Is 5 the Magic Number?

How about that 5-Rock Rule?

The World Curling Tour’s Player’s Association has decided to trial a 5 rock rule at the upcoming Grand Slam event in Kingston, December 14 to 18th (which one is it again, Masters or Open?)  The rule would make the 4^th rock of 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^th rock, most likely the 7th rock of the end.  Essentially 4 rock means that 3 rocks are safe from removal (if put in the correct location, between house and hogline) and subsequently 5 rock rule means that 4 rocks are now safe from harm.  Confused yet?

Though I applaud the WCT and their PA for doing what many other athletes would like to do, which is have a direct influence on their sport (ask the NBA PA how they feel these days), I don’t believe this new version of Curling will have a significant impact and may in fact result in the opposite desire than is intended.  But perhaps 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 less offense to ensure a close game, but needs scoring to be exciting.  It is a game where being 3 or more down with hammer or 2 (or even one) down without  becomes no longer interesting, and progressively so as the ends tick away.  If more offense opportunity creates higher scores early, teams will then be apt to stay out of trouble, let the team behind take chances, and capitalize on their risks (when they fail) and end the game even earlier.  As boring as it sounds, a classic game of no free guard zone which is blanked for 9 ends and played tied in the 10^th is closer (though clearly not as exciting) as a game where a team cracks three early, gives up a single and then score two (and after three ends we are off to the other sheet for coverage, hopefully).  Imagine most any boxing match with Bernard Hopkins, grappling, pacing, counter punching and plodding along until he wins on a decision as opposed to a Haggler vs Hearns with an explosion of attack until only one stands after a few short rounds.  So my position is, more offense is not necessarily good.  Perhaps what we mean to 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 lead so we ensure a close race?  As I stated above, even with the 4 rock rule a team can quickly move from a close game to a position of Dominance with a quick three and then hold their opponent to 1.  So can a 5 rock rule allow a game to stay closer, allowing for more comebacks? 

I traditionally felt 4 rock was the “fairer” rule to the old 3 rock, in that some edge was given to the team without hammer (2 rocks protected, versus 1), to offset the large advantage the team with hammer is given.  Despite this edge however, teams still only win 25% of the time (closer to 20% in Grand Slams) when tied without hammer and one end to play.  So can 5 rock change this?

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

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 the team with hammer either tied or behind.  The most likely scenario where we have hammer and the lead in three is to take 2 in the first then force my opponent to one.

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

So what about later in the game?  Today, tied in the final end, the team with last rock has a significant advantage (75 to 80%).  5 rock is not going to help the team without hammer in that situation.  If you are one down with hammer in the final end, stats show a 40% chance of winning the game.  Here, this rule could bump up that percentage but doubtful how much and, frankly, 40% is already competitive and engaging to the viewer.  It’s rare that a one point lead in the final end doesn’t create excitement, so why change for that?  Maybe if we are two down with hammer coming home, our chance might increase from 12%, but realistically to what?  Even if you get your deuce to tie (considerably more likely than a three), you are in the same spot tied without hammer 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^th end in a 10 end game), has often provided some of the most interesting situations since curling moved to free guard zone.  Take for example the GP Grand Slam Quarterfinals, where Howard, one up against 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 not going to be forced into any different situation than today’s rules.  They may elect to more aggressively attempt a deuce, at the consideration that being one up in the last end without hammer is less advantageous, but I doubt the thinking will change drastically.  Today, most teams recognize a blank is less likely and the team without hammer is forcing the issue to have a score (be it a steal or surrender a single).  When a team with hammer is one down, there becomes even less incentive to score a deuce, as they would have most likely greater than 40% chance if they remain one down with but their chances when tied without hammer doesn’t increase from the rules today.  O the flip side, the team one up without in 7 or 9, is just as likely to be aggressive, risking a deuce at the hope of stealing or forcing the opponent to a single.  They may be slightly more aggressive, but this 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 them well.  Though I suspect the impact will be hardly noticeable, perhaps it will keep a few games from getting less competitive early and make for more dramatic contests.  I doubt it.

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

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

The World is Flat(ened)

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

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

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

• The great job by the City of St. Albert (and Edmonton). The volunteers and 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 if it probably isn’t).  Take note WCT, perhaps a Grand Slam in a smaller venue with full stands would change our impressions (including sponsors).
• Team North America were almost too impressive, reminding us all that though the game has become an Olympic sport and many governments are funding hand chosen players in an effort to usurp Canada, there is still a long way to go.  
• The wild Olympic cheering which surprised all of us regular curling fans cannot and perhaps will not be duplicated.  Several efforts were attempted, and with some level of success, but the age and soberness of the fans limited their ability to reach Vancouver decibel levels.
• Skills competition (Singles), though different, should not be a “regular draw”.  I sat beside a man and his grandmother.  Confused by what was happening, she kept asking him why they weren’t curling.  Unfortunate for her but Saturday afternoon was her one chance to take in the Continental Cup and for $30 she got to watch a really neat practice. One volunteer had trouble looking up from her Sudoku during this portion of the event.  The lack of excitement is evident and, even if you’re following the points, there aren’t enough at this stage of the competition to even matter.  Every time the announcer called out the results, 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 to the beginning of the competition and make it no charge, in an effort to increase sales.  Possibly a Wednesday night event and include a private party with the teams for those who purchase special weekend packages.
• Only two games over the first two days were close (and one was Mixed Doubles).  That’s a whopping 11% of excitement. 
• John Morris also appeared to be confused by the format.  I won’t fault him, few fans can follow it either.  While skipping during Saturday night’s Mixed Skins, he repeatedly mentioned they were playing for a “conservative” deuce in the 7^th end.  This was incorrect strategy.  If they get a deuce, NA gains 6 points.  A conservative end should reduce chance for a steal but increase the possibility of a carry-over, in which case Team World gets hammer in the final end with a possible 15 skins. If NA gives up a steal, they still have hammer and a chance at 9 points.  I’ll skip the math formulas, but given where NA was at the time, the preferred approach is to go all out for the deuce in the 7^th end.  Likely John was following a reasonable logic of 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 pleased with the outcome of the 2011 Continental Cup.  I do believe there is room on the calendar for this event and many reasons 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 final television numbers, although the real opportunity is for this event to reach beyond a Canadian audience and help market the game around the world.  Until they are able to host this across the pond in Europe, that may simply not be possible.

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

Strange.

Live (nearly) from the Continental Cup

Let me start with the apology, for those who actually follow my regular blog.  I have pages of notes from the first 3 major events of the year, but have yet to produce a new article.  I should have some analysis out very 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 actually recall ever watching more than a few ends of the “Ryder Cup of Curling” in its first 6 iterations.  My parents even lived in Medicine Hat when it was the host city and I never bothered to make the trip, despite living in Calgary at the time.

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

Some impressions:

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

Fan turnout was ok, lots of chairs appeared empty but there were 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 little steep.  Or maybe 34 below and TSN coverage is keeping some at home.

The North American ladies started a cheer during the early ends.  It brought some mild enthusiasm from the fans, though it paled to my Olympic memories.  Perhaps it was the age difference in the stands or maybe the fact the actual cheer seemed more complicated than the format for this event.

Someone please tell me why you get 6 points for win (team competition)?  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 damned if I have been able to figure out how this thing works without a detailed program and a financial calculator at my disposal.  If I can’t follow easily, how can the average fan 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 format of this event as simple as possible for the senior crowd.  It is not.

What is “simple” about the structure is the fact a losing team can make a valiant comeback on Sunday and win.  In fact, with 400 points up for grabs, a NA or World team can be shut out for the first 2 days and still have a fighting chance on the weekend to win.  I understand 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 gain traction with a new event, it is imperative to keep the fan interested to the bitter end.  As a fair method to determine the winner, or a way of simplifying things, this approach fails miserably.  Golf’s Ryder Cup had no fan interest for nearly 60 years.  Each match was 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.  Only once the European teams began to win did the event take off and become what it is 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 final day/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 means something.  The cameras need to try and capture as much of this as possible.  I noticed Blake MacDonald give Kevin Martin a big high five after the gold medal squad scored a three.  Granted, Kevin looked less coordinated than Tiger after his chip-in at the 16^th during the 2005 Masters, but exciting nonetheless.

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

I got a chance to speak with Team NA 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 in this type of format.  Actually, I forgot to 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 and mixed 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 a player jump up from their slide and run ahead to sweep the rock without recalling my days long ago in Winnipeg, practicing against my teammates…. when I  was 13!  It looks and feels strange.  With that many players on both sides, can’t they allow one sweeper?

Some of you may have seen the TSN camera crew spot me in the crowd 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 plug for his local St Albert sports bar, “The Rink”.

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

Curling Season started?

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

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

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

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.