How much evidence does it take for you to accept 3:2 odds that your team will win the match given your prior understanding of each team’s performance at various stages of a game?
So I actually have this idea of doing a series (or just a couple) of top level posts about rationality and basketball (or sports in general). I’m partly holding off because I’m worried that the rationality aspects are too basic and obvious and no one else will care about the basketball parts.
But sports are great for talking about rationality because there is never an ambiguity about the results of our predictions and because there are just bucket-loads of data to work with. On the other hand, a surprising about of irrationality can be still be found even in professional leagues where being wrong means losing money.
Anyway, to answer your question: You get two kinds of information from play at the beginning of the game: First, you get information about what the final score will be from the points that have been scored already. So if my team is up 10 points the other team needs to score 11 more points over the remainder of the game in order to win. The less time remaining in the game the more significant this gets. The other kind of information is information about how the teams are playing that day. But if a team is playing significantly better or worse than you would have predicted coming in, their performance is most likely just noise. Regression to the mean is what should be expected. So my prediction of a team’s performance for the remainder of some game is going to be dominated by my priors (which hopefully are pretty sophisticated and based on a lot of data, for college basketball I start here and then adjust for a couple things that can’t be taken into account by that model (the way individual players match up against each other, injuries, any information about the teams’ mental states, etc.)
If you have all this information you can actually give, at any point during a game, the odds for you winning (there are a couple other factors that need to be considered as well, in particular you need to estimate how many possessions there will be in the rest of the game because the information we have about team performance is per/possession not per minute). I’ve also ignored fan attendance in this comment but that is really important evidence as well. I ended up attending the game in person and when I arrived I realized the venue included at least as many fans of the other team as there were fans of my team—and right there the probability my team was going to win dropped by 10%.
How much evidence does it take for you to accept 3:2 odds that your team will win the match given your prior understanding of each team’s performance at various stages of a game?
So I actually have this idea of doing a series (or just a couple) of top level posts about rationality and basketball (or sports in general). I’m partly holding off because I’m worried that the rationality aspects are too basic and obvious and no one else will care about the basketball parts.
But sports are great for talking about rationality because there is never an ambiguity about the results of our predictions and because there are just bucket-loads of data to work with. On the other hand, a surprising about of irrationality can be still be found even in professional leagues where being wrong means losing money.
Anyway, to answer your question: You get two kinds of information from play at the beginning of the game: First, you get information about what the final score will be from the points that have been scored already. So if my team is up 10 points the other team needs to score 11 more points over the remainder of the game in order to win. The less time remaining in the game the more significant this gets. The other kind of information is information about how the teams are playing that day. But if a team is playing significantly better or worse than you would have predicted coming in, their performance is most likely just noise. Regression to the mean is what should be expected. So my prediction of a team’s performance for the remainder of some game is going to be dominated by my priors (which hopefully are pretty sophisticated and based on a lot of data, for college basketball I start here and then adjust for a couple things that can’t be taken into account by that model (the way individual players match up against each other, injuries, any information about the teams’ mental states, etc.)
If you have all this information you can actually give, at any point during a game, the odds for you winning (there are a couple other factors that need to be considered as well, in particular you need to estimate how many possessions there will be in the rest of the game because the information we have about team performance is per/possession not per minute). I’ve also ignored fan attendance in this comment but that is really important evidence as well. I ended up attending the game in person and when I arrived I realized the venue included at least as many fans of the other team as there were fans of my team—and right there the probability my team was going to win dropped by 10%.