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Wednesday, October 20, 2010

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"
, it's an in-depth read.  Also recommend "Mathlectics" -

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.

Thursday, March 25, 2010

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

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.

Saturday, March 6, 2010

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:


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.


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: 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.

Sunday, February 21, 2010

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 related to, 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:

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.

Friday, January 29, 2010

Notes from the BDO Grand Slam

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 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.

Wednesday, January 13, 2010

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

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

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.

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:

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:

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

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.

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.

  1. 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.
  2. 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.
  3. 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.
  4. 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 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.