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28 Dec 2009 Kevin 0 comments
28 Dec 2009 Kevin 0 comments
Yes readers, yours truly, the Curl with Math guy (perhaps a better moniker would help my marketing efforts), will be joining Luke Coley in the broadcast booth for several draws during the Roar of the Rings! Actually, I prefer the name “Olympic Trials”, as it more clearly states what is actually going on. ROTR seems to be a screenwriter’s pitch to Warner Brothers for a new movie…. “Lion King meets Lord of the Rings….and we’ll film it in Edmonton; parts of it look just like Mordor and the locals look like Hobbits”.
Let’s begin our Preview show…
Men’s Teams
The “Big Four” are Martin, Howard, Ferbey and Stoughton. No slight to Middaugh, who is a two time Brier champion or Koe who is an original 4 qualifier, but those four teams have the most wins, best records and greatest success against the field going back many years. It would not be a surprise if any of these teams won, and the numbers will show us why.
The Favorites
Kevin Martin is 76-35 (68%) since start of the 06/07 season against this field and is 41-19 (also 68%) against the rest of the Big Four.
Howard is 13-13 against Martin and 7-8 since 06/07. However, they are also .500 against the others in the Big Four, 31-31 overall and 17-17 since 06/07.
Martin has outscored all Trials teams by nearly a point per game. Howard and Ferbey are around a half point.
Martin is 22-18 against Stoughton historically but 11-2 since the 2007 Brier.
Provincial Rivals – both Favorites have been dominant:
Martin is 20-7 against Ferbey since 06/07 and 27-10 overall.
Howard is 12-5 since 06/07 (70%) and 25-14 historical numbers against his ex-teammate, Wayne Middaugh.
Contenders
Ferbey is only 16-29 (36%) since 06/07 against other Big Four teams but minus Martin, they are 9-9 against Stoughton and Howard since then and 21-17 overall against those two teams.
Stoughton is 80-74 against the entire Field but has beaten Gunnlaugson (including Carruthers) 10 times. Jeff is 37-46 overall against the other Big Four teams including a mere 13-22 (37.1%) since 06/07.
Challengers
As a top 4 qualifier Koe has a (somewhat) easier start, not facing Howard, Martin or Ferbey until their final three games. Their opening game is against Simmons, against whom they are 11-0. They are 7-6 vs Stoughton but against Howard, Martin and Ferbey they are 18-41 overall and 18-37 since 06/07.
Middaugh plays Martin well (11-12 and 4-4 in last 3 years) but Howard (see above) and Ferbey (4-11) both seem to have his number. Middaugh is 7-0 vs Carruthers/Gunnlaugson.
Underdogs
Simmons, is he an underdog? Numbers indicate yes. They have only won 32% against this field and haven’t shown to be any stronger since 2006. They are 5-1 against Middaugh in the last few years and…if they can finally win against Koe….
Gunnlaugson has no chance, mathematically. But then again, Gushue probably didn’t have much chance last time either, even Stoughton said so….
With their small sample size, we don’t have much to analyze. Including Carruthers, Daley Peters and Gunnlaugson as skipping the squad is 12-37 against this field. However, Gunner is 3-5 as a skip and has beaten Howard, Koe and Stoughton. If only he’d picked up a veteran to play front end….
Play-off Bound?
Let’s examine chances of outcomes. These are based on handicapping analysis I have done. I will spare you the details of the numbers, other than to say if you’d like to bet on any games, please let me know.
Martin has 7% chance and Howard a 4% chance to go undefeated.
At least 5 Wins – Howard is around 54%, Martin near 65%. Next closest is Ferbey at 32%.
At least 4 Wins – Howard is 80% likely, Martin 86%, Ferbey 62%, Stoughton 58%
Koe is 49% likely to get to 4 wins, Middaugh is 45% and Simmons 16%
Gunnlaugson is calculated at approximately 7% chance at 4 Wins. As I stated earlier, this is based on small sample size and with other skips, so if someone offers you better than even money that Gunner will win 2, then it is a good bet. Of course, he still might go Winless (12% chance).
Women’s Teams
The Women’s Trials teams have the Big Two but also 3 others who are very close. Jones and Lawton then Scott , Bernard and Kleibrink. Let’s call them the Top 5.
It would not be a surprise if any one of these five finished as the winner. It should be noted, the sample size (or numbers of games played) amongst these teams is far smaller than those for the Men’s. This leads to more variability in probable outcomes. But let’s still take a look…
The Favorites
Jones is 39-23 (63%) and 29-21 against the other top 5 teams. She is 8-1 against Bernard, 4-0 against McCarville but 6-9 against Scott.
Lawton is 38-25 against this field including 27-19 (59%) against the other top 5. They are 9-3 against Scott and 0-3 against McCarville.
Heads up Jones edges Lawton 6-5.
Contenders
Scott is 33-30 against the other Top 5 and 12-5 against Bernard. Interestingly, she’s only 2-5 against Holland.
Kleibrink is only 41% against the other Top 5 and, though 10-9 against Scott they are 7-3 in the last 10 meetings.
Bernard is 40% against the other Top 5. Strong against her Calgary opponents: 8-4 against Kleibrink and 6-0 against Webster.
Challengers
McCarville’s numbers are close to Kleibrink, Scott and Bernard. They are 46% against this field while the others are 48-50%. However, her sample size is much smaller and we can expect her success at this level of competition is not on par, so we will put her in this category (so that we have someone!).
Underdogs
Webster played well at the Pre-Trials, qualifying in A, but historically they are 10-24 against this field. It’s not likely, but if given the right odds, some would say it’s good to bet a streak.
Holland is 16-27 against these teams but is 5-2 versus Scott. Being the last qualifier they have a tough start but who knows….
Play-off Bound?
Jones has a 6% chance and Lawton a 4% to go undefeated.
At least 5 Wins – Jones is 59%, Lawton is 50%. Next closest is Scott at 25%.
At least 4 Wins – Jones is 84%, Lawton is 78%, Scott and Bernard 53%, and Kleibrink (50%).
McCarville has a 47% expectation for 4 wins and Holland is 25% likely.
Webster is 11% likely to get 4 wins and 9% likely to be Winless.
Predictions
So now that we’ve looked at the records, who do I like? The correct answer is always whoever gives me the best odds, but if we aren’t taking Gunner at +380 to beat Stoughton, then I suppose I’ll go with my gut (and not my wallet)…
Howard, Martin, Ferbey all get in the play-offs. 2006 was an anomaly and these guys are all more prepared and playing better against the field coming in than they did in 2006. I think one or two others may also be in tie breakers, likely Stoughton and possibly Middaugh – but he needs a good start. Koe has a chance to get on a roll with some early wins but will need to hold on. Simmons had a good Pre-Trials but they may get called for too many men on the ice. I think if Gunner goes 0-7 its possible to have a 6-way tie at 4-3. Wouldn’t that be something?
Women’s? I don’t watch/study this game as much and think anything is possible. Many of these teams have the big game experience and should be able to play to their potential despite the magnitude of the event. The qualifying format through a Pre-Trials likely helped teams like Webster and McCarville in this regard and make them possibly more dangerous than some would suspect.
Play-off predictions?
I’ll wait until Thursday.
Note: the accuracy of these records is the responsibility of CurlingZone. We may be out by a game or so, but we have to start somewhere. If anyone has numbers which contradict these, please e-mail Dallas or Gerry @ CurlingZone.com.
Another note: These numbers don’t rank the value of a win based on the importance of the game. For example, a win or loss could come in the Brier or in the opening round of a WCT cashspiel. We could try to add this to our analysis, but I do have a day job and I don’t know how much more value it gives us.
And yet another note….
PLEASE, PLEASE, PLEASE…will PinnacleSports or some other betting web site offer the Canada Olympic Trials? Four years ago some great gambling opportunities and the Brier last year was a potential gold mine. And finally, this year, I do all the prep, analyze the records, am prepared to lay down my money….and no where to put it. Guess we’ll have to wait for Vancouver….
Two other Math notes this month…
If you happen to be at the Trials in Edmonton and read my articles, whether you agree, disagree or really don’t care, please come say hello. I’ll be the person in the CurlTV booth most likely to be fired.
02 Dec 2009 Kevin 3 comments
I’m struggling with this event called the Road to the Roar or more aptly named Pre-Trials. It reminds me of the NFL deciding to increase playoff teams from 10 to 12 in order to generate more games (and more revenue) on opening “Wild-card” weekend. It’s not that the entertainment isn’t there, but why not just have 16 teams at the Trials in December? Money must have something to do with it. Or perhaps the 400 or so people in the stands in Prince George demanded their opportunity to shine in the spotlight.
Some random thoughts and analysis….
This is an important point in the game. Simmons is two up and holding Stoughton to one is a huge advantage. Simmons chances of winning goes from 67% (tied with hammer and just barely Control) to 86% (and Dominant Control) if he holds Stoughton to a single instead of the two he surrendered. Even if Stoughton makes a circus shot and takes three, Simmons still has 37% chance to win. I prefer the draw for these reasons and if he comes short he still leaves a very difficult shot for two.
Draw: Let’s expect Pat makes a reasonable attempt to draw to the face of Mike’s stone but Mike makes his draw 50% of the time.
W = .5(.67) + .5(.37) = 52%
Run-back: How often does Pat need to make the shot for it to be the correct call?
W = .52 = x(.67) + (1-x)(.37)
Note we assume Mike always scores two – in the actual game his rock caught debris and he did not, but that is assumed to be minimal for our analysis and then can be factored into our decision later.
We can see that if x (Pat’s chance of the run-back) is greater than 50% then it is the correct call. If we assume Mike makes the draw 60%, then x = .4 and Pat only needs to make the runback 40% for it to be the correct call. Further examples show it as a linear equation in that Pat needs to make his shot more often than Mike misses a draw for it to be the correct call. The readers can decide if Pat made the “correct” choice.
Good luck to all in the “Actual” Trials, which I suppose we could now call the “Pre-Olympics”. Final thought…..is it too late for some young team to pick up Russ Howard?
15 Nov 2009 Kevin 0 comments
Well, the new Curling Season is here and though I’m disappointed in the end to golf season I am anxious for the Olympic Trials. The Olympics themselves, sadly, I’ve never had much interest in. Why is it every four years I’m suppose to get excited about sports which I’ve never cared to watch during the past 1460 days since the last Olympiad? I never tuned in to CBC for skiing during the World Championships in 2008, so why now? If not for Curling, Hockey, and perhaps women’s’ short track speed skating (it’s like a cat fight on skates!), I’d likely pass on the entire thing completely. And don’t even get me started on the Summer Games – days on end of coverage from multiple networks, journalists, etc – and the only thing worth watching is 9.7 seconds of men running and a couple of laps in a pool (which took slightly longer). Better to watch the highlights on the internet after it’s all over.
In any event, we’re back into the “sweep” of things and need to begin.
Shorty Jenkins: Martin vs. Matchett
Gerry Geurts of CurlingZone relayed this shot call to me and he may have not remembered exactly right, but the analysis should still be interesting. In the semi-finals at the recent Shorty Jenkins event, Kevin Martin was one down playing the 7th, with hammer, against Dale Matchett. Matchett had a rock in the outside rings, perhaps biting eight foot, and there was a slightly off-centre guard. Martin, on his first stone, chose to play for his deuce by drawing around the guard. Remember, this is an 8 end game and only the final end remains. Kevin is forgoing an attempt at a blank, attempting to take two, with an increased risk of being held to one or even giving up a steal.
The chance of winning up one without hammer coming home is roughly 60%. If held to one, Martin’s chances drop to 25%. The difference in outcome between a successful two or held to one is greater here than at any point during a game. Let’s look at each option:
Draw: Assuming the draw takes away any chance of a blank, let’s determine how often Kevin must get a deuce to make this a correct call.
W = d(.6) + s(.25)
Where d = chance of a deuce and s = chance we are held to one. Assuming these are the only likely outcomes (blank and steal of two not likely), we solve for s= 1-d
W = .6d + .25(1-d).
To complete this calculation, we need to compare against the scenario if Kevin hits the stone.
If Kevin hits the open stone, Matchett either hits the Martin stone (trying to roll behind the guard I expect) or simply draws around the guard attempting to force Martin to a single point.
What likely entered Kevin’s thought process “if I hit and stick, Dale will draw around the guard and now I may be forced to one. My chances are better at two if I force the play now.”
When guessing what an opponent may do, we can estimate what the chance is they will make a certain play and evaluate further. For example, let’s start to analyze what happens if Kevin hits open stone.
Assumptions:
Martin will always hit and stick successfully.
If hit and roll succeeds, Martin always draws for one successfully (assuming the roll puts the rock in the back rings).
If hit and roll doesn’t succeed, a blank always occurs.
Let’s first examine what happens is Matchett draws or hits:
Where:
x = Odds of winning if tied without hammer = 25%
y = Odds of winning one down with hammer = 40%
z = Odds of winning if two down with hammer = 12%
Hit: Estimate a roll successful 25% of the time.
W (Martin) = x(.25) + y(.75)
W = .363
Draw: Estimate with a draw Matchett steals 20%, Martin takes one 60% and he gets a deuce 20%…
W (Martin) = x(.6) + (1-y)(.2) + z(.2)
= .294
Matchett should draw (based on our estimates are correct) – but perhaps he will only draw half the time. Then we weigh the chance of winning as:
W (Martin) = .5(.363) + .5(.194) = .33%
Therefore, using this in our original equation:
.33= .6d + .25(1-d) solving for d = .23
Therefore, Martin only has to get his deuce 23% of the time in order for the decision to be correct. Note that if Matchett always plays the draw, then Martin needs to make a deuce even less often (12.5%):
.294 = .6d + .25(1-d) solving for d=.125
Masters Final: Koe vs. Howard
It was an entertaining game last Sunday with Howard winning yet another Grand Slam. This was clearly one that could have gone the other way. An early steal of two had Glenn and his squad battling back. There were some timely misses by the Koe rink, but also some interesting decisions which may have provided them better opportunity to clinch a victory rather than being a bridesmaid for yet another Grand Slam final.
Some observations….
Second End:
Matt Hames in his Curling News blog suggests Koe could have played the in-turn draw instead of leaving Howard an opening for one…
http://curlnews.blogspot.com/2009/10/world-cup-sweeping-rant.html
I would tend to agree. At this stage he’s 2 up and if he does make a poor shot, at worse Howards gets a deuce and Koe’s odds are at 61% tied with 6 ends remaining. A steal would have put the Koe rink at odds of 89% chance to win. That is a chance you want to take during the Early Game, IMHO.
Third End:
Blake throws two draws. One appears 20 feet heavier than the next (according to the assessment by announcer Mike Harris). The sweepers are surprised and there is some discussion that his stones aren’t matched. How can teams at this level not have properly matched stones in a final of this type of event? Situation seemed very strange.
Fourth End:
Koe appears to be sitting third stone in the top eight foot, Howard is first, second and fourth. Kevin calls a hit on his own stone (driving it onto 4th rock), rolling across the house to then double the Howard stone. If successful, Howard would have a shot to hit and stick and sit two. Koe then would have had a double to force Howard to one. I thought the correct call on his first was the one he played on his final stone. Double the 1st and 2nd rocks and roll behind his other rock. If successful, Howard would be left with a choice to either draw around Koe’s top stone or attempt a difficult hit which appeared to be unlikely to allow him to sit two.
Sixth End:
Howard places a centre guard. Please see my articles from January 2009 and March 2009 for the analysis of why this not the “correct” call. I wonder if it was an intentional decision on the part of Howard to choose an alternate strategy, or if he is unaware of the analysis.
Interesting call on Howard’s first. Rather than hit the open stone, he plays into the centre and leaves a (albeit) long run back double for Koe to lie two. This is not a good position to give up a deuce, Howard’s odds of winning would drop to
15% if Koe pulls out the miracle. The flip side is, a steal of one for Howard puts the odds at him winning to 63%. Howard’s call into the rings on his last was clearly an intent to tempt Koe into a big weight shot rather than a draw. He could have instead placed a guard, leaving him a draw – but Koe may have hit no matter what the result. Also, a poor guard could have left a soft double with the inturn and a possible deuce for Koe.
Seventh End:
Blake’s second shot, after much debate, Koe’s team agrees to play a run back. In their position the centre guard is a critical stone to help plug up the four foot in an attempt to force Howard to one. The risk of a deuce is worth the attempt to steal or force a single. Playing the run back was an attempt to take a three out of play – which ultimately succeeded. However, if Blake plays a freeze, Howard may again play a draw, but more likely remove the guard and give Kevin a chance to clear the house on his first shot – or have the option to guard again. If Howard draws, then the play is into the middle with a centre guard and likely a good position for Koe to force a single. Continually attempting run backs is generally counter-intuitive to what a team one up without in the second last end wants to do: force the play to the centre and force the opponent to a single and have a 75% or better chance in the last end – with a risk of giving up a deuce and having a 40% chance coming home. The small chance to steal one, leaving Howard a 12% to win, also supports a draw strategy. In Koe’s defense, playing to avoid a three was perhaps his motive and they were comfortable with that style. It is a case where the risk of a three is minute compared to the great advantage of forcing one or stealing – but sometimes it’s difficult for a team to want to take additional risk if they feel it could take them out of the game. Let’s attempt to analyze the shot call. This involves VERY rough estimates of final outcomes, but allows us to examine how to reach a decision.
Draw:
Koe steals = .1
Howard scores one = .4
Howard scores two = .3
Howard scores three = .2
W (Koe) = 53%
Koe chose the hit, which ultimately resulted in two. Let’s estimate what outcomes may have been most likely:
Hit:
Blank = .1
Koe steals = 0
Howard scores one = .3
Howard scores two = .6
Howard scores three = 0
W (Koe) = 53%.
If Howard scores a deuce more than 60%, then Koe wins less than 53%. The decision appears close. Ultimately, it depends on Koe’s estimation of Howard’s chance at scoring 3 and ensuring that Howard never scores 3 when they attempt the run-backs. I would prefer the draw but it is closer than I had first thought.
Eighth End:
Blake’s first rock, they attempt to come around Howard’s stones staggered in front of the rings. An alternate play would be to double those top stones out and sit 2nd and 3rd shot. By playing to the middle it left a greater chance of only a single and increased chance of a steal. This is the style of play I suggested earlier Koe could have chosen in the 7th, but here the opposite is perhaps true and opening up the play may have increased his chance at a deuce and provided a greater chance at a single if he needed a draw on his last.
A good game and one where a few more made shots on the part of Koe’s rink could have changed the outcome. Whether the decisions we’ve examined here may have had any difference is up to the reader to determine.
Until next month, Happy Halloween!
30 Oct 2009 Kevin 2 comments
What is it that makes sports entertaining? Is it watching the thrill in victory, or the agony of defeat? Do we admire and respect our sports figures for their immense talent and skill, something we do not possess, or for their ability to face the challenge and, sometimes, fail to over come it. Golf, baseball and, similarly curling, present a case for the latter. Do we remember Greg Norman for his heroic achievements at the British Open, or for his complete collapse at the 1996 Masters. The answer is pretty clear. By showing us the same frailty in their inability to overcome the tension of the moment, we see these stars are human. We share the same nervous anxiety when we stumble giving a presentation to a large audience, three-putt from ten feet for a $5 Nassau, or babble incoherently when asking the pretty girl to go on a date.
We still marvel at the feats of Tiger Woods or Michael Jordan, who may lose to an opponent who bests them on a certain day, but never seem to “choke” when the opportunity for greatness is at hand. Jack Nicklaus was the Greatest, but Arnold Palmer and his collapses in the US Open, Masters and PGA, along with his wins, make him “The King”. Something to me is very appealing in experiencing these moments of sport. Moments with a Greg Norman, Jean Van De Velde, Kenny Perry and, yes, a Kevin Martin.
Kevin Martin does not have the records in world competition that anyone would expect from (arguably) the greatest pure curler this country has produced. Kevin Martin beats EVERYONE. Regardless of his team, Kevin has been at the top of Men’s Curling for almost twenty years. He simply Wins. Against every team, at every event….except on the World stage. Is it something more than poor ice, off-days or random chance?
In watching Team Canada’s struggles against Scotland in each game they played, I was trying to determine if it was more Scotland playing great or Canada flat. It was clear Scotland took Canada off their game and disrupted their rhythm. Unlike other games the past two seasons, Kevin never appeared to have a clear sense of his strategy or an ability to dictate the flow of play in each game. In the finals, they looked to have this solved, but the final end proved otherwise.
Most of the discussion in future years, over a cold one at the local rink, will be the call to throw first skip stone away. This shot does appear bizarre and I prefer the option to drive the top yellow stone into the pile – but this is more an opinion versus a fact. Kevin made a very difficult choice, one he must have known would be scrutinized for the remainder of his life and beyond. However, on his last shot, he had two possible options, both likely better than 50%, to win the World Championship. I believe a different choice could have left him a better chance or possibly made Murdoch’s last more difficult, bringing the chance of a hand shake before the final rock. However, several options, such as a guard or a slightly missed hit, could also have left Kevin with less than 50% chance to win. It is my opinion Kevin could do better choosing an alternate shot call. It is a fact that with second’s first stone in this situation: peel the guards. Why does Kevin Martin call Marc Kennedy to play a soft hit and roll into the four foot, when two centre guards sit covering the four foot, in the final end, when tied with hammer? I suspect two things may have led to this critical mistake:
I obviously can’t say if the latter was the case. Kevin has been in similar pressure situations many times and shown the ability to overcome these nerves. From my vantage point, and my analysis of the three games played, something with team Martin just didn’t seem right when matched against Scotland. They did not look like the same team that plowed through Canada’s best all year. It seemed to be more than simply shot making. I expect Team Martin will prepare, focus and do all they can to ensure next time to execute to their peak ability and with clear thinking, when the “moment” happens again.
Some other notes from the recent Mens’ World Championships:
26 Apr 2009 Kevin 0 comments
During his round robin game with Ontario, Kevin Martin says to TSN: “It’s a real Math Test out there!” Could he perhaps be a fan of this blog? Does he have his own computer programs to analyze data? What goes on in his mind during a game and will he share it with us some day?
Kevin in my opinion appears to make more correct decisions, and in a quicker and more decisive manner, than any other skip. It doesn’t hurt that he and his team have missed very few shots in the last two years either.
I had a great time at the Brier, if only for one afternoon and at the patch later that evening. I’ve finally reviewed all of the Tivo recordings I made from the event, and have started to gather some random thoughts and ideas. I may yet come back to a specific situation again, but for now, below are some non-sensible ramblings.
An interesting situation developed in the 9th end. Ontario leads 5-4 and Alberta has the hammer. Forgive me if I’ve stated this before, this is the best time in the game to be one up without. Howard will aggressively attempt to steal (90% chance to win) or force Martin to a single (74% chance to win), at the risk of giving up a deuce, where they still have a 38% chance to comeback and win in the 10th end. Martin is sitting one, with a Howard stone covering it in the rings. Howard begins placing centre guards and Martin is peeling these guards. For some observers, this could appear a strange situation. Why is Ontario guarding when their opponent is sitting one and they are up one? With 7 stones remaining, John Morris is about to throw a peel, when he heads down to the other end to discuss with Kevin and they instead decide to draw into the rings. Howard actually avoids giving up three, but surrenders a deuce. He is unable to score his deuce in the 10th end and Alberta wins.
I did not like Howard’s decision to play a guard on Richard’s first stone and, regardless of outcome, Martin’s decision to draw seemed correct. How might we analyze this situation mathematically?
Let’s assume a peel will result in either a blank or Martin being forced to one. I suspect if that Ontario would have tried a soft hit and roll to split the rings and lie two with Richard’s next shot. This would have forced Alberta to make a double in order to blank. We’ll estimate a blank 80% of the time – i.e. where the rocks were lined up, given three chances, Martin will clear the rings 4 in 5 tries.
W = (1-.74)(.2) + (.38)(.8) = 35.8%
With a come around, there are several rocks to come and difficult for us to determine outcome. Clearly, a blank will not occur, we need to estimate what the odds are Martin is able to score two (let’s assume no three is scored) versus a steal or held to one. We need to come up with Variables, which are estimates of an outcome.
X = Howard steals one
Y = Martin takes one
Z = Martin takes two
W = x(1-.9) + y(1-.74) + z(1-.38)
Initially, let’s assume Howard doesn’t steal. Set W to .358 and y=(1-z) and solve for Z
.358 = (1-z)(.26) + z(.62)
Z = .281
Assuming Howard does not steal, we need to expect a deuce 28% of the time, in order for the draw to be the correct call. Factoring for a possible steal, let’s suggest that at least 1/3rd of the time we need to score two. Is that the case given Martin’s team, a guard and shot stone? I suspect it is, but that is up to Martin to decide. Adding in even a slight chance for three, and 90% chance to win, it is very favorable to take the risk now. Thinking ahead, Martin would consider Howard’s likely call on Richard’s last stone and his chances of blanking when that occurs.
What should Howard do? Perhaps placing the guard off-centre on the other side of the four foot and giving themselves an open shot at their stone may have provided more options for them. Depending where John’s stone landed, Rich would have a potential double or at least a hit to lie 2nd and 3rd with rocks in good position above the four foot. I am more inclined to have Rich hit and roll to lie two and take the chance Martin is unable to double them out for a blank. Worst case is you are 1 up coming home and 62% likely to win. I expect Glenn, like many teams, expect Martin to score his deuce more often than 40% - and this could weigh in his decision to play the 9th more aggressively than he may have given another opponent. I will continue to argue the case that Martin has no more than a slight advantage over 38% against a team of Howard’s ability. Our study of Grand Slam events supports this argument – but it remains an argument where some will always side against the numbers. Good luck to those who choose luck as the basis for their strategy.
20 Mar 2009 Kevin 0 comments
Jennifer Jones’ Team Canada rink made some interesting decisions in their round robin game against Ontario at the 2009 Scott Tournament of Hearts (Scotties). During the 6th end, Team Canada (TC), one down without hammer, could have chosen a more aggressive route during the latter part of the end. Instead of drawing around their opponent’s stones in front of the rings, they instead chose to hit the Ontario stone towards the back of the rings and play out the end as a blank. Was this the correct decision? Recall:
Statistics for Women’s Curling
| Ends Remaining* |
Tied with Hammer** |
Down 1 with Hammer |
Down 2 with Hammer |
Down 3 with Hammer |
Down 4 with Hammer |
Up 1 with Hammer |
Up 2 with Hammer |
Up 3 with Hammer |
|||
| 1 | 0.691 | 0.397 | 0.145 | 0.020 | 0.001 | 0.865 | 0.973 | 0.997 | |||
| 2 | 0.611 | 0.371 | 0.166 | 0.068 | 0.018 | 0.834 | 0.928 | 0.975 | |||
| 3 | 0.602 | 0.391 | 0.208 | 0.083 | 0.039 | 0.816 | 0.882 | 0.952 | |||
| 4 | 0.596 | 0.402 | 0.216 | 0.123 | 0.062 | 0.763 | 0.886 | 0.923 | |||
| 5 | 0.613 | 0.433 | 0.242 | 0.152 | 0.086 | 0.779 | 0.849 | 0.917 | |||
| 6 | 0.600 | 0.413 | 0.263 | 0.163 | 0.089 | 0.756 | 0.854 | 0.930 | |||
| 7 | 0.585 | 0.413 | 0.280 | 0.183 | 0.092 | 0.766 | 0.847 | 0.940 | |||
| 8 | 0.562 | 0.444 | 0.290 | 0.156 | 0.123 | 0.734 | 0.866 | 0.927 | |||
| 9 | 0.556 | 0.454 | 0.281 | 0.176 | 0.080 | ||||||
| * takes into account 8 and 10 end games | |||||||||||
| ** For 1 Ends Remaining includes extra end games | |||||||||||
Notice that if the end is blanked, TC has a 24% chance. At the beginning of the 6th they had a 22%. In fact, their odds get slightly better if the end is blanked.
If they play aggressive and steal, they increase their chances to 40%. Holding Ontario to one is 22%. In fact, a blank appears to be 2% better than actually forcing Ontario to a single point! It appears the risk of attempting a steal at this stage is not necessary.
What about in the next end? If it had been the 7th instead of 6th end, the decision is very different. Now, entering the 8th end when 1 down without hammer, the odds are only 18%. Holding Ontario to a single gives a 21% chance. A steal in 7 instead of 6 still leaves them 40% - no change. It would be more tempting to play the final rocks aggressively if it were the 7th end. If the 7th were to be blanked and TC is one down without hammer playing 8, it is imperative to either score a steal or force opponent to a single. When entering the final two ends 1 down without hammer, a teams chance drops to 16% - but more importantly, a steal in 9 gains less. A steal in 8 would produce a tie and a 39% chance, but a steal in the 9th to tie the game is only 30%.
The 5th and 8th Ends
Recall my previous article on Early, Middle and End Game. The Early Game is the first 4 (or 2) ends. At this stage, most top teams will play aggressive attempting to take control or dominant control as soon as possible. In the End Game (final 3 ends), teams will play the scoreboard more closely, attempting to be tied with hammer or two up without hammer in the final end of a close game. So what is Middle Game Strategy?
Middle Game is the 5th through 7th ends in a ten end game (or 3-5th in an 8 end game). Recalling my previous description, statistical changes start to appear in the middle game. Trends appear for each situation (tied with hammer, 1 up without, etc). So what are some considerations when determining our Middle Game Strategy?
The first decision is whether to continue aggressive play. This is usually the case early in each end, but as the end develops a team will choose shot calls based more on scoreboard and ends remaining before the End game. So to start discussion on Middle Game strategy, let’s start by examining which scenarios are more favorable in the End Game.
I will use a 10 end game from now on, the reduce complication. To transfer this analysis to an 8 end game, just subtract 2.
In the 9th End, one down with hammer is a disadvantage greater than any other point in the game. In fact, only the scenarios starting the 9th and 6th ends have tied without hammer the same (less than 1%) as one down with hammer. In all other cases, one down with hammer is preferred position. If we have the hammer in a close game the ends previous (5th and 8th), it allows us to take some additional risk with less penalty for being forced to a single point. Recall a Close game is one in which a team is down one with hammer anytime or tied prior to final two ends.
One down with hammer:
In the 5th and 8th ends we can aggressively play for two or three and if we are forced to one, our chances are actually the same as if we had blanked the end. If we instead are one down with hammer in other ends, if our aggression results in being held to one, we are worse than if we blanked the end.
One up without hammer:
Conversely, forcing our opponent to one in this situation (5th or 8th end) gains no advantage over blanking the end. The risk of playing aggressive to force our opponent to one, which may result in a deuce, provides no advantage – a steal is required to gain any advantage. Stealing in the 5th puts us at a 76% winning probability (Control). Stealing in the 8th an 85% chance (Dominant Control). Blanking 5 and then stealing in the 6th in fact gives us now an 80% chance. I’d suggest a sensible play is to tempt our opponent into blanking the 5th end and force our position without hammer in the next end. Blanking the 8th was discussed in our last article and is more open to debate.
Tied without hammer:
If we force our opponent to a single, we again gain no advantage to blanking. However, a steal is a significant advantage over our current position. For the 5th end, in our previous example (one up without) a steal takes us from a 61% chance to 76%. If we are tied and steal, we move from 39% to 61%. Using our analysis from the last article, switching from 39 to 61 is 50% better, whereas 61 to 76 is only 25% better. For the 8th end we go from 34 to 65 (91% better). It would appear we are more inclined to attempt to steal in this scenario. However, stealing is always difficult and we risk our opponent making a multiple score. We are forced to be more aggressive because of our position but being one down with hammer gives us an ability to be aggressive without the same risk.
Tied with hammer:
Being forced to one in the 5th or 8th end is no mathematically disadvantage. In all other ends, being held to one is a disadvantage over a blank. Again, per situation one down, we can be very aggressive at the risk of being held to one. However, as pointed out above, a steal is very bad for us in this position. In fact, a steal is very bad for us every time in this position. It is most critical in the 9th where we drop from 74% to 38%.
In every case, having hammer appears to be a greater advantage in this position. We can be aggressive without any risk of being “held to a single” as it is virtually no different mathematically from a blank.
So…what is our finding? In a close game, we’d prefer to have hammer in the 5th and 8th ends. We may in fact make decisions in the ends previous which will force this situation. For example, if we are tied playing the 4th with hammer and have an opportunity to blank, we are more inclined to take this route. If we are one up in the 4th or 7th, we should force our opponent into scoring, even at the risk of a deuce, in order to have hammer in following end. Eight end games become interesting because the advantage exists in the 3rd end. A team may even choose to tempt a blank if they are without hammer in the first end, to force their opponent to score in the second end, in order to have hammer in the third. This seems drastic and I’d suggest the advantage is not significant enough to “drop an end”. But further analysis might disprove my initial thinking.
Some readers may have noticed that there are two ends between the 5th and 8th. This means, without a blank or a steal, if we have hammer in one of these ends, our opponent has hammer in the other end. For example, say having hammer in the 5th when one down results in a deuce. We are now one up. If our opponent is held to one and then we are held to one, we are now one up without in the 8th end. However, if our opponent ties us in the 6th and we instead manage a blank in the 7th, we are now tied in the 8th with hammer.
I would not suggest this analysis should be a factor in how a team begins play in and end. The modern game does not allow a team to force a blank end at will. However, as an end develops we may be more inclined to “bail out” of certain ends in order to better position us in ends where we have greater advantage with hammer in a close game.
20 Feb 2009 Kevin 0 comments
There were several decisions made during the 6th and 7th ends of the 2009 BDO Quarterfinal between Glenn Howard and local favorite Kerry Burtnyk. This month I will attempt to breakdown some of the decisions and determine how math could be applied to each scenario or shot call to support or contradict the final decision.
At this stage, the game is tied 4 -4 and Howard has the hammer. The 6th end is, per my definition, the beginning of the “End Game” (see November 2008 article). Statistics indicate that Burtnyk at the beginning of the 6th end (in an 8 end game) has a 35% chance to win. (Math whizzes may have already guessed Howard has a 65% chance).
Let’s begin by reviewing the probabilities that Burtnyk will win, based on various outcomes of the 6th end (percentage chance to win with two ends remaining):
With two ends remaining:
Tied without hammer (Howard blanks 6th) = 34%
Down one with hammer (Howard takes 1 in 6th) = 35%
Down two with hammer (Howard takes two in 6th) = 15%
Up one without hammer (Burtnyk steals in 6th) = 65%
The numbers indicate that holding Howard to a single, in the 6th end, is in fact not much different than a blank. This is NOT the case if Howard is forced to one in the 7th, the difference is 25% (if Howard maintains hammer) to 38% (if he is forced to one).
A steal, however, is a great advantage in the 6th (65%). In fact, it is the most mathematically advantageous point in the game in which to be up one without. At all other times, chances are 61% or less.
Let’s ask a few questions:
Should Burtnyk play a centre guard or place the first stone in the four-foot?
In the game, Garth Smith placed the first stone in front of the rings. I would suggest this is the incorrect call…and here is why…
If Burtnyk places the first rock in the rings, should Howard play for a blank or attempt to score a deuce?
Howard now has to determine if he will play a corner guard, using hammer aggressively in an attempt to score two (or more) or instead play out a blank. We’ve seen above a blank is identical to a single point. In fact, if Howard plays out for a blank and noses his final stone, there is statistically no difference!
There are few skips at this level that would not prefer to force the issue while they have hammer with 3 ends remaining. The key reason: a deuce results in a high probability of winning. Two up without hammer during the End Game is as follows:
Two Up without hammer wins:
1 End remaining = 90%
2 Ends remaining = 85%
3 Ends remaining = 80%
4 Ends = 80%
All earlier ends = 74-75%
Howard’s only reason to wait to the next end is for a 5% advantage – IF he is able to score a deuce. Is the difference of 85 to 90% enough to make up for the risk of sacrificing an end with hammer? I don’t believe it is, and here is why. Recall my article from Dec 2008 describing a game as Close or one team being in Control or Dominant. A deuce in the 6th or 7th end results in a Dominant position for Howard.
For those who understand how chip values change in a Poker tournament, a similar analysis can be used here. In a poker tournament, as you collect chips, each additional chip’s “value” is less than those previously acquired. For those interested in understanding this better, read David Sklansky’s “Tournament Poker for Advanced Players”.
Each percentage point in probability of winning becomes less important, the higher your chances are. The difference between having a 50% chance versus 55% is more important that 85% to 90%. Another way to examine this is the advantage in the first scenario is 10% better, but in the latter it is only 5.8%. Some readers may also note the contrary is true. A team that is behind sees a greater benefit from small percentage changes. The advantage of a 15% chance over a 10% probability is 50% better!
If Howard blanks the 6th and either team scores one in the 7th, the game remains “Close”. He has essentially given up an opportunity to take a Dominant position; with very little risk of Burtnyk taking it at this stage (unlikely Kerry will steal two).
Also, recall that being forced to 1 is fine in the 6th but not the desired outcome in the 7th. Howard should be more inclined to be aggressive in 6 where a single is more advantageous, whereas in the 7th he would then much prefer a blank to being forced to a single point.
So….
Given that Howard would statistically prefer not to blank and Burtnyk is statistically indifferent, Kerry should place the rock in the four-foot. If Howard chooses not to play a corner guard, by not making the correct play he is giving some (however slight) advantage to Kerry. The outcome for Burtnyk is good positioning for a possible steal and reduced chance for a deuce or worse.
However…
All of this analysis does imply that a team prefers to place a stone and then place a guard (after the corner) – rather than having your opponent draw to the four-foot and then corner freezing to their stone (eliminating the placement of a corner guard). Burtnyk may prefer not to have a corner in play and prefers positioning stones to the middle of the rings, even if Howard initially has shot rock. I’d be very interested in the perspective of that discussion.
Burtnyk sits top eight (biting four-foot) and Howard sits to the side, biting the four, guarded by two of Kerry’s stones. Despite repeated rewinding on my Tivo, I could not determine who was shot. Howard also sits third and fourth.
Kerry called for a double run-back by Walchuk. He suggested it was either that or play the guard. The result was removal of the Howard stone and sitting two, but both guards were removed and Howard remained with 3rd and 4th shot. This call appeared to be conservative, attempting to lower the chance at 2 or 3 and increase the chances to force Howard to 1. A steal seemed very unlikely at that stage. It appeared a deuce was probable, but Richard missed his next shot. It is my opinion that, given the difficult position if Burtnyk gives up a deuce (15%), keeping the guards and pursuing a more aggressive strategy, with a higher chance at a steal would increase their chances to win. In either case, they were in a difficult spot. Making some very rough estimates of probable outcomes for both calls:
Double Run-back:
Howard take 1 = 60%
Howard take 2 = 30%
Blank = 10%
W = 28.6%
Guard
Howard take 1 = 50%
Howard take 2 = 40%
Burtnyk steal 1 = 10%
W = 30%
These estimates are highly debatable, given the number of rocks remaining. However, on the basis that a three or two has little difference at this stage (see my comments above regarding Dominant position). Kerry should be trying to avoid a deuce at all costs while also trying to steal (not an easy task). It is my opinion (perhaps not his or others) that removing the two guards greatly reduces a chance to steal and may in fact increase the chance for an easy deuce.
Kerry had an option to either draw around the centre guard and attempt a steal or remove the Howard stone and possibly roll behind cover and force Howard to a single. This is an interesting scenario. Per above, a steal is a significant advantage, but a deuce is also a huge risk at this stage of the game. A single by Howard or blank has virtually no difference mathematically. In fact, it was statistically irrelevant for Burtnyk to spend extra effort in attempting to roll their rock behind cover – either outcome produces the same mathematic result. Kerry might, however, determine an advantage to be either one down or tied. Also the added chance Glenn might miss his draw for one (however remote) could be considered a slight advantage in this situation. I want to stress that the mathematic analysis does not take into account other factors, ice conditions, opponent, etc, which Kerry may have considered.
Mathematically, how often would Kerry have to make a perfect draw for the steal attempt to be the correct call?
W = x(.65) + y(.35) + z(.15)
Where x = chance of a steal
y = chance Howard takes one
z = chance Howard scores two
We know Burtnyk’s hit results in a likelihood of 35%, set W = .35
.35 = x(.65) + y(.35) + z(.15)
Let’s choose a value for y and solve for x.
We estimate y = .3. That is, Howard will score one 30% of the time
Z = 1 – (x + y) = .7 – x
,35 = x(.65) + .3(.35) + (.7-x)(.15)
X = 28%
Conclusion, if Burtnyk believes Howard will likely take one 30% of the time, he needs to be successful with a steal > 28% in order to attempt the draw. If he actually believes Howard may only score a single half the time, it drops to 20%. If instead you assume no single and either a steal or a deuce, he must be successful stealing > 40%. Ultimately there are many factors, amount of curl and length of guard being most critical.
I found it interesting that, debating whether or not to attempt a steal is an unclear decision. Meanwhile, the very capable commentating team of Mike and Joan (ranking above their TSN counterparts, in my humble opinion) were instead focused on Burtnyk possibly drawing to the back or playing a roll in order to force Howard to one. As we’ve pointed out above, this decision has no statistical impact!
On Howard’s final stone, assuming Burtnyk’s rock was easily accessibly, should he draw for one or blank the end? As we’ve stated above, mathematically there is no difference. Ice conditions, your opponent and other factors would likely come into play.
I would be tempted to blank, but the decision is not as clear as some might suspect. Many teams could choose to draw for one and they may very well be correct. If your team can hit well and possibly clear the mess your opponent is likely to create in the 7th end, increasing potential for a blank in the 7th, blanking the 6th end might be your preference. If your team prefers aggression and is more comfortable forcing the issue without hammer, by all means take 1 in the 6th and attack in 7. Also, you may asses your opponent is stronger with hammer and would prefer to keep it. Or the opposite may be true, and their ability to set-up an end without hammer may be something you wish to avoid.
In the 7th end, Burtnyk was faced with another interesting decision. One down with hammer and a corner guard. No other rocks in play. Third’s first stone. Rather than attempt a deuce (and risk being held to one or surrender a steal) they chose to peel and play for a blank.
Blank results in Burtnyk being one down with hammer and one end remaining.
W = 38%
How often would Burtnyk need to score a deuce in order to attempt a draw, rather than blank.
Let’s assume that if they attempt a draw around the corner, a steal or blank will not occur. Either Burtnyk is forced to a single or he scored a deuce.
X = Burtnyk takes 1
Y = Burtnyk takes 2
.38 = x(.26) + y(.62)
x = 1 – y
.38 = (1-y)(.26) + (y)(.62)
y = 35%
Burtnyk will have to score a deuce greater than 35% of the time for the draw (rather than peel) to be correct. Some of our recent analysis indicates that top teams in fact win slightly more than 74% when tied in the final end. Combine this with some small chance of a steal, Burtnyk would need even greater confidence in his chances to score two.
Whew! That’s it for this month. Congrats and good wishes to Team Pahl (Alberta) and Team Lobel (Ontario) in qualifying for their respective provincials. And good luck to all readers of Curl with Math, whether you are chasing your first or fourteenth Purple Heart.
26 Jan 2009 Kevin 0 comments
We’ve finally gathered data for Women’s Curling events. This data is taken from 4-rock games played during Provincial, Scotties (i.e. Canadian National Championship), World Championships, Olympic Trials, Olympics and WCT events over the last several years. Unfortunately our sample size is larger (more than double) for the men’s events. However, we have enough numbers to give some indication of general trends and comparisons with the games of their opposite sex counterparts. So what do we find?
Statistics for Women’s Curling
| Ends Remaining* |
Tied with Hammer** |
Down 1 with Hammer |
Down 2 with Hammer |
Down 3 with Hammer |
Down 4 with Hammer |
| 1 | 0.691 | 0.397 | 0.145 | 0.020 | 0.001 |
| 2 | 0.611 | 0.371 | 0.166 | 0.068 | 0.018 |
| 3 | 0.602 | 0.391 | 0.208 | 0.083 | 0.039 |
| 4 | 0.596 | 0.402 | 0.216 | 0.123 | 0.062 |
| 5 | 0.613 | 0.433 | 0.242 | 0.152 | 0.086 |
| 6 | 0.600 | 0.413 | 0.263 | 0.163 | 0.089 |
| 7 | 0.585 | 0.413 | 0.280 | 0.183 | 0.092 |
| 8 | 0.562 | 0.444 | 0.290 | 0.156 | 0.123 |
| 9 | 0.556 | 0.454 | 0.281 | 0.176 | 0.080 |
| Ends Remaining* |
Up 1 with Hammer |
Up 2 with Hammer |
Up 3 with Hammer |
| 1 | 0.865 | 0.973 | 0.997 |
| 2 | 0.834 | 0.928 | 0.975 |
| 3 | 0.816 | 0.882 | 0.952 |
| 4 | 0.763 | 0.886 | 0.923 |
| 5 | 0.779 | 0.849 | 0.917 |
| 6 | 0.756 | 0.854 | 0.930 |
| 7 | 0.766 | 0.847 | 0.940 |
| 8 | 0.734 | 0.866 | 0.927 |
| 9 |
| * takes into account 8 and 10 end games | |
| ** For 1 Ends Remaining includes extra end games | |
Tied with Hammer
Within 1-2% of the men until the End Game (last 3 ends). During final ends, winning chances for women are 60, 61 and then 69% in the final end vs. 65, 66 and 75% for men.
1 Down with Hammer
Of all the scenarios, this is most similar to men’s numbers. Usually only 1-2% better chance for women to overcome the deficit of 1 down with hammer to win. Final three ends have same pattern: women’s is 39% to 37% to 39% (38, 35 and then 38% for men).
2 Down with Hammer
Women’s teams are again 1-2% more likely to win in this position except for the final end where data shows a 14.5% chance for a women’s team versus 10% chance for a men’s.
3 Down with Hammer
A 2-4% better chance for women’s team throughout the game.
Down 4 or more with hammer
Shows generally 2-4% increase in chance for women’s team.
1 Up with Hammer
A 2-3% better chance of holding this lead for men’s teams than for women’s.
2 Up with Hammer
Within 2-3 % early on but actually men’s teams hold on to win 4-6% more often from the Middle Game onward, with the exception of the final end where the difference is only 2%
3 Up or more with Hammer
Within 2-3 % early on but actually men’s teams hold on to win 4-6% more often during the Middle Game. The results from the End Game (final 3 ends) are nearly the same – you win nearly every time if you are in this spot.
What does this tell us about Women’s Curling?
Women’s teams tend to have a higher chance of coming back from a deficit and, subsequently, less chance of holding onto a lead. The difference is less noticeable in close games (tied or 1 up) and tends to widen as one team takes a more dominant position. That is, the greater the lead the greater the difference versus men’s teams in likelihood of a comeback. If we believe the ability to throw heavy peel weight successfully is the major difference in women’s and men’s games, then these numbers look much like what we would expect.
The most noticeable and important difference seen is the case of tied with hammer or down two with hammer in the final ends. The difference is about 5%. These numbers provide some support to determine how women’s teams might approach the game differently than men’s teams. For example, if tied with hammer with 3 or 2 ends remaining, a women’s team may be less inclined in blanking to retain hammer than in forcing a score. Tied with hammer is, during these ends, not a statistical advantage over 1 up without. In fact, with 2 ends remaining, women’s teams have a slight (2%) statistical edge in being 1 up without hammer! In the men’s game tied with hammer is an advantage of 3-4% with 3 ends remaining and 1% with 2 remaining.
What is Control?
A common term heard over drinks at curling rinks across the globe is “Control”. “If we make this shot for two that will put us in control”. “You had control from the 5th end on”. And, the most hated phrase “We had control the whole game and lost it at the end”. So, statistically speaking, what do we think is meant by “Control”?
I propose that there are actually three positions during a game a team can be in. If one is Control it follows that there must be another type of game that is closer than this, which I will call a “Close” game. It also then is reasonable to suggest there is a position where you are even better than in control, let’s call this “Dominant” position.
If we assign the game condition based on a probable outcome:
Close occurs when the odds for a win is no greater than 66% for either team. Another way to say this is the team behind has better than 2-1 odds of winning.
Control exists when one team has greater than 66% but less than 80% odds of winning. This range is between 2-1 odds and 4-1 odds for the team that is behind.
Dominant position is when one team holds a greater than 80% statistical chance of winning. Another way to show this is greater than 4-1 odds of a comeback.
Based on these numbers:
“Control” occurs when team is:
With three and four ends remaining, 2 up without hammer is right at 79 and 80% respectively. With two or fewer ends left, you are Dominant in this position. When statistically in “Control” Up 1 with hammer, you are between 77 to 80%, with the exception of the third end in a ten end game where your chances are 75%.
“Close” position occurs when a team is:
When tied with hammer and 2 ends remaining, chance of winning is exactly 66% - so we could argue whether a team has Control at this stage or it is Close.
“Dominant” position occurs at any other score during the game.
We can start to analyze our pre-game and in-game strategy using the definitions of Control, Close and Dominant. I’d also suggest incorporating the definitions for which section of the game, based on Early, Middle and End Game (from article of Nov 2008, “Is Curling a Battle For Hammer?”). Recall the End Game is the final 3 ends and extra end if required. The Middle Game is the middle 3 ends and the Early game is then either 4 ends for a 10 end game or 2 ends for an 8 end match.
Using this model creates the following 9 game scenarios:
Early-Close
Early-Control
Early-Dominant
Middle-Close
Middle-Control
Middle-Dominant
End-Close
End-Control
End-Dominant
I’d suggest teams could use this model as a way to develop pre-game strategies for how to approach each of these positions. I might even tack a stab at examining these, but that will have to be left for another article…
Statistics for Grand Slams
Watching the Masters a short while ago (except the semi’s which were on the BOLD network –wherever that is), I started to question the statistical basis we are using and see if there are some discrepancies for the Slam events versus the entire dataset for all WCT (including Slams), Olympics, Olympic Trials, Brier, Worlds and Provincials. Our data size is still very small but I wanted to get a general sense if we saw any differences. Tied with hammer in final or extra end is currently nearly 80% for Slams versus 75%. 1 down with hammer in 9 was 39%, close to our baseline of 38%. Down two with hammer was about 12% versus 10%. The only major difference appears to be tied with hammer. The Slams numbers are based on sample size of about 270, compared to over 3000 in our full dataset. Assuming that Grand Slam teams are generally stronger than the other fields; does this mean better teams win more than 75% when tied with hammer? Possibly yes, but difficult to say for certain without a larger sample.
If Martin played Howard a single end game 20,000 times, each team having hammer for 10,000, what do you think the percentages would look like?
26 Nov 2008 Kevin 0 comments
Back during the era of the Grand Old Game; before push brooms, The Ryan Express and Shorty Jenkins ice moved us all to Free-Guard Zone; it was often heard at most every club by players at every level (of play and inebriation) that “Curling is a battle for the hammer”. To some degree this may have been true, though the strategies of teams like Savage and Werenich, Burtnyk and Olson and the Howard brothers opposed this mentality with their aggressive play. Rather than “Take 2 then Give 1”, these Superteams preferred to put constant pressure, take many and then steal until the opponent shook hands.
The question I raise is, in Today’s 4-rock game, is it still possible that Curling can be a Battle for Hammer? In my analysis, I will touch on several areas and provide some data which may help us find and answer.
The Hammer Advantage
Starting with hammer is an advantage. We know this because every time your team wins the toss, you don’t think too long about whether or not to choose stone colour. I expect some Ontario folks will shout out “I remember this one time so and so knew the rocks were bad and chose colour instead of hammer” – but I expect this is not a common occurrence.
The “draw to middle” or pre-selecting number of games in a round-robin where teams get hammer also indicates its importance.
We also have some data which tells us how often the team beginning with hammer wins. Unfortunately not all events keep proper track of who started the game with hammer and our sample size is not as large as we would like. One way to take a sample of data is looking at 10 end games that are tied after 2 ends (i.e. now an 8 end game). Our results show us a 61% winning percentage.
This doesn’t tell us much more than we already know, except to help us understand if 8-end games are fair. That is not, however, the purpose of this article (though we may return to this idea).
The Early Game
I believe Curling, sometimes called “Chess on Ice”, has an Early, Middle and an End Game (no pun intended, honest). End Game is the final 3 ends and extra end if required. The Middle Game is the middle 3 ends and the Early game is then either 4 ends for a 10 end game or 2 ends for an 8 end match. I haven’t chosen these game sections based on my best guess or what I’d like them to be, I’ve looked at the numbers and they reveal something very interesting:
The Odds of winning at the completion of each end during the Early game is nearly equal.
This is a fascinating discovery that not only explains why the Early Game doesn’t end until 6 ends remain in the game, but supports the theory that an 8 end game is competitively equal to a 10 end game. If you extrapolate the numbers, we might be even safe in assuming 12 ends or even 14 would also have the same outcome. The only benefit of a longer game (other than perhaps more beverage sales to the fans) is that the more ends played, the greater advantage a stronger team will have over a weaker team. The analysis behind that theory is not the purpose of this discussion, so back to where we were…
Middle Game
Odds of winning during the Middle Game start to trend in a specific direction.
End Game
Odds of winning in during the End Game trend steeply in one direction. The exception is 1 down with hammer, which drops then rises before the final end.
I have a graph which best shows this trend, but am unable to figure out how to insert it this blog. So, you’ll have to read into this chart to see what I mean….
| Score |
|
|
|
Ends Remaining |
|
|
|
||
| 9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
|
| Tied with hammer |
0.602 | 0.612 | 0.607 | 0.619 | 0.613 | 0.625 | 0.648 | 0.662 | 0.743 |
| 1 down with hammer |
0.429 | 0.421 | 0.422 | 0.428 | 0.393 | 0.407 | 0.383 | 0.347 | 0.383 |
| 2 down with hammer |
0.272 | 0.264 | 0.262 | 0.245 | 0.243 | 0.200 | 0.206 | 0.146 | 0.104 |
| 3 down with hammer |
0.147 | 0.146 | 0.149 | 0.129 | 0.113 | 0.096 | 0.068 | 0.046 | 0.010 |
| 4 down with hammer |
0.092 | 0.067 | 0.075 | 0.053 | 0.042 | 0.037 | 0.019 | 0.010 | 0.001 |
| 1 up with hammer |
0.751 | 0.783 | 0.770 | 0.801 | 0.788 | 0.835 | 0.868 | 0.896 | |
| 2 up with hammer |
0.868 | 0.899 | 0.883 | 0.894 | 0.930 | 0.943 | 0.967 | 0.989 | |
| 3 up with hammer |
0.882 | 0.942 | 0.957 | 0.957 | 0.979 | 0.985 | 0.993 | 0.998 | |
Some comments:
Tied with hammer: Winning percentage is within 60-62% until 3 ends remain where it jumps more dramatically to 65%. That is, a tie game has nearly the same statistical outcome for all ends until the End Game is reached (starting the 6th or 8th).
1 down with hammer: Maintained around 42-43% until 5 ends remain, where drops to 39% in the Middle Game. It then rises back over 40% and during the End Game, 1 down winning percentage drops to 38%, then down below 35% and back above 38%. This phenomenon was discussed in the article “To go for two… or not? Masters of Curling final: Howard vs. Ferbey” from Black Book of Curling 2007-08.
Two down with hammer shows 27 to 26 % during Early Game than a drop below 25% beginning the Middle Game and a drastic drop to 20% with 4 ends remaining.
3 down with hammer: Stays around 15% until 6 ends remain then drop to 13%, then flat at 11 to 10% with another drastic drop beginning the End Game of below 7%.
1 up with hammer: Stays fairly constant, from 75% then leveling in the range of 77-80% until the End Game begins and it jumps to 84%.
The other scenarios are not as common, but do have some interesting results:
4 down with hammer: Transitions, oddly enough: 9-7-7-5-4-3-2-1-0%. Short answer – don’t be 4 down after the Early Game or you’re screwed.
2 up with hammer: 87-90% until we reach the final stage of the Middle Game (93%).
3 up with hammer: In an 8-end game, anytime you are in this position you shouldn’t lose. In a 10 end game – just get past the 3rd and it would take a monumental collapse to lose (though we’ve all been there once or twice).
Battle For Hammer?
To try to answer our original question, we need to define what is meant by “Battle for the Hammer”.
Let’s assume “Battle for Hammer” implies a team which starts with hammer wishes to keep it and the opposition is trying to gain that position (tied with hammer). The advantage of tied with hammer is only slight, roughly 60 to 40, until the End Game. Teams who win 60% of their games don’t often place high in the money and they certainly don’t win Briers or Olympic Gold. We don’t gain a substantial position until the final end, where we still lose 1 of every 4 games. By this definition, I’d suggest Curling is not a Battle for Hammer.
Now, if assume we this phrase to mean a battle to gain hammer with the lead, then it could be argued Curling is a Battle for Hammer. 1 up with hammer with 8 ends remaining is the same as tied with hammer at the end of the game (75%)! Having hammer with a lead of 2 or more points is very strong. It is preferred to 3 up without during every stage of a game, except for the final end where both positions are equal.
How Important is the Hammer?
So how do we begin to analyze the importance of last rock? At any time during a game we can determine its statistical value. We’ve determined that leading with hammer is a strong position, stronger than being further ahead without hammer. But by how much? Let’s compare tied and 1 up without, 1 up with and 2 up without, and 2 up with versus 3 up without.
Tied with hammer vs. 1 up without hammer
Often, in a tie game, when a team is forced to 1 we state the opposition has done their job and taken away control. However, stats show us that there is only a small difference between tied or 1 up without
| Score |
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Ends Remaining |
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| 9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
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| Tied with hammer |
0.602 | 0.612 | 0.607 | 0.619 | 0.613 | 0.625 | 0.648 | 0.662 | 0.743 |
| 1 up without hammer |
0.571 | 0.579 | 0.578 | 0.572 | 0.607 | 0.593 | 0.617 | 0.653 | 0.617 |
During the Early Game the difference is about 2-3%. It jumps to 5% at the beginning of the 5th end, or Middle Game. Then ranges between 0-3% until the last end where it jumps to 12% advantage for tied with hammer.
1 up with hammer vs. 2 up without hammer
| Score |
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Ends Remaining |
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| 9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
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| 2 up without hammer |
0.728 | 0.736 | 0.738 | 0.755 | 0.757 | 0.800 | 0.794 | 0.854 | 0.896 |
| 1 up with hammer |
0.751 | 0.783 | 0.770 | 0.801 | 0.788 | 0.835 | 0.868 | 0.896 | |
When 1 up with hammer you are stronger than 2 up without by 2-4% until 4 ends remain, where it reverses to 1% advantage when 2 up, then back to advantage of 4% to 2% then 0% for the final end.
2 up with hammer vs. 3 up without hammer
| Score |
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Ends Remaining |
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| 9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
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| 3 up without hammer |
0.853 | 0.854 | 0.851 | 0.871 | 0.887 | 0.904 | 0.932 | 0.954 | 0.990 |
| 2 up with hammer |
0.868 | 0.899 | 0.883 | 0.894 | 0.930 | 0.943 | 0.967 | 0.989 | |
Again, up with hammer is slight advantage, usually only 1% with the exception of 7 or 4 ends remaining where it is 3-4%. In real terms, these two positions are essentially equal.
So, what does this mean?
There is clearly not a significant difference in each of these scenarios. In each case having hammer while up is a slight advantage, but usually only 2-4%. Therefore, I disagree with the theory that Curling is a Battle for Hammer. Take, for example, an 8-end game where you have hammer and are held to one in the first end. Instead of having a 60% winning percentage you drop to 58%. Your position is in fact not much different than where you were at the beginning of the game. Much more significant is to have a shot for one and instead give up a steal in the first end, going from 58% to 42%.
Interesting to point out that often when the team without hammer holds the opposition to one in the first end it is perceived they have “won” the end or done their job. In reality, they have only gained a 2% advantage from where they were. More correct perhaps to state they have successfully “avoided” the position of falling behind by two or more.
Next article I will be revealing data on the Women’s Game and also attempt to tackle the question of what is “Control”.
26 Oct 2008 Kevin 0 comments
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