Wednesday, February 08, 2017
Do Markov chains work in baseball?
?Something interesting came as a result of the Patriots comeback, where the "models" had them at 99.5%+ of losing at their peak, and 95%+ at the half, while the bettors had them at under 90% at the half.
The way the BASIC models work is very simple math: just use a transition matrix for various situations that do NOT consider the score, nor the time remaining. This is the way I do it for baseball. But I must admit, I never actually tested it.
In football, we may consider that if a team has a 21+ point lead that the two teams are going to play radically different. I know this is somewhat true in hockey, where the team that is DOWN by 2 goals is more likely to score the next goal then the team that is up by 2. This happens because the leading team giving up a goal (so they are only up by 1) costs more than the leading team gaining a third goal. So, what they basically want to do is reduce the goals they allow by say 20%, at the cost of themselves scoring by say 30%. It's a "small ball" kind of tactic. At the same time, the team that is behind want to increase the goals they score by 20% even if it means increasing the goals they allow by 30%. The net effect is that it does NOT cancel out.
So, we know hockey teams play differently. We suspect that maybe football teams play differently, hence the idea that the Patriots had a 99.5% chance of winning is probably wrong. Indeed, someone tweeted out that when you look at teams where the model said they had a greater than 95% chance of winning, they actually ended up winning less than 90% of the time. The models, therefore, were too basic.
How about baseball? Well, that was a great idea, so I applied it to baseball, 2010-2016. I looked for all games where the home team FIRST had a 95%+ chance of winning, prior to the 5th inning. Remember, my Markov chain is based just on the run expectancy, and so, is unaware of the change of strategy. Does it matter? So, there were 1122 games that met the criteria. The average estimated win probability was 0.958. The actual number of wins was 1082 and actual losses was 40, for a win% of 0.964. So, that one works.
How about a 99%+ chance of winning, in the 8th or later innings? The average estimated was 0.994 The actual was 4268 wins and 11 losses, for an actual of 0.997.
It seems therefore that in baseball, when we say that the chance of a comeback is 99%, we actually do mean it is 99%.
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