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Tuesday, March 17, 2009

Brier Notes: Martin’s Math Test

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

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

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

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

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

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

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

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

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

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

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

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

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

Z = .281

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

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

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

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

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