3 ms·

Can you describe how/why a bayes approach would work better than frequentist in situation like NFL?

PaulRobinson 7y ago
The frequentist approach states (in simple terms), the observations I have made will help me predict future outcomes, because they are a good measure of the inherent probabilities inherent in what I'm observing. The bayesian approach says the data is fixed, and the probabilities might change. If I look at the stats for the NE Patriots, for example (http://www.nfl.com/teams/newenglandpatriots/statistics?team=NE http://www.nfl.com/teams/newenglandpatriots/statistics?team=...) I see that their first down conversion rate is 30/56 so 53%. Imagine I am watching a game and I am betting in play. I am offered odds of 1.9 (decimal odds) that they will convert the third down they are about to try and convert into a first down. The frequentist approach says given the implied odds of past behaviour is 1.88 (we can convert percentages into decimal odds by dividing 100 by the percentage, so 100/53 = 1.88), and I am being offered 1.9, I should bet! Kelly says I should bet 0.78% of my bankroll, as I have an edge here. Now, does that make sense to you? 30/56 is what happened in the past, and we're using that as an indicator as to what to do next. Would you take that bet? The problem with this approach, I think, is that frequentist approaches whilst practical assume there is an underlying probability we can uncover by measuring it. The Bayesian approach (in simple terms), says we can't be that precise, and the probabilities change over time based on the context. This makes more intuitive sense: the probabilities in poker are fixed and calculable, it seems to me they are much less so in NFL games. In the Bayesian approach, we broadly need to think of a probability distribution and understand our confidence interval, and we use priors and observations to help us calculate both. Doing some maths we might say the chance of the Patriots getting the third down conversion is with 95% confidence the chance of between 51.5% and 54.5%. Well, now the 1.9 on offer isn't quite so sweet - it's within the confidence interval, albeit off to the edge. Getting to that distribution and narrowing your confidence interval (it would be great if we could say it was 52.8% to 52.9%, for example), and then figuring out how to use Kelly accordingly, is relatively state of the art. Doing this in the NFL might be tricky because the data sizes are relatively small - the confidence intervals might be too broad. Also, the frequentist approach is provenly useful in some situations: Bill Benter is richer than either of us, and I don't believe he ever used bayesian statistics. People often think of gamblers as slightly grimy/shady characters with a gold chain and a wad of bills in their hand. That might happen, but all the ones I speak to spend their weekends reading PhD theses from maths and finance departments where people have been trying to figure out this stuff. I hope this answer gives you a flavour.
- audiometry 7y ago
  Yeah this is interesting, thanks. I might be mis-reading your answer, but would it be fair to (over?) simplify it to "bayesian estimates are frequentist estimates + confidence intervals around them?"

The frequentist approach states (in simple terms), the observations I have made will help me predict future outcomes, because they are a good measure of the inherent probabilities inherent in what I'm observing. The bayesian approach says the data is fixed, and the probabilities might change. If I look at the stats for the NE Patriots, for example (http://www.nfl.com/teams/newenglandpatriots/statistics?team=NE http://www.nfl.com/teams/newenglandpatriots/statistics?team=...) I see that their first down conversion rate is 30/56 so 53%. Imagine I am watching a game and I am betting in play. I am offered odds of 1.9 (decimal odds) that they will convert the third down they are about to try and convert into a first down. The frequentist approach says given the implied odds of past behaviour is 1.88 (we can convert percentages into decimal odds by dividing 100 by the percentage, so 100/53 = 1.88), and I am being offered 1.9, I should bet! Kelly says I should bet 0.78% of my bankroll, as I have an edge here. Now, does that make sense to you? 30/56 is what happened in the past, and we're using that as an indicator as to what to do next. Would you take that bet? The problem with this approach, I think, is that frequentist approaches whilst practical assume there is an underlying probability we can uncover by measuring it. The Bayesian approach (in simple terms), says we can't be that precise, and the probabilities change over time based on the context. This makes more intuitive sense: the probabilities in poker are fixed and calculable, it seems to me they are much less so in NFL games. In the Bayesian approach, we broadly need to think of a probability distribution and understand our confidence interval, and we use priors and observations to help us calculate both. Doing some maths we might say the chance of the Patriots getting the third down conversion is with 95% confidence the chance of between 51.5% and 54.5%. Well, now the 1.9 on offer isn't quite so sweet - it's within the confidence interval, albeit off to the edge. Getting to that distribution and narrowing your confidence interval (it would be great if we could say it was 52.8% to 52.9%, for example), and then figuring out how to use Kelly accordingly, is relatively state of the art. Doing this in the NFL might be tricky because the data sizes are relatively small - the confidence intervals might be too broad. Also, the frequentist approach is provenly useful in some situations: Bill Benter is richer than either of us, and I don't believe he ever used bayesian statistics. People often think of gamblers as slightly grimy/shady characters with a gold chain and a wad of bills in their hand. That might happen, but all the ones I speak to spend their weekends reading PhD theses from maths and finance departments where people have been trying to figure out this stuff. I hope this answer gives you a flavour.

audiometry 7y ago
Yeah this is interesting, thanks. I might be mis-reading your answer, but would it be fair to (over?) simplify it to "bayesian estimates are frequentist estimates + confidence intervals around them?"