taking it at this stage (unlikely Kerry will steal two).

Also, recall that being forced to 1 is fine in the 6th but not the desired outcome in the 7th. Howard should be more inclined to be aggressive in 6 where a single is more advantageous, whereas in the 7th he would then much prefer a blank to being forced to a single point.

So….
Given that Howard would statistically prefer not to blank and Burtnyk is statistically indifferent, Kerry should place the rock in the four-foot. If Howard chooses not to play a corner guard, by not making the correct play he is giving some (however slight) advantage to Kerry. The outcome for Burtnyk is good positioning for a possible steal and reduced chance for a deuce or worse.

However…
All of this analysis does imply that a team prefers to place a stone and then place a guard (after the corner) – rather than having your opponent draw to the four-foot and then corner freezing to their stone (eliminating the placement of a corner guard). Burtnyk may prefer not to have a corner in play and prefers positioning stones to the middle of the rings, even if Howard initially has shot rock. I’d be very interested in the perspective of that discussion.

The 6th End: Walchuk’s last shot
Burtnyk sits top eight (biting four-foot) and Howard sits to the side, biting the four, guarded by two of Kerry’s stones. Despite repeated rewinding on my Tivo, I could not determine who was shot. Howard also sits third and fourth.

Kerry called for a double run-back by Walchuk. He suggested it was either that or play the guard. The result was removal of the Howard stone and sitting two, but both guards were removed and Howard remained with 3rd and 4th shot. This call appeared to be conservative, attempting to lower the chance at 2 or 3 and increase the chances to force Howard to 1. A steal seemed very unlikely at that stage. It appeared a deuce was probable, but Richard missed his next shot. It is my opinion that, given the difficult position if Burtnyk gives up a deuce (15%), keeping the guards and pursuing a more aggressive strategy, with a higher chance at a steal would increase their chances to win. In either case, they were in a difficult spot. Making some very rough estimates of probable outcomes for both calls:

Double Run-back:
Howard take 1 = 60%
Howard take 2 = 30%
Blank = 10%

W = 28.6%

Guard
Howard take 1 = 50%
Howard take 2 = 40%
Burtnyk steal 1 = 10%

W = 30%

These estimates are highly debatable, given the number of rocks remaining. However, on the basis that a three or two has little difference at this stage (see my comments above regarding Dominant position). Kerry should be trying to avoid a deuce at all costs while also trying to steal (not an easy task). It is my opinion (perhaps not his or others) that removing the two guards greatly reduces a chance to steal and may in fact increase the chance for an easy deuce.

6th End, Burtnyk’s last rock
Kerry had an option to either draw around the centre guard and attempt a steal or remove the Howard stone and possibly roll behind cover and force Howard to a single. This is an interesting scenario. Per above, a steal is a significant advantage, but a deuce is also a huge risk at this stage of the game. A single by Howard or blank has virtually no difference mathematically. In fact, it was statistically irrelevant for Burtnyk to spend extra effort in attempting to roll their rock behind cover – either outcome produces the same mathematic result. Kerry might, however, determine an advantage to be either one down or tied. Also the added chance Glenn might miss his draw for one (however remote) could be considered a slight advantage in this situation. I want to stress that the mathematic analysis does not take into account other factors, ice conditions, opponent, etc, which Kerry may have considered.

Mathematically, how often would Kerry have to make a perfect draw for the steal attempt to be the correct call?

W = x(.65) + y(.35) + z(.15)

Where
x = chance of a steal
y = chance Howard takes one
z = chance Howard scores two

We know Burtnyk’s hit results in a likelihood of 35%, set W = .35

.35 = x(.65) + y(.35) + z(.15)

Let’s choose a value for y and solve for x.

We estimate y = .3. That is, Howard will score one 30% of the time

Z = 1 – (x + y) = .7 – x

.35 = x(.65) + .3(.35) + (.7-x)(.15)

X = 28%

Conclusion, if Burtnyk believes Howard will likely take one 30% of the time, he needs to be successful with a steal > 28% in order to attempt the draw. If he actually believes Howard may only score a single half the time, it drops to 20%. If instead you assume no single and either a steal or a deuce, he must be successful stealing > 40%. Ultimately there are many factors, amount of curl and length of guard being most critical.

I found it interesting that, debating whether or not to attempt a steal is an unclear decision. Meanwhile, the very capable commentating team of Mike and Joan (ranking above their TSN counterparts, in my humble opinion) were instead focused on Burtnyk possibly drawing to the back or playing a roll in order to force Howard to one. As we’ve pointed out above, this decision has no statistical impact!

6th End – Howard’s Last Rock
On Howard’s final stone, assuming Burtnyk’s rock was easily accessibly, should he draw for one or blank the end? As we’ve stated above, mathematically there is no difference. Ice conditions, your opponent and other factors would likely come into play.

I would be tempted to blank, but the decision is not as clear as some might suspect. Many teams could choose to draw for one and they may very well be correct. If your team can hit well and possibly clear the mess your opponent is likely to create in the 7th end, increasing potential for a blank in the 7th, blanking the 6th end might be your preference. If your team prefers aggression and is more comfortable forcing the issue without hammer, by all means take 1 in the 6th and attack in 7. Also, you may asses your opponent is stronger with hammer and would prefer to keep it. Or the opposite may be true, and their ability to set-up an end without hammer may be something you wish to avoid.

7th End – Playing the Blank with 7 rocks to go
In the 7th end, Burtnyk was faced with another interesting decision. One down with hammer and a corner guard. No other rocks in play. Third’s first stone. Rather than attempt a deuce (and risk being held to one or surrender a steal) they chose to peel and play for a blank.

Blank results in Burtnyk being one down with hammer and one end remaining.

W = 38%

How often would Burtnyk need to score a deuce in order to attempt a draw, rather than blank?

Let’s assume that if they attempt a draw around the corner, a steal or blank will not occur. Either Burtnyk is forced to a single or he scored a deuce.

x = Burtnyk takes 1
y = Burtnyk takes 2

.38 = x(.26) + y(.62)

x = 1 – y

.38 = (1-y)(.26) + (y)(.62)

y = 35%

Burtnyk will have to score a deuce greater than 35% of the time for the draw (rather than peel) to be correct. Some of our recent analysis indicates that top teams in fact win slightly more than 74% when tied in the final end. Combine this with some small chance of a steal, Burtnyk would need even greater confidence in his chances to score two.

Whew! That’s it for this month. Congrats and good wishes to Team Pahl (Alberta) and Team Lobel (Ontario) in qualifying for their respective provincials. And good luck to all readers of Curl with Math, whether you are chasing your first or fourteenth Purple Heart.

Statistics for Womens’ Curling and What is “Control”?

2008-11-17T01:58:00.000-07:00

We’ve finally gathered data for Women’s Curling events. This data is taken from 4-rock games played during Provincial, Scotties (i.e. Canadian National Championship), World Championships, Olympic Trials, Olympics and WCT events over the last several years. Unfortunately our sample size is larger (more than double) for the men’s events. However, we have enough numbers to give some indication of general trends and comparisons with the games of their opposite sex counterparts. So what do we find?

Tied with Hammer

Within 1-2% of the men until the End Game (last 3 ends). During final ends, winning chances for women are 60, 61 and then 69% in the final end vs. 65, 66 and 75% for men.

1 Down with Hammer
Of all the scenarios, this is most similar to men’s numbers. Usually only 1-2% better chance for women to overcome the deficit of 1 down with hammer to win. Final three ends have same pattern: women’s is 39% to 37% to 39% (38, 35 and then 38% for men).

2 Down with Hammer
Women’s teams are again 1-2% more likely to win in this position except for the final end where data shows a 14.5% chance for a women’s team versus 10% chance for a men’s.

3 Down with Hammer
A 2-4% better chance for women’s team throughout the game.

Down 4 or more with hammer
Shows generally 2-4% increase in chance for women’s team.

1 Up with Hammer
A 2-3% better chance of holding this lead for men’s teams than for women’s.

2 Up with Hammer
Within 2-3 % early on but actually men’s teams hold on to win 4-6% more often from the Middle Game onward, with the exception of the final end where the difference is only 2%

3 Up or more with Hammer
Within 2-3 % early on but actually men’s teams hold on to win 4-6% more often during the Middle Game. The results from the End Game (final 3 ends) are nearly the same – you win nearly every time if you are in this spot.

What does this tell us about Women’s Curling?

Women’s teams tend to have a higher chance of coming back from a deficit and, subsequently, less chance of holding onto a lead. The difference is less noticeable in close games (tied or 1 up) and tends to widen as one team takes a more dominant position. That is, the greater the lead the greater the difference versus men’s teams in likelihood of a comeback. If we believe the ability to throw heavy peel weight successfully is the major difference in women’s and men’s games, then these numbers look much like what we would expect.

The most noticeable and important difference seen is the case of tied with hammer or down two with hammer in the final ends. The difference is about 5%. These numbers provide some support to determine how women’s teams might approach the game differently than men’s teams. For example, if tied with hammer with 3 or 2 ends remaining, a women’s team may be less inclined in blanking to retain hammer than in forcing a score. Tied with hammer is, during these ends, not a statistical advantage over 1 up without. In fact, with 2 ends remaining, women’s teams have a slight (2%) statistical edge in being 1 up without hammer! In the men’s game tied with hammer is an advantage of 3-4% with 3 ends remaining and 1% with 2 remaining.

What is Control?
A common term heard over drinks at curling rinks across the globe is “Control”. “If we make this shot for two that will put us in control”. “You had control from the 5th end on”. And, the most hated phrase “We had control the whole game and lost it at the end”. So, statistically speaking, what do we think is meant by “Control”?

I propose that there are actually three positions during a game a team can be in. If one is Control it follows that there must be another type of game that is closer than this, which I will call a “Close” game. It also then is reasonable to suggest there is a position where you are even better than in control, let’s call this “Dominant” position.

If we assign the game condition based on a probable outcome:

Close occurs when the odds for a win is no greater than 66% for either team. Another way to say this is the team behind has better than 2-1 odds of winning.

Control exists when one team has greater than 66% but less than 80% odds of winning. This range is between 2-1 odds and 4-1 odds for the team that is behind.

Dominant position is when one team holds a greater than 80% statistical chance of winning. Another way to show this is greater than 4-1 odds of a comeback.

Based on these numbers:
“Control” occurs when team is:
Tied with hammer in the final two ends or extra end.
Up 2 without hammer anytime before two ends remain.
Up 1 with hammer anytime before the final four ends

With three and four ends remaining, 2 up without hammer is right at 79 and 80% respectively. With two or fewer ends left, you are Dominant in this position. When statistically in “Control” Up 1 with hammer, you are between 77 to 80%, with the exception of the third end in a ten end game where your chances are 75%.

“Close” position occurs when a team is:
Down 1 with hammer
Tied with hammer anytime before the final two ends
When tied with hammer and 2 ends remaining, chance of winning is exactly 66% - so we could argue whether a team has Control at this stage or it is Close.

“Dominant” position occurs at any other score during the game.
We can start to analyze our pre-game and in-game strategy using the definitions of Control, Close and Dominant. I’d also suggest incorporating the definitions for which section of the game, based on Early, Middle and End Game (from article of Nov 2008, “Is Curling a Battle For Hammer?”). Recall the End Game is the final 3 ends and extra end if required. The Middle Game is the middle 3 ends and the Early game is then either 4 ends for a 10 end game or 2 ends for an 8 end match.

Using this model creates the following 9 game scenarios:
Early-Close
Early-Control
Early-Dominant
Middle-Close
Middle-Control
Middle-Dominant
End-Close
End-Control
End-Dominant

I’d suggest teams could use this model as a way to develop pre-game strategies for how to approach each of these positions. I might even tack a stab at examining these, but that will have to be left for another article…

Statistics for Grand Slams
Watching the Masters a short while ago (except the semi’s which were on the BOLD network –wherever that is), I started to question the statistical basis we are using and see if there are some discrepancies for the Slam events versus the entire dataset for all WCT (including Slams), Olympics, Olympic Trials, Brier, Worlds and Provincials. Our data size is still very small but I wanted to get a general sense if we saw any differences. Tied with hammer in final or extra end is currently nearly 80% for Slams versus 75%. 1 down with hammer in 9 was 39%, close to our baseline of 38%. Down two with hammer was about 12% versus 10%. The only major difference appears to be tied with hammer. The Slams numbers are based on sample size of about 270, compared to over 3000 in our full dataset. Assuming that Grand Slam teams are generally stronger than the other fields; does this mean better teams win more than 75% when tied with hammer? Possibly yes, but difficult to say for certain without a larger sample.

If Martin played Howard a single end game 20,000 times, each team having hammer for 10,000, what do you think the percentages would look like?

Is Curling a Battle for the Hammer?

2008-10-26T02:03:00.000-06:00

Back during the era of the Grand Old Game; before push brooms, The Ryan Express and Shorty Jenkins ice moved us all to Free-Guard Zone; it was often heard at most every club by players at every level (of play and inebriation) that “Curling is a battle for the hammer”. To some degree this may have been true, though the strategies of teams like Savage and Werenich, Burtnyk and Olson and the Howard brothers opposed this mentality with their aggressive play. Rather than “Take 2 then Give 1”, these Superteams preferred to put constant pressure, take many and then steal until the opponent shook hands.

The question I raise is, in Today’s 4-rock game, is it still possible that Curling can be a Battle for Hammer? In my analysis, I will touch on several areas and provide some data which may help us find and answer.

The Hammer Advantage
Starting with hammer is an advantage. We know this because every time your team wins the toss, you don’t think too long about whether or not to choose stone colour. I expect some Ontario folks will shout out “I remember this one time so and so knew the rocks were bad and chose colour instead of hammer” – but I expect this is not a common occurrence.

The “draw to middle” or pre-selecting number of games in a round-robin where teams get hammer also indicates its importance.

We also have some data which tells us how often the team beginning with hammer wins. Unfortunately not all events keep proper track of who started the game with hammer and our sample size is not as large as we would like. One way to take a sample of data is looking at 10 end games that are tied after 2 ends (i.e. now an 8 end game). Our results show us a 61% winning percentage.

This doesn’t tell us much more than we already know, except to help us understand if 8-end games are fair. That is not, however, the purpose of this article (though we may return to this idea).

The Early Game
I believe Curling, sometimes called “Chess on Ice”, has an Early, Middle and an End Game (no pun intended, honest). End Game is the final 3 ends and extra end if required. The Middle Game is the middle 3 ends and the Early game is then either 4 ends for a 10 end game or 2 ends for an 8 end match. I haven’t chosen these game sections based on my best guess or what I’d like them to be, I’ve looked at the numbers and they reveal something very interesting:

The Odds of winning at the completion of each end during the Early game is nearly equal.

This is a fascinating discovery that not only explains why the Early Game doesn’t end until 6 ends remain in the game, but supports the theory that an 8 end game is competitively equal to a 10 end game. If you extrapolate the numbers, we might be even safe in assuming 12 ends or even 14 would also have the same outcome. The only benefit of a longer game (other than perhaps more beverage sales to the fans) is that the more ends played, the greater advantage a stronger team will have over a weaker team. The analysis behind that theory is not the purpose of this discussion, so back to where we were…

Middle Game
Odds of winning during the Middle Game start to trend in a specific direction.

End Game
Odds of winning in during the End Game trend steeply in one direction. The exception is 1 down with hammer, which drops then rises before the final end.

This graph best shows this trend:

Some comments:

Tied with hammer: Winning percentage is within 60-62% until 3 ends remain where it jumps more dramatically to 65%. That is, a tie game has nearly the same statistical outcome for all ends until the End Game is reached (starting the 6th or 8th).

1 down with hammer: Maintained around 42-43% until 5 ends remain, where drops to 39% in the Middle Game. It then rises back over 40% and during the End Game, 1 down winning percentage drops to 38%, then down below 35% and back above 38%. This phenomenon was discussed in the article “To go for two… or not? Masters of Curling final: Howard vs. Ferbey” from Black Book of Curling 2007-08.

Two down with hammer shows 27 to 26 % during Early Game than a drop below 25% beginning the Middle Game and a drastic drop to 20% with 4 ends remaining.

3 down with hammer: Stays around 15% until 6 ends remain then drop to 13%, then flat at 11 to 10% with another drastic drop beginning the End Game of below 7%.

1 up with hammer: Stays fairly constant, from 75% then leveling in the range of 77-80% until the End Game begins and it jumps to 84%.

The other scenarios are not as common, but do have some interesting results:

4 down with hammer: Transitions, oddly enough: 9-7-7-5-4-3-2-1-0%. Short answer – don’t be 4 down after the Early Game or you’re screwed.

2 up with hammer: 87-90% until we reach the final stage of the Middle Game (93%).

3 up with hammer: In an 8-end game, anytime you are in this position you shouldn’t lose. In a 10 end game – just get past the 3rd and it would take a monumental collapse to lose (though we’ve all been there once or twice).

Battle For Hammer?

To try to answer our original question, we need to define what is meant by “Battle for the Hammer”.

Let’s assume “Battle for Hammer” implies a team which starts with hammer wishes to keep it and the opposition is trying to gain that position (tied with hammer). The advantage of tied with hammer is only slight, roughly 60 to 40, until the End Game. Teams who win 60% of their games don’t often place high in the money and they certainly don’t win Briers or Olympic Gold. We don’t gain a substantial position until the final end, where we still lose 1 of every 4 games. By this definition, I’d suggest Curling is not a Battle for Hammer.

Now, if assume we this phrase to mean a battle to gain hammer with the lead, then it could be argued Curling is a Battle for Hammer. 1 up with hammer with 8 ends remaining is the same as tied with hammer at the end of the game (75%)! Having hammer with a lead of 2 or more points is very strong. It is preferred to 3 up without during every stage of a game, except for the final end where both positions are equal.

How Important is the Hammer?
So how do we begin to analyze the importance of last rock? At any time during a game we can determine its statistical value. We’ve determined that leading with hammer is a strong position, stronger than being further ahead without hammer. But by how much? Let’s compare tied and 1 up without, 1 up with and 2 up without, and 2 up with versus 3 up without.

Tied with hammer vs. 1 up without hammer
Often, in a tie game, when a team is forced to 1 we state the opposition has done their job and taken away control. However, stats show us that there is only a small difference between tied or 1 up without
During the Early Game the difference is about 2-3%. It jumps to 5% at the beginning of the 5th end, or Middle Game. Then ranges between 0-3% until the last end where it jumps to 12% advantage for tied with hammer.

1 up with hammer vs. 2 up without hammer
When 1 up with hammer you are stronger than 2 up without by 2-4% until 4 ends remain, where it reverses to 1% advantage when 2 up, then back to advantage of 4% to 2% then 0% for the final end.

2 up with hammer vs. 3 up without hammer
Again, up with hammer is slight advantage, usually only 1% with the exception of 7 or 4 ends remaining where it is 3-4%. In real terms, these two positions are essentially equal.

So, what does this mean?
There is clearly not a significant difference in each of these scenarios. In each case having hammer while up is a slight advantage, but usually only 2-4%. Therefore, I disagree with the theory that Curling is a Battle for Hammer. Take, for example, an 8-end game where you have hammer and are held to one in the first end. Instead of having a 60% winning percentage you drop to 58%. Your position is in fact not much different than where you were at the beginning of the game. Much more significant is to have a shot for one and instead give up a steal in the first end, going from 58% to 42%.

Interesting to point out that often when the team without hammer holds the opposition to one in the first end it is perceived they have “won” the end or done their job. In reality, they have only gained a 2% advantage from where they were. More correct perhaps to state they have successfully “avoided” the position of falling behind by two or more.

Next article I will be revealing data on the Women’s Game and also attempt to tackle the question of what is “Control”.

What strategy should I employ when one down with hammer in 9th end?

2008-01-17T09:13:00.000-07:00

One of the most difficult situations towards the end of a game is one down with hammer playing the next to last end (9th or 7th). Statistically, the lowest probability of winning when one down with hammer is in the next to last end (34.9%). In the last end or with two ends remaining it is over 38%. In fact, tied with hammer with two ends to play is 67.5%, only 2.4% higher than if you are one up without!

I have seen every type of play in this situation, from both teams keeping it clean to produce a blank (and a 5 minute end) to every rock in play. So, using mathematics, what is the correct strategy, or at the very least, how do we approach this scenario to be better prepared when it happens?

Recall statistical outcomes for the final end:

Expected Results (ER) in the final end:
Odds of winning if tied with hammer (x) = 74.5%
Odds of winning if one down with hammer (y) = 38.2%
Odds of winning if two down with hammer (z) = 11.0%

So how should we play the end to maximize our chances and overcome our unenviable position? Also, our opponent without hammer can dictate the early part of an end by placing guards, how does this impact our decisions?

Let’s start by examining the numbers. Clearly, the best scenario is to take three (or more). If we score three we have an 89% chance to win. The next best scenario is to score a deuce and have a 61.8% chance in the final end. If we play aggressive and are forced to one, however, we win only 25%. In fact, if the end results in a draw for two and we miss, only scoring one, our chances flip from 61.8% to 25% - a huge difference. A blank is better than scoring a single, leaving us at 38.2%, but still we can expect to lose more than half the time.

Let’s also examine the competition’s strategy. If they read my articles, they know the correct play in this situation is to force the action and attempt a steal or force or a single, at the risk of a deuce.

Let’s assume for now our opponent will place a centre guard.

Option 1:
First, let’s attempt to play a clean end with the expected outcome a blank. After the opposition places a centre guard, we choose to draw to the side. Our opponent will most likely hit our rock and stay in the rings. Assuming we exchange shots and no one rolls their shooter to center, we can remove the centre guard with the 6th rock of the end. If the opposition splits the rings (most likely) we then are playing out the end trying to make a double in order to blank. If we fail to make a double and our opponent does not roll out, we will be forced to a single point and left with a 25% chance of winning with one end to play.

This option appears to be a losing strategy. No chance for three and not likely two, so our only outcomes are less than 50%. Let’s estimate some outcomes based on this strategy:

Score Three = 0
Score Two = 5%
Score One = 30%
Blank = 60%
Steal = 5%

W = 34%

Option 2:
Let’s try a very aggressive strategy. Come around with our first rock, corner freeze if our opponent does also, and continue drawing or soft taps until an opportunity develops for a “big shot” at scoring multiple points. Let’s again make some rough estimates based on this strategy:

Score Three = 10%
Score Two = 30%
Score One = 40%
Blank = 0%
Steal = 20%

W = 40%

Even if we could successfully blank 100% of the time, we do better playing very aggressive.

These numbers are not completely fabricated; they are based on existing data. For example, as of this writing, during this season (2007/08); Howard, Ferbey and Martin score three 13% of the time across all ends played with hammer. Taking an average of three “average” WCT teams results in 8%. These numbers can be skewed due to the better teams (aka Howard, Ferbey and Martin) being ahead more often and their opponents need to take greater risks – often resulting in big ends during later stages in a game.

Option 3:
Let’s think of a third scenario. We come around the guard, buried in the top eight foot, possibly biting the four foot. Our opponent successfully corner freezes. We now have several options:

Corner freeze to the opponent stone
Draw to the side of the rings
Split the centre guard with a “tick”.

Shot Call 1 will lead us to the scenario in Option 2 above. What about the other two?

2. Draw to side of rings:
If we can sit second stone, our opponent has several options, depending on how all the stones are sitting. In most cases, we could expect he will attempt a hit on the open rock and try to roll to the centre, behind cover, to sit either first or second. If he is successful, we are back to Option 2 (Very Aggressive) above and we are likely behind in the end. We will need a big shot or mistake from our opponent, but the aggressive nature of the end now makes that more likely. If our opponent does not roll successfully, we can attempt a hit and roll. In either case, if we instead choose to remove the guard or run it back, a steal becomes less likely, however a chance for a single increases and a three is highly unlikely. We can expect the end will look more like Option 1 above, with our best outcome a blank or low probability of a deuce.

3. Split the centre guard:
This is the scenario which I don’t recall seeing in a game but appears powerful. If we can split the guard and create two corner guards, our opponent now is left with an unclear decision. Does he put a centre guard back, even though you’re shot stone? Does he peel a single corner, or attempt a double peel (if it is even possible). Does he run his stone onto yours, attempting to lie two? This last option seems the best scenario but, it will leave two guards, an open four foot, and most likely both rocks will not sit perfectly behind cover above the tee line. Even if they do, a corner-freeze is available and with two guards, one which is now yours and could be driven back later on, the advantage appears to be with you. If our opponent gets cautious and elects to peel the guards, we now have options to play for a blank (if we choose), place another guard or move rocks around in the house and attempt our deuce with minimal chance for a steal.

Ultimately, a team must determine which option maximizes a chance for two or three, limiting the times you get a single point AND minimizes a steal by your opponent. Not an easy answer. The difficulty is that a blank, which is preferred to a single, is not a high occurrence if you attempt to score two or three. This specific scenario, one down with hammer with two ends to go, is one of the most interesting in the game and possibly more intriguing than the final end.

What If Our Opponent draws into the rings?
Instead of a centre guard, our opponent puts his first rock in the rings. We can now place a corner guard or hit the rock in the rings. If we call for a guard, our opponent could now choose a centre guard. We then draw around and are back to scenario in Option 2 above, though we are behind in the end. If we hit the stone, we are playing for a blank which, in this case, is very likely. For the team without hammer, assuming we will place a corner guard, this appears to be a stronger play than above. The team with hammer now faces the corner freeze and could have more difficulty getting shot stone.

This decision stems more from a team’s strategy of preferring to sit shot or be positioned frozen to shot stone in order that a shot can be played later in the end. I can see advantages for both cases and will leave it up to the reader to determine what they prefer in this situation.

Conclusion:
Appears there is no clear answer to our original question. It is clear that attempting a blank is a less risky play but provides no upside and most likely results in us winning less than one in three times. Playing aggressive increases our chances, but also creates a complex end; producing many options for both teams and presenting opportunities to stay aggressive or bail out. For fans, it is clearly the most interesting scenario in a game and, for a skip, one that cannot be simply “played by the book”.

Curling Myths: How do we calculate the Truth?

2007-11-17T09:16:00.000-07:00

I was recently doing some research on available documents related to strategy for Curling. Needless to say, there is very little available. I discovered Russ Howard is writing a book and, given the lack of current information, I’m looking forward to seeing if it includes much strategic material. If anyone can point me to other papers, articles or other strategy books, please send a Private Message to milobloom at Curlingzone, or post a comment here.

I did come across a PDF document posted at a CCA website entitled 4rockstrat. In it, I read many of the common “traditional” ideas regarding basic curling strategy. The purpose of this article is to challenge some of its logic. I certainly hope the CCA plans on expanding their available material in future. It is clear the authors were trying, but the lack of detailed information is apparent. I will attempt to dispute a couple of the Myths this document supports and are commonly accepted by many curlers and fans.

Myth #1: Keep it simple in the early ends
Excerpted from 4rockstrat.pdf:

SHOT SELECTION OPTIONS

Early ends (1 to 3) Without Last Rock

Most teams will attempt to implement a defensive game plan during this segment of the game especially as it pertains to avoiding high risk finesse shots. Remember, you do not have to score (steal) in the early ends without last rock to ensure victory. It is more important to keep the score close as you build your team’s confidence while learning the ice and assessing the abilities of the opposition. A general objective is to limit the opposition to scoring a single point when you do not have last rock. Even a two-ender is acceptable.

Early Ends (1 to 3) - With Last Rock

Teams may be a little more aggressive in early ends when they have the advantage of last rock but generally speaking, still try to avoid risky situations that require the making of finesse shots. Last rock skips will also tend to play a defensive style of play as they build the confidence of their teammates while assessing the ability of the opposition and learning the ice. They will attempt to score their 2+ points to the side of the sheet but will not be overly concerned about scoring a single point, blanking the end or giving up a steal of one.

The author comments in both cases about building confidence of your team and evaluating ice conditions. In today’s game this is less significant than years past. Consistent ice surfaces throughout an event, practice ice and the skill level of top teams lead me to believe this is minimal. If you’re a skip and worried about your team adjusting, then you won’t be competing at the highest levels.

Let’s address “with hammer” situation first. Assume a steal of a single is the most likely outcome of a poor end. Why then, would a team play defensive, risking at worse being down one starting the second end? The correct strategy for a team with hammer in the first end should be the most aggressive play possible, perhaps more than in later ends. Reasons:

A deuce in the first end will result in a win 73% of the time (74% for an 8 end game). A three results in 85% chance and a four is 91%.

A steal leaves a 43% chance to win, being 1 down with hammer after first end.

A steal of two, though unlikely, still leaves a 27% chance to win and is no different (mathematically, perhaps not psychologically) than surrendering a deuce without last rock.

Combining the significant advantage a large score gives you, with the greater odds, because of the number of ends remaining, to come from behind if a steal occurs, leads me to suspect aggression is the correct approach. Let’s try to use math to prove our theory.

Let’s estimate some outcomes based on our strategy and calculate or win percentage:

Expected Results (ER) with 9(7) ends remaining:
Odds of winning if tied with hammer (x) = 60.3% (60.7%)
Odds of winning if one down with hammer (y) = 43% (42.7%)
Odds of winning if two down with hammer (z) = 27.1% (26%)
Odds of winning if three down with hammer (m) = 14.7% (15%)

Notice that an 8 end game (7 ends remaining) does not change the outcomes much at all, so we will disregard for now.

Option 1: Aggressive starting the game
Blank (b) = 0%
Take 1 (t) = 30%
Take 2 (u) = 30%
Take 3 (v) = 10%
Steal = (s) 30%

Win (W) = bx + t(1-y)+u(1-z)+v(1-m)+sy

W = 60%

Option 2: Conservative starting the game
Blank = 20%
Take 1 = 50%
Take 2 = 20%
Take 3 = 0%
Steal = 10%

W = 59%

A nearly identical outcome. If we expect our chance of allowing a steal in the first end less than 30%, when playing Aggressive, we increase our chances further. For example, in Option 1 (Aggressive) if s=.2 and t=.4 we now win 62%.

Given the early stages of a game, I suspect the differences in actual results between teams would be significant. For example, Kevin Martin will win higher than 60% if tied with hammer after 1 end and, I suspect, the lower teams on the WCT rankings would be the opposite. The more ends remaining, we would expect a greater discrepancy between teams. But as a comparison, the analysis shows us being conservative is not the correct strategy as believed, it is actually the same or slightly worse than being aggressive.

The outcome for 8 end games is, oddly enough, nearly identical.

Now, what about when we do not have last rock? This decision appears to be obvious by answering this simple question:

When tied without hammer, starting the 3rd end of a ten end game, what strategy would we use?

I expect nearly every team would choose to place a centre guard, and attempt to play for a steal. Mathematically, the 3rd end of a 10 end game is identical to the 1st end of an 8 end game. I’ll leave any further estimation to be done by the reader, as I am already convinced based on this fact alone. There is no doubt, risk of a deuce or three is high in the first end and puts us into a poor position. However, it doesn’t get any better as the game progresses and the more ends remaining to come back, the better our chances. A team without hammer should play the first end to steal or force opposition to one. In my opinion, the best way to achieve this is by aggressive play early (centre guard, draws to middle of house).

It is perhaps simplistic to say Aggressive vs. Conservative play. Commonly a team may move from one strategy to the other, and back, during a single end. However, the common misconception that supports conservative play in early ends does not appear correct.

Myth #2: A deuce early is not significant
In the CCA document, it is suggested that, when starting without hammer:

A general objective is to limit the opposition to scoring a single point when you do not have last rock. Even a two-ender is acceptable.

The author then goes on to suggest placing the first rock of the game in the four foot! Per Myth 1, this is not the approach I would recommend. So, is surrendering a deuce acceptable? From Myth 1, we now know down two after the first end puts us at a 26% or 27% chance of winning (based on 8 or 10 end game). This doesn’t sound acceptable to me. We may need to surrender a deuce because that is how the end develops, but we certainly should not play the end to make a deuce acceptable.

Let’s take a scenario where two rocks remain in the first end and we do not have last rock. Our team has missed a few shots and we are in trouble. Our opposition, holding hammer, lays two. One rock is open in the twelve foot; the other is partially buried in the top four foot. We can hit the open rock and surrender a deuce or try a corner freeze on shot rock to force the opposition to 1. What percentage do we need to succeed to make the draw the correct call? We’ll use the statistics from 8 end games for this analysis.

Hit
W (if down two) = z = 26%

Draw
Assumptions
The team with hammer either scores three or is held to one. The chance for a steal or deuce is considered negligible.

Variables
Successful draw (hold team to one) = d

W = dy + (1-d)m

Setting W to 26%

.26 = d(.43) + (1-d)(.26)

Solving for d = .395

We need to make the draw greater than 40% of the time for it to be correct call. Given skills of top skips, I would suggest the correct play is the draw and “accepting a deuce” is not the correct decision. Better to risk a three at the possibility of forcing opposition to a single.

Myth #3: Play conservative against a stronger team
It is a commonly held belief that when playing a team that is stronger than yours; play conservative, keep the game close and hope to win a close battle at the end. The U.S. team in the 2007 World Championship appeared to use this strategy to perfection against Team Canada during the round robin. I don't entirely agree with this approach and will attempt to explain why….in another article.

Blackbook of Curling 2007/08 - Reprints

2007-10-17T09:25:00.000-06:00

1.To go for two… or not? Masters of Curling final: Howard vs Ferbey
Ontario’s Glenn Howard squad had a spectacular Seasons of Champions run in 2006-07, going undefeated throughout the Ontario playdowns, and losing only a single round-robin game at the Tim Horton’s Brier and the Ford World Men’s Championship. Earlier in the season, they defeated Edmonton’s Randy Ferbey in the finals of The Masters, one of the four Grand Slam events. An intriguing situation occurred during that final, showing that even the best teams in the world are not always certain of the “correct” strategic decision… even when faced with a common scenario.

It is the sixth end of the new Grand Slam format – eight-end games – and there are only two ends remaining. Howard has the hammer, the teams are tied at 3-3 and Randy Ferbey, throwing third stones, has just placed his first stone behind a centre guard. It is hanging on the back side of the button. These are the only two rocks in play.

The first indication from Glenn is for third Richard Hart to throw his lefty out-turn (in-turn for a right hander) and draw to the face of the Ferbey stone, to possibly sit shot-stone. While sitting in the hack, Richard sees another option – a soft hit on the Ferbey stone situated out of the rings with his in-turn, and roll to the open.

After much debate, they agree to hit the Ferbey stone. The decision centers on whether the preference is to aggressively play for a deuce – at a risk of a steal or possible single point scored – or to play conservatively, to increase the possibility of a blank end, in order to keep last-rock advantage in the seventh end. The outcome, at this stage, is unimportant, the question is: what is the correct call?

The dilemma Team Howard faced is very common. With three ends remaining, tied with hammer, what position would I prefer to have going into the second-last end, and what risk should I take in order to get to that position? It is quite fascinating to note that at the highest levels of the sport, much of this decision is made on instinct or “situational analysis”… because, in fact, we can examine the decision using mathematics.

Let’s attempt to analyse the situation based on available statistics and mathematical in-game analysis. To examine the decision, we need to determine all the Expected Results (ER) and Variables (V) to be included and state which are being omitted. ERs are numbers, in percentages, taken from existing statistics. Variables are numbers, in percentages, which are estimated during a game situation. Variables are based on the chance of making a single shot or the expected outcome following a succession of shots during an end. The ERs, Vs and related assumptions I used are listed below. I have indicated in each case which letter is used to represent each ER or V.

Expected Results (ER) with 2 ends remaining:
Odds of winning if tied with hammer (x) = 68.3%
Odds of winning if one down with hammer (y) = 35.2%
Odds of winning if two down with hammer (z) = 14.8%
Odds of winning if three down with hammer (m) = 4.5%

These Expected Results are based on available statistics for four-rock FGZ games played in the Brier, European and World Championships, Grand Slams and other WCT events, Provincial Championships, Olympic Games and Olympic Trials. In using these statistics, we assume skill is relatively equal, conditions are similar and shotmaking ability is similar. These assumptions are clearly debatable, but we disregard any difference in skill level amongst specific teams or events.

Assumptions:
· If Howard attempts to draw a blank will not occur
· Howard will not score 3
· The most Ferbey will steal is a single point
· Richard Hart will not have a complete miss. He will either:
o Draw and place his stone in the rings (counting first or second)
o Hit and remove Ferbey stone or remove the guard
· Richard attempts a soft hit and will not roll his shooter out if he removes the Ferbey stone.

Option 1: Draw
With his opponent on the back of the button, a draw around the guard is clearly the aggressive play. Assuming Richard will not miss, two outcomes exist – Howard will sit one or Ferbey will sit one. For each outcome, we can assess the possible outcomes of the ends and assign probabilities to each:

Variables:
Howard sits shot stone:
Score two (a) = 30%
Score one (b) = 60%
Steal (c) = 10%

Howard sits second shot:
Score one = (d) 60%
Steal (e) = 40%
We assume Glenn Howard will have a similar chance at scoring one, regardless of the shot’s outcome. We also assume a deuce is not likely if Richard does not achieve shot-stone position. Both of these assumptions are, as always, debatable, but for our analysis we consider such possibilities negligible.

This appeared to be a difficult shot. Let’s assume Hart will achieve shot-stone position 50% of the time. He might argue this point, but we’ll save that for later analysis.

Win (W) = (.5)(a(1-z)+b(1-y)+cy) + (.5)(d(1-y)+ey))

W = 60.5%

Option 2: Hit and roll
Variables:
Howard sits shot:
Blank (a) = 75%
Score two (b) = 5%
Score one (c) = 15%
Steal (d) = 5%

Howard removes guard, Ferbey sits shot:
Blank (e) = 40%
Score one (f) = 40%
Steal (g) = 20%

We’ll assume Richard will remove the shot stone ¾ of the time (75%).

Win (W) = (.75)(ax + b(1-z) + cy + c(1-y)) + (.25)(ex + fy + g(1-y))

W = 61.6%

It would appear the correct call is the hit – but it is very close. If Howard believes Hart can achieve shot-stone position greater than 50% of the time, the draw would appear to be correct. If in Option 1, for example, Howard “gets shot” 60% W = 62% and at 75% W = 64.2%.

We are using many variables in this analysis (5 and 7 respectively), which can lead to greater variance in our final numbers. For example, with Option 1, if we set d=40% and e=60%, W drops from 60.5% to 57.5%. And because we are examining a situation in which several (in fact seven) rocks have yet to be thrown, this analysis becomes very difficult.

What is perhaps more important than the analysis of this specific situation is the common situation of a close game with two ends remaining. An interesting trend was uncovered when we started digging into available game statistics. Virtually every scenario (tied with hammer, two down without, three down without, one up with, etc.) shows a steady increase or decrease in probability of a Win as you near the final end. For example, tied with hammer reads as follows:

Your chance of winning with hammer increases from being 61% with five ends remaining to 75% in the last or extra end.

However, the scenario of one up without hammer is shown in the next table:

The results show a 3-4% difference both up and down, depending on end completed. The most interesting point we see is the increased chance of winning when one up with hammer with two ends remaining, versus three or one end remaining. 65% versus 62%. Now, commonly a team tied with three ends to play may risk a steal in an attempt to score two. The next table shows the outcome based on two down with hammer:

If the team with hammer in the eight end (or sixth of an eight-end game) scores the deuce, their opponent still has a 15% chance of winning and, surprisingly, statistics show a 4% chance when three down with two ends to play.

Yet another interesting indication is that two down with hammer is difficult. A team will win only 24% in this situation after playing the second end in an eight-end game. Useful for a future discussion on the danger of eight end games, but let’s digress…

Statistics would indicate a team with hammer should ensure a blank or score to be in control with two ends remaining, rather than risk a possible steal. Let’s choose variables which represent likely outcomes, based on our approach to strategy in the third-to-last end. For example, if we play aggressively, our chance of a blank is estimated to be 0% and a steal is 30%.

Aggressive starting the 8th (or 6th) end
Blank (b) = 0%
Take 1 (t) = 40%
Take 2 (u) = 25%
Take 3 (v) = 5%
Steal = (s) 30%

Win (W) = bx + t(1-y)+u(1-z)+v(1-m)+sy

W = 62.5%

Conservative starting the 8th (or 6th) end
Blank = 20%
Take 1 = 60%
Take 2 = 10%
Take 3 = 0%
Steal = 10%

W = 64.6

Based on my estimated variables, it appears the conservative approach, with three ends to play, is the preferred strategy. I’d be interested to see what percentages others might estimate for these variables. Once we have enough shot data collected, we may eventually be able to change these numbers from estimates to actual statistics.

Going back to our original game situation, Team Howard appeared to be unsure of their desired outcome for the end. If top teams use statistics to analyse both in game shots and late game situations, they can be better prepared to make these decisions while “on the clock”.

In case you don’t remember or didn’t see the outcome, Howard took one in the sixth, Ferbey took one in the seventh and Glenn made a great shot in the final end to win the game 5-4.

2. Go hard and go home 2007 Brier Final: Howard vs. Gushue
The most interesting – ie. debated – shot call of the 2006/07 curling season was that of Newfoundland’s Brad Gushue during the seventh end of the Brier final versus Glenn Howard. The Gushue team, despite missing the grizzled veteran of their gold medal win at the 2006 Olympics – Glenn’s brother Russ – were on the verge of adding a Canadian championship to their resume. After getting off to a rocky start at 1-3, the young foursome from the St. John’s Curling Club in Newfoundland had reeled off eight straight wins and was now in control, tied with the hammer, with four ends left to play. The critical seventh end came down to a decision of whether to attempt a difficult double-takeout for a possible score of three, or take a single point via the much easier shot of hitting the open stone belonging to the Howard team. The stakes were high as the Ontario team currently sat two, and any miss by Gushue could be disastrous. The reward of a three-shot lead and near certain victory, it seemed, was too great and the decision was made to play the double take-out. Ultimately, crashing on a guard led to a steal of two for Ontario and eventually a Brier and World Championship for the Howard team.

Mathematically, how do we analyse this situation, and what was the correct call?

Expected Results (ER) with 3 ends remaining:
1. Odds of winning if tied with hammer (x) = 64.6%
2. Odds of winning if one down with hammer (y) = 38.2%
3. Odds of winning if two down with hammer (z) = 19.8%
4. Odds of winning if 3 down with hammer (m) = 6.9%

Assumptions

Gushue will be successful 100% of the time if he chooses to hit the open stone. Newfoundland will always score 1 point.

Option 1: Hit the open stone:
No variables, assuming 100% success, results in:

Win = (W) = 1-y = 61.8%

Option 2: Double attempt:
Many outcomes appear possible with the double attempt. Choosing the variables and estimating each of them may not be easy. Let’s try to choose most likely outcomes:

Successful double and stay, Newfoundland scores three points (a)
Successful double but the third Gushue stone is removed from play and Newfoundland scores two points (b)
Double is missed; Newfoundland scores a single point (c)
Double is missed; Ontario steals a single point (d)
Double is missed; Ontario steals two points (e)

Win (W) = a(1-m) + b(1-z) + c(1-y) + dy + ez

Recalling the situation, the target stone belongs to Team Gushue. They are attempting to jam it onto a Howard stone (removing it), roll to another Howard stone (also removing it) and keep the shot stone, the target stone and a third Gushue rock at the back of the house all in the rings. In discussions following the game, opinions were varied. Many people believed the double for three may not have been possible, that Gushue at best could score two (possibly spinning the target stone out of play). The outcome made this evaluation more difficult. By wrecking on the front guard, fans were unable to see what would happen if Gushue were to hit the target stone. In future, technology may allow us to study the behaviour of stones and, by mapping location, use a computer to determine the outcome of a shot. This type of analysis is likely possible now… however, the work required would be significant and I am doubtful the various curling governing bodies, would approve. Can you imagine if Gushue were to call a time-out and have his coach, sitting in the stands with a computer, advise them the shot was not possible based on a software analysis?

We will attempt to assign some estimates to all the variables and determine a possible outcome.

Variables:
Newfoundland scores three points (a) = 10%
Newfoundland scores two points (b) = 20%
Newfoundland scores a single point (c) = 10%
Ontario steals a single point (d) = 50%
Ontario steals two points (e) = 10%

Win (W) = a(1-m) + b(1-z) + c(1-y) + dy + ez

W = 52.6%

If we believe missing the guard will result in no worse than a steal of one, this analysis gives us a good start. Unfortunately, it is well below the known Expected Result for Option 1, 61.8%.

Let’s keep a and e constant at 10% and build a table of possible estimates for further analysis:

Interesting results. For Estimate #3, if Gushue can score 80% of the time, even if he only scores a single point 50%, the call is nearly identical to Option 1. In Estimate #7, if we assume a score of one is not possible but Gushue will score half the time, the shot call will result in two or three points scored (40% and 10%) or a steal of one or two surrendered (40%, 10%) and Gushue wins 58.7%, below Option 1. However, increase the result of a deuce by 10% in Estimate #10 (steal of one becomes 30%) and we are above Option 1 at nearly 63%.

Two other likely extremes:

Set a, c and e to zero and assume outcome of either a deuce or a steal of one. If Gushue succeeds 60% of the time, W = 63.3%.
Set b, c, and e to zero and assume either a score of three or a steal of one. Gushue needs to be successful more than 43% of the time to make this the correct call.

The numbers might start to confuse us and the final decision, which at first appeared incorrect, now appears fairly close. The ultimate answer depends on your assessment of how rocks will collide and move around the house, and the ability of Brad Gushue to hit what appears to be a small target on his front stone.

In this scenario, we are less concerned with assessing Brad’s abilities. The final outcome, wrecking on the front guard, was unexpected and likely a low probability. If he attempted this shot repeatedly, under the same conditions, I suspect he would hit the target stone at least 9 times out of 10. What we are more interested in is our estimate of the action on the stones, and who will score what once the dust has cleared. Unfortunately, this will never be known. If someone set the stones up exactly as they were situated we could, perhaps, try to recreate the outcome. If one of our readers decides to attempt this experiment, or if you already have, please let us know. In all seriousness!

Bringing some additional “non-math” analysis into the equation, if you will, is the consideration for the enormity of the moment, and the event. It is the Brier final and the position of being one up without hammer with three ends to play is, while positive, still only 62% headed to victory. Brad was no doubt drawn to visions of three points and a virtual lock on the Brier title (93% in fact). Even with a deuce the Newfoundland rink would be heading to the world championship 80% of the time. Looking back at all of our estimates, we still have Newfoundland winning greater than 50% of the time this shot is attempted. Perhaps it is worth the attempt at the big shot now – in the fourth-to-last end – when the opportunity presents itself, and take pressure off your team in the later ends of a tight game.

Just as in golf, some curlers choose to “grip-it-and-rip it” with an aggressive style, whereas others are tacticians who plod about the course and minimize both risks and mistakes. Personally, I trust the mathematics and believe the shot call Gushue attempted was indeed too risky. Specifically due to doubts about the shot being make-able for three; not because his ability is in question. One point for Howard or Gushue appeared the most likely outcome, with some possibility of a deuce (no better than estimate #2 in table above). It is, unquestionably, up to the skip to come to a final decision. As always, if you use math, it might make the decision clearer.

3. Hitting the post Canadian Olympic Trials semi-final: Morris vs. Stoughton
The use of mathematics to analyse game situations is useful in the later stages of a game and also for critical shot calls during the early ends. The John Morris call during the semi-finals of the 2005 Canadian Olympic Trials is a prime example of an early game decision that proved costly.

After stealing a single in the second end, the Jeff Stoughton team had scored a deuce in the third end to go one up without the hammer. Morris then found himself in deep trouble, facing three Stoughton counters and several guards. The two apparent options available for the Calgarians were to either a draw to force Stoughton to a steal of one point, or attempt a difficult hit between two guards and remove shot stone to count a single.

The port appeared small, but Morris was certain he could thread the needle and succeed in putting the score back to even. The shot wrecked on the front guards and Stoughton was handed a critical steal of three points. Despite a valiant comeback attempt throughout the remaining ends, Stoughton prevailed and advanced to the final, where his Winnipeg foursome eventually lost to Brad Gushue in the finals.

What mathematics can help us determine is: how certain did Morris have to be that he could make the called shot in order for it to be the correct decision?

If John makes the shot 100% of the time, it is the best call. He would much rather be tied without hammer than down two. Using available statistics, we can determine how assured he must be in order for the shot to be the correct decision.

Expected Results (ER) with 6 ends remaining:

1. Odds of winning if tied with hammer (x) = 61.8%
2. Odds of winning if one down with hammer (y) = 42.7%
3. Odds of winning if two down with hammer (z) = 24.3%
4. Odds of winning if 3 down with hammer (m) = 12.7%
5. Odds of winning if 4 down with hammer (n) = 5.4%

Assumptions

The draw is successful 100% of the time. Stoughton will always be held to a single point. The chance of John being unable to draw the full eight-foot rings is considered negligible.
The hit either results in a single for Morris or a steal of three for Stoughton. The chance of rolling out is negligible.

Draw:

No variables to examine, we assume 100% success. This results in:

Win (W) = z = 24.3%

Hit:

We will choose S as the single variable, indicating a successful shot by Morris.

W = S(1-x) + (1-S)n

Setting W to the result for a draw, .243…

.243 = S(1-x) + (1-S)n

We now solve for S

S = .577

The math shows us that if Morris expects to make his shot through the port more than 58% of the time, it is the correct call.

What at first appeared to be a foolish call now looks like a reasonable decision, based on statistical analysis. You are welcome to debate the shot call, and outcome, but the ultimate decision rests with John Morris himself, to assess if he can make the shot more than six times in ten attempts.

John may have felt his chances were much higher; others would counter it was lower, but the numbers tell us how he can best make the final decision.

Given an assessment of the Stoughton team and their abilities, Morris may determine that coming back from two down will be more difficult than 24.3%. Also, a draw is never 100% certain, therefore he may be more inclined to attempt the hit, even if his chances are as little as 50%.

Howard versus Stoughton in 2007 Brier: The 9th End

2007-03-19T01:17:00.000-06:00

With all due respect to Linda Moore and Ray Turnbull, the recent game of Howard versus Stoughton during the round robin game of the 2007 Tim Horton’s Brier showed how even some of the most knowledgeable don’t understand statistics as it relates to curling.

Howard is one up without hammer in 9th end. Two rocks remain. There is a corner guard and a Stoughton rock on the opposite side of the sheet in the back twelve foot. Richard Hart, the Ontario third, and Glen Howard discuss the options. Glen prefers a freeze to the back stone, but eventually Richard convinces him to play a draw around the corner guard. Rich’s argument is their uncertainty of the ice on the freeze attempt – Glen’s concern is the amount of curl he will get with his come-around attempt.

Linda’s comments were something to the effect “Howard wants Stoughton to score here and prefers giving up a deuce to a blank”. Perhaps Linda did not properly express what she meant or in fact, does not recognize the real numbers.

Howard would, mathematically, prefer a blank over Stoughton’s deuce. If, as the announcers stated, Howard preferred a deuce to a blank – why didn’t Stoughton take out his own rock rather than draw for two?

Recall the statistics:

Expected Results in the 10th end
Odds of winning if tied with hammer (x) = 75.7%
Odds of winning if one down with hammer (y) = 39.5%
Odds of winning if two down with hammer (z) = 11.7%

If Howard is one up, he should win about 60% and if he’s one down with hammer he will win 40%. It is clear that a blank is preferred to surrendering a deuce.

Then why, might you ask, does he not hit the Stoughton stone out?

What the TSN crew perhaps meant to say, or misunderstood, is:

Howard is willing to risk a deuce by Manitoba because the chance that he may either steal or force Stoughton to one increases his chance to win.

If Howard steals, he wins 88% of the time. If Stoughton is forced to one, he wins 75%. The chance that one of these outcomes may happen, overcomes the difference between 60 and 40 for one down versus one up.

Let’s examine the Ontario decision and also determine if Richard or Glen had the correct call.

From my previous article, “One up in Nine without Hammer” if we expect to give up a deuce roughly less than half the time, we should draw around the guard. I assume we all agree Glen can be expected to make a successful draw (where Stoughton cannot score two) more often than 50%. I’d suspect it’s as high as 80%, but he was unsure of the ice and considered the freeze instead. Because a steal is less likely (corner guard instead of centre guard) – it’s likely higher, say even 60% (see previous article for more precise numbers).

Referring to the article “Aggressive Play in 9th end”, where no guard was available, I roughly determine that Howard needs to make either a freeze or “near-freeze” and avoid a deuce at least 80% of the time.

Based on these numbers, our rough estimate to attempt a come-around is the correct shot.

Let’s examine a little closer…

Hit:
Assuming Stoughton will blank 95% of the time Howard attempts a hit, we know from previous articles:

W = 61%

Come-around:
Assume a steal will not occur.
a = Stoughton takes one point = 75%
b = Stoughton scores two points = 25%

W = ax + by

= 67%

Freeze
Assume a steal will not occur.
a = Stoughton takes one point = 50%
b = Stoughton scores two points = 25%
c = Stoughton blanks = 25%

W = ax + by + c(1-y)

= 63%

This shows us mathematically that Richard’s call is correct. If you include the slight chance at a steal, we could also expect it more likely with the come-around than the freeze.

A few observations:
Blank is not likely with the come-around. A freeze attempt makes a blank very possible.

A deuce is, perhaps in Glen’s opinion, more likely to occur with a missed come-around. Though I’ve used 25% in both calculations for a deuce, Howard may determine he is more likely to give up the deuce on a come-around and would prefer the freeze in order to add the possibility of a blank.

Ice conditions – Glen was not comfortable with the ice and with the shot and that can have an impact (though not mathematical). In hindsight, appears to be the case, Glen put his draw through the rings.

Assuming acceptable ice conditions, I would play the come around every time. What would you do?

Extra-end
Why do some players and possibly announcers believe it is preferable to be one down with hammer?

Statistics show that one up without wins roughly 60% of the time. Why would skips choose to be one down with hammer instead? I have two theories:

They don’t know it’s 60%…and more importantly

They want the last rock.

Top skips believe last rock puts the outcome in their hands. What they fail to realize, I suspect, is that very often the end results in no opportunity at two and, sometimes, a very difficult shot for one in order to force an extra end. In the example above, Howard needed to make a double on his last shot to score one and had no realistic chance at two as the end developed.

My belief is the preferred position is actually one up without hammer in the 9th end.

Four rock free-guard zone allows the team without hammer to force the play. The risk of a three exists, but I suspect the opportunity to steal or force your opponent to a single, and greatly increase your chance to win, is much higher. You are able to aggressively play the end with the risk of giving up a deuce and still having a 40% chance to win in 10.

We have not yet derived the statistics to analyse 9th end results, but once we do I will be examining the numbers to determine if they support or dispute my theory.

Ferbey vs Dacey Brier Final - Part 2

2007-02-19T01:25:00.000-07:00

This article continues the discussion from “Curling with Math”, included in the 2006/2007 Black Book of Curling, available from Curlingzone at www.blackbookofcurling.com. Also reprinted in Dec 2006 article.

Let’s start by repeating the background from that article:

It’s the 2005 Brier Final. Ferbey, appearing in the final game for a 5th straight year, is facing what appears to be a simple decision. It is the 9th end, and the game is tied. A miss by the opposing skip, Shawn Adams of Nova Scotia, has left the Alberta rink lying one with no other rocks in play. It is commonly accepted curling strategy to play for two (or more) when you have the hammer and hold your opponent to one (or steal) without last rock. In this case, Ferbey would be expected to draw to the open side of the rings and likely have a final shot at two or perhaps three if Adams attempts a freeze and makes a poor shot. David Nedohin, who throws the final rocks for the Ferbey team, discusses the options with Randy. Much to the surprise of fans and commentators, they decide to remove their own stone and play out the end for a blank in order to keep the hammer in the 10th end. The final outcome eliminated any need for second guessing the decision, as Ferbey won - David making a draw to the open four foot in the 10th end for the victory.

Specifically we used math and statistics to analyse the decision by Ferbey to attempt a blank end in 9 in order to secure last rock coming home. An assumption made from that article was that Adams will always attempt to freeze to the Alberta stone, if Ferbey chooses to draw and lie two.

Our intention in this article is to:
1. Determine the correct choice for Adam’s shot, if Ferbey attempts a multiple score.
2. Re-examine the Ferbey decision based on a weighting factor of Adam’s decision.

First, we need to determine all the Expected Results (ER) and Variables (V) to be included and state which are being omitted. ERs are numbers, in percentages, taken from existing statistics. Variables are numbers, in percentages, which are estimated during a game situation. Variables are based on the chance of making a single shot or the expected outcome following a succession of shots during an end. The ERs, Vs and related assumptions I used are listed below. I have indicated in each case which letter is used to represent each ER or V.

Expected Results in the 10th end
Odds of winning if tied with hammer (x) = 75.7%
Odds of winning if one down with hammer (y) = 39.5%
Odds of winning if two down with hammer (z) = 11.7%
Odds of winning if 3 down with hammer (m) = 0.4%

These Expected Results are based on available statistics for 4-rock games played in the Brier, European and World Championships, Grand Slam and other WCT events, Provincial Championships, Olympics and Olympic Trials. In using these statistics, we assume skill is relatively equal, conditions are similar and shot making ability is similar.

Situation 1. Adams Decision
Game Situation Assumptions:

Alberta chooses to draw and lie two. Nedohin’s first stone lands on the tee-line in the eight foot, higher than shot stone, leaving a possible freeze, double or hit and roll.
If Adams attempts a hit, he will not miss both rocks. Alberta cannot score greater than two.
When going for two in 9th, it is assumed that at worse Alberta will take 1. Odds of a steal for Nova Scotia are considered negligible.
If we miss the double, Alberta will always score two. The chance they will miss is considered negligible.

Expected Results:

x = Odds of winning tied with hammer = .757

y = Odds of winning if one down with hammer = .395

z = Odds of winning if two down with hammer = .117

m = Odds of winning if three down with hammer = .004

Variables:

a = Odds of forcing Alberta to 1 with a freeze = .75

b = Odds of Alberta scoring 2 = .2

c = Odds of Alberta scoring 3 = .05

d = Odds of double = .75

These numbers are estimates based on evaluation of where the rocks may have been positioned. We have assumed Ferbey places the second stone on the tee-line, higher than shot stone, making a double possible. Specific location will impact our estimate of the ability to make a specific shot. If we evaluate our chances of making a double the same as the freeze (75%):

Freeze

W = ay + bz + cm = 32%

Double

W = d(1-x) + (1-d)z = 21%

Based on the analysis, the freeze is the correct call. If we are 100% sure of making a double, we are still only 24% likely to win. If we estimate our chance of the freeze as 50%, W= 24.5% and the decision is much closer if the double is 100%

Situation 2: Weighing the options

In the Ferbey decision, we assumed that Nova Scotia will always attempt a freeze. Now that we have analysed their options, let’s use a weighting factor to determine and re-examine Alberta’s options.

We are Alberta, faced with an option to blank or attempt a multiple score in the 9th end. If we expect to make a perfect shot 50% of the time and leave little option for a hit and roll, then Adam’s will have no choice but to choose a freeze. But, perhaps 50% of the time our shot leaves an easy double. Let’s estimate that when this happens, 10% of the time Adam’s will freeze, 40% attempt a double.

If Alberta also estimates Adams is successful 75% of the time with his freeze, we score a deuce 20% and three points 5%, resulting in a win percentage of 68%. Using results from Situation 1 above:

W = .5(.68) + .1(.68) + .4(.79) = .72%

What is very clear is our desire for Adams to choose to hit. This increases our statistical probability of winning. What also comes into mind is the possibility of enticing Nova Scotia to attempt the double, by intentionally placing the rock in a better position for them to choose this option.

This leads us into another application of statistical analysis, where we choose shots which may appear to be the incorrect call, but in fact are intended to lead the opposition into choosing an incorrect shot call in order to increase our chance of winning. For now I will leave it to the reader to ponder similar examples.

Extra-End: Martin vs. Koe - Provincial Finals

There were very dramatic events in the recent final game to determine Alberta’s 2007 Men’s Provincial Champions. Kevin Martin took the game in heart wrenching fashion when Blake MacDonald, skip for the Koe rink, missed a draw in 10 and another in the extra end to hand him the title.

An interesting moment is Martin’s decision in the 9th end. Kevin was down 2 with hammer, 7-5, and Koe had a single rock in the twelve foot. With their last stone, the Martin team opted to draw for a single point rather than blank and keep the hammer in the 10th. Feedback I’ve read on Curlingzone forums is that Martin felt taking two on the rather straight ice would be more difficult than stealing a single. What is the math in this situation?

Expected Results:

Odds of winning if two down with hammer = .117

Odds of winning if one down without hammer = .103

The mathematical difference is very small, less than 1.5%. This makes 2 down with or 1 down without as nearly a coin-flip decision. In this case, Martin weighed in the impact of ice conditions and determined a steal was more likely. The numbers indicate that when this situation occurs, a team should not quickly assume a blank the correct call.

Aggressive play in 9th End

2007-01-19T01:25:00.000-07:00

Here’s a scenario that was described to me by a friend of mine.

One down playing the ninth end and our hero, throwing Red stones, has the hammer. His opponent is throwing his final stone, Blue. There are no rocks in play except for one Red stone at the back of the eight foot. The Blue skip is about to throw his last rock. We would expect him to hit and stick, hoping our hero noses for one or, at worse, blanks and remains one down coming home.

Instead, the Blue skip chooses to attempt a freeze. This shot call appears to conflict with common curling strategy, but, using math, what is our analysis of this play?

Expected Results in the 10th end
Odds of winning if tied with hammer (x) = 75.7%
Odds of winning if one down with hammer (y) = 39.5%
Odds of winning if two down with hammer (z) = 11.7%

Option 1: Hit
Let’s assume the odds of Blue missing the hit as negligible. Either he rolls out and a blank is assured or, Red rolls out most of the time for a blank. To simplify, let’s state the odds of a blank are 95%.

W = (1-y)(.95)+x(.05)

= .6126

Option 2: Freeze
Possible outcomes after Blue’s shot:

If Blue makes the perfect freeze, our hero is forced to draw for one.
If the freeze is off slightly (call it a “near-freeze”), the deuce is not likely but Red will be able to blank by blasting both rocks and rolling out as well.
If the freeze attempt is too heavy or light or fails to cover part of the Red stone, a chance for two becomes possible.

Blue needs to initially estimate his chances of making the freeze. Let’s estimate this and other Variables:

Blue’s shots:

f = Odds of the freeze, Red must draw for 1 = 25%
n = Odds of near-freeze = 50%
m = Odds of a miss = 25%

Assumptions:
Initially, let’s try to simplify our analysis as much as possible…
· If Blue freezes, Red will always score 1
· If Blue misses, Red will always make the shot for two.

Further math is then required for the “near-freeze”. Let’s start by estimating that, after a near-freeze, Red will always attempt a hit. Variables as follows:

b = blank = 70%
t = take 1 = 20%
s = steal = 10%

W = fx + my + n(b(1-y) + tx + s(1-z))

= ..6196

Very close to our original result. This would imply that, based on our estimates, either decision is correct.

Using some other values for b, t, s

Not very drastic changes, even if Blue steals 20% and forces Red to one 30%, we only increase our chances 3% over hitting. Given these numbers are very close, let’s use 62% (our original estimate), and make changes to the original variables on Blue’s shot.

(Variables: b = 0.7, t = 0.2 and s = 0.1)

What does this show us? If Blue can make the freeze 60%, even if Red scores a deuce the other 40% of the time, our decision is equal to hitting. If, however, Blue gives up a deuce at least half the time, they are making the wrong call.

However, making a perfect freeze, even at the top level, is very difficult. Our original estimate of 25% is likely high. I suspect the chance of a near-freeze is greater than 50% and the chance of a deuce is the greatest Variable in our decision. Notice if f = 0.2, n = 0.8 and m=0, we jump to 68%, but if we add 10% chance of a deuce we drop down to 64.5%. It is my opinion that Blue must be confident they will not allow Red to score a deuce more than 20% of the time, in order for the reward to be greater than the risk.

I suspect that Blue was not aware of the actual statistics for 1 down in the 10th with hammer. Many competitive curlers believe (incorrectly) the number to be greater than 40%. I know many players who felt that it was 50% or slightly higher – prior to Curlingzone statistics being available. At first looking at these numbers, I myself was surprised at the results seen in 4 rock play.

For what it’s worth, in this example Blue made a perfect freeze, Red was held to one and lost in the 10th end.

Extra End:

Let’s go back to our original Assumptions:

If Blue freezes, Red will always score 1
If Blue misses, Red will always make the shot for two.

We simplified in order to do a quick analysis. If we dig deeper, let’s create some additional scenarios.

If Blue freezes, 95% Red scores one and 5% Blue steals.
If Blue misses, 90% Red scores a deuce and 10% Red scores one.

W = f(.95x + .05(1-z)) + m(.9y + .1x) + n(b(1-y) + tx + s(1-z))

Using our original values, f=0.25, n=0.5, m=0.25, b=0.7, t=0.2, s=0.1

W = 63%

Only 1% higher than our original analysis. Our assumptions appear to be accurate for our purposes.

Extra-extra End:

Some readers have mentioned that, though interesting, these studies are not practical for game situations. I disagree, and here’s why:

Many game situations are similar and occur often enough that “off-ice” analysis can prepare a team better for these game situations. The article here is one example. This is similar to how poker players practice decisions away from the table.

A coach could have a computer with a spreadsheet available to run scenarios and a time-out can be used to discuss.

Players can make these decisions on ice and, with some work and practice, can examine even more complex situations.

Let’s re-examine this article doing quick “in-head” analysis on the ice, per comment number 3.

Blue skip thought process…

¼ of the time I give up a deuce. If I do, I win 40% so ¼ of 40 is 10.

¼ of the time I force Red to one and win 75% so ¼ 75 is about 19.

Half the time I make a near freeze. Usually Red will blank, and I win 60%, but sometimes we can steal or hold them to one, let’s say we win 64%. Half of 64 is 32.

10+19+32 = 61%

That’s nearly the same as hitting, but:

a. I have confidence and think a deuce is less that ¼, therefore I will draw

b. I don’t trust the ice or my weight, I will hit because a deuce is likely greater than ¼.

Some may argue “but I knew that already, I draw if I can make it!”

In poker, an amateur player may make the same decision as the world class player on whether to raise or call. However, the ability to work through the process and make more correct decisions and know why they are making them, is the difference between an average player who breaks even or loses, and a world class player who wins all the money. I believe this analogy applies not only to curling but many other areas in sport, the stock-market, and in life.

Ferbey vs Dacey Brier Final - Part 1 Reprint

2006-12-19T01:39:00.000-07:00

This article is a reprint of the 2006/07 Black Book Curling article.

It’s the 2005 Brier Final. Ferbey, appearing in the final game for a 5th straight year, is facing what appears to be a simple decision. It is the 9th end, and the game is tied. A miss by the opposing skip, Shawn Adams of Nova Scotia, has left the Alberta rink lying one with no other rocks in play. It is commonly accepted curling strategy to play for two (or more) when you have the hammer and hold your opponent to one (or steal) without last rock. In this case, Ferbey would be expected to draw to the open side of the rings and likely have a final shot at two or perhaps three if Adams attempts a freeze and makes a poor shot. David Nedohin, who throws the final rocks for the Ferbey team, discusses the options with Randy. Much to the surprise of fans and commentators, they decide to remove their own stone and play out the end for a blank in order to keep the hammer in the 10th end. The final outcome eliminated any need for second guessing the decision, as Ferbey won - David making a draw to the open four foot in the 10th end for the victory.The question I immediately asked myself was, is that the right decision? Not in terms of gut feelings of the moment or using hindsight, but if the game was played 1,000 times or 10,000 or infinite times, what would be the correct play based on mathematics and statistical analysis? Could this be done and, if so, how valid are the results?Now, let’s attempt to analyse the situation based on available statistics and mathematical in-game analysis. To examine the 9th end decision, we need to determine all the Expected Results (ER) and Variables (V) to be included and state which are being omitted. ERs are numbers, in percentages, taken from existing statistics. Variables are numbers, in percentages, which are estimated during a game situation. Variables are based on the chance of making a single shot or the expected outcome following a succession of shots during an end. The ERs, Vs and related assumptions I used are listed below. I have indicated in each case which letter is used to represent each ER or V.

Expected Results in the 10th end
Odds of winning if tied with hammer (x) = 75.7%
Odds of winning if one down with hammer (y) = 39.5%
Odds of winning if two down with hammer (z) = 11.7%
Odds of winning if 3 down with hammer (m) = 0.4%

These Expected Results are based on available statistics for 4-rock games played in the Brier, European and World Championships, Grand Slam and other WCT events, Provincial Championships, Olympics and Olympic Trials. In using these statistics, we assume skill is relatively equal, conditions are similar and shot making ability is similar. This assumption is clearly debateable but we will disregard for now any difference in skill level amongst specific teams or events.Game Situation Assumptions:

Nova Scotia will attempt a freeze on the rock in the back four (they will not try a double) if Alberta draws to lie two.

When going for two in 9th, it is assumed that at worse Alberta will take 1. Odds of a steal for Nova Scotia are considered negligible.

Let’s examine the options Alberta faces, to try for a blank or attempt a multiple score.

Option 1. Blank attempt

Expected Results:
x = Odds of winning tied with hammer = .757
y = Odds of winning if one down with hammer = .395

Variables:
b = Odds of blanking = 95%

This number is an estimate a Skip would make based on experience and analysis of the individual shot and subsequent shots to come. Many skips will often evaluate these types of variables at key points during a game. Let’s estimate a team at this level will succeed in blanking 95%.

Win (W) = bx + (1-b)(1-y) = (.95)(.757) + (.05)(.605) = .7494 or 75%

Lose (L) = b(1-x) + (1-b)y = (.95)(.243) + (.05)(.395) = .2506 or 25%

You may notice a faster way to determine the odds of losing is to subtract the odds off winning from 1. 1 -.7494 = .2506 or 25%We have determined that Ferbey can expect to win three of every four times that they choose the questionable call of removing their own stone in an attempt to blank the 9th end. Option 2.

Attempt to score two or more
Expected Results:
x = Odds of winning tied with hammer = .757
y = Odds of winning if one down with hammer = .395
z = Odds of winning if two down with hammer = .117
m = Odds of winning if three down with hammer = .004

Variables:
t = odds of taking 1 in 9th = .75
u = odds of taking 2 in 9th = .20
v = odds of taking 3 in 9th = .5

As we did previously, these numbers are an estimate done by a skip prior to calling the critical shot in the game. Let’s start by estimating that 75% of the time Adams will make a great shot with a freeze and hold Ferbey to 1 (t). If his shot is not successful, let’s assume that 20% of the time Ferbey scores two and another 5% they score three.

W = t(1-y) + u(1-z) + v(1-m) = (.75)(.605) + (.2)(.883) + (.05)(.996) = .68015 or 68%

L = ty + uz + vm = (.75)(.395) + (.2)(.117) + (.05)(.004) = .31985 or 32%

Assuming that Adams will be successful three of every four attempts, blanking will increase the chance for an Alberta win by 7%. What at first appears to be a controversial call, is in fact the correct call, if our assessment of Adams’ abilities is correct.Using some other estimates for the variables t, u and v, we can determine when a blank attempt is the incorrect call:

Once our assessment of Adams’ chance drops to 50%, the decision to blank is questionable.Three other factors can also weigh into the decision:

Our original assumption was that Nova Scotia would not steal if Alberta attempts a multiple score. It is possible (though not likely) that Adams could in fact steal if Alberta attempts a difficult shot for two or three and misses.

Consider Ferbey’s confidence in being an “above average” team and in their ability to win if tied coming home. The Expected Result tied with hammer in the 10th end is nearly 76%, but Alberta may believe their chances are in fact higher.

By blanking the end, Ferbey keeps greater control over the final outcome. The Variable t in Option 2 is an estimate of their opponent’s odds of making his final shot of the end. Though they can asses the chances, Alberta cannot impact the final result. If Adam’s makes the perfect shot, Alberta may have no choice but to settle for 1. In Option 1, there is no Variable associated with their opponent.

Now, what about these Expected Results and the numbers associated with them? Our sample size of data is still small, only having a few years of 4-Rock Curling in Canada. As the sample size grows, our confidence in these numbers will increase. What about evaluation of our team skill and our opponents? Maybe the average Brier or WCT team wins 40% when 1 down, but what if I’m team Ferbey, are we 5% more likely to win? 10%? What if I’m playing Martin instead of Adams? It would take much more math to examine these questions in detail, and I suspect we do not yet have enough data to develop a clear answer. We can, however, use the average analysis and apply it to a given situation. For example, Ferbey may decide their chance is greater than the ER of 76% to win with last rock. This simply reinforces their decision to attempt a blank.The use of these numbers is applicable to any competitive team and useful for many game situations. Examine the scenario of being down one with the hammer in the 10th end, facing a difficult shot for two or a simple draw for one to tie the game and play an extra end. Math tells us that we should attempt the shot at two, even if we expect to miss 3 out of every 4 times that we try the shot!

1 Up in 9th End Without Hammer

2006-10-19T01:47:00.000-06:00

It’s down to the final two rocks of the end. You are Team A, and do not have last rock. You have a 1 point lead and the house is open except for your opponent’s stone in the eight foot at the tee-line and a center guard. What should you do and, more importantly, what analysis can you do to determine the correct decision?

Assumptions:
1. The guard is halfway from the 12 foot to the tee line. It is your rock.
2. Ice conditions are perfect or near perfect.
3. If we attempt a hit we will not miss the rock completely.

Expected Results (ER) in the 10th end
Odds of winning if tied with hammer (x) = 75.7%
Odds of winning if one down with hammer (y) = 39.5%
Odds of winning if two down with hammer (z) = 11.7%

These Expected Results are based on available statistics for mens 4-rock games played in the Brier, European and World Championships, Grand Slam and other WCT events, Provincial Championships, Olympics and Olympic Trials.

We have three options:

1. Hit and stick.
Variables
b = Blank = 95%
We estimate that if we attempt to hit and stay, the chance we roll out or the chance our opponent hits and rolls out successfully to be 95%.

W (Win) = b(1-y) + (1-b)x = 61%

2. Hit and attempt a roll behind the guard
Variables
c = Team A steals 1 = 5%
d = Blank = 70%
e = Team B takes 1 = 25%

We estimate that 70% we miss the hit and roll enough that our opponent is able to blank. Of the 30% we make the hit and roll, we steal 5% and Team B draws for 1 25%.

W = c(1-z) + d(1-y) + ex = 66%

3. Attempt to draw behind the guard
Variables
t = Team A steals 1 = 25%
u = Team B takes 1 = 50%
v = Team B scores 2 = 25%

We estimate half the time we can hold our opponent to 1, one in 4 attempts we steal one and the other quarter of the time Team B scores a deuce.

W = t(1-z) + ux + vy = 70%

Based on our estimates, we have determined that our best choice is to disregard the opponent stone and draw around the center guard.

Let’s compare the Option 2 and 3 using different values for the variables.

Hit and Roll

*Option 1

Draw

With a hit and roll, we need to allow a blank no more than 50% of the time to have at least a 68% chance to win.

With a draw, if we expect to avoid a deuce 75% of the time, we range from 67% to 76%, depending on our estimate to steal a point.

The draw is the correct call, based on this assessment of the situation and our skills. If, however, we expect to give up a deuce half the time or more, the hit appears to be the correct call.

Now, let’s consider if the hit and roll is a very difficult option, with the rock on the edge of the back rings, far from the guard. If we expect the hit and roll to succeed 5% of the time, the option appears clear to draw behind the guard as we are only 62% chance to Win, very close to Option 1. We still, however, need to ensure the draw gives our opponent a deuce less than half the time in order to attempt this shot. What this tells us is the decision is based less on where our opponent’s rock is in the rings and more on our confidence in making the draw around the guard.

What if the guard is our opponent’s stone instead of our own? What if it is 2 or 3 feet from the rings? Now, the added chance of a run back for two may sway our decision as well. Assume every time we make a perfect draw (one that would steal in our original analysis, 25%) our opponent tries a run back. Let’s estimate that of that 25%, 10% we steal, 10% Team B scores 1 and 5% Team B scores 2.

Variables
t = Team A steals 1 = 10%
u = Team B takes 1 = 60%
v = Team B scores 2 = 30%

W = 66%

Identical to our original Hit and Roll analysis, making either decision the correct call.