I've been experimenting in Poker Tracker using the Wilson Score Interval formula to show ranges on my HUD instead of the actual percentages. My reasoning is that it provides a more accurate indication of how significant the sample size on an opponent is.
For example, someone with a 30 VPIP of 10 hands of data might be shown with a VPIP of 20-40, where as someone with 2k hands might be 28-32 (I haven't calculated what would actually be shown - yes, I'm lazy)
My only issue with this is the one as stated on Wikipedia, being that the central point is a weighted average of .5 and the actual proportion (with the weight of .5 being reduced as the sample size increases). I would prefer that, instead of using .5, the average of the stat is used instead (e.g., something like .25 for VPIP).
Is there a way to modify the Wilson Score Interval to achieve this?
I did try messing with the numbers a little, but this usually resulted in impossible ranges (e.g., negative numbers).
I've been experimenting in Poker Tracker using the Wilson Score Interval formula to show ranges on my HUD instead of the actual percentages. My reasoning is that it provides a more accurate indication of how significant the sample size on an opponent is.
For example, someone with a 30 VPIP of 10 hands of data might be shown with a VPIP of 20-40, where as someone with 2k hands might be 28-32 (I haven't calculated what would actually be shown - yes, I'm lazy)
My only issue with this is the one as stated on Wikipedia, being that the central point is a weighted average of .5 and the actual proportion (with the weight of .5 being reduced as the sample size increases). I would prefer that, instead of using .5, the average of the stat is used instead (e.g., something like .25 for VPIP).
Is there a way to modify the Wilson Score Interval to achieve this?
I did try messing with the numbers a little, but this usually resulted in impossible ranges (e.g., negative numbers).
You don't need to make that modification. The purpose of the .5 is so when you have say 3 hands of data and the player has bet 0 hands you don't get an interval centered at 0 or if he bets all 3 intervals so you don't get an interval centered at 1. Once the sample size has increased the affect of the .5 is quickly swamped out by the actual proportion. If this still bothers you though why don't you consider just using a confidence interval. As long as the vpip isnt close to 0 or 1 that should work just as well.
As mkelly000 says, the constant doesn't make much difference. However the reason for using a weighted average between the observed fraction and 0.5 is not that you believe 0.5 is the central value for the population.
The reason is that the closer a true proportion is to 0.5, the larger the standard deviation of observed proportions. For example, suppose you observe 3 successes out of 10 trials. If the true probability of success is 0.2, you have a 20% chance of observing 3 out of 10. You have the same 20% probability if the true probability of success is 0.41476. Therefore, if you're creating a confidence interval for the two proportions, it makes sense to center the interval not on the observed proportion (0.3 in this case), but on something closer to 0.5. This is true whether or not you expect the true proportion to be close to 0.25 or 0.5 or anything else.
If you do have an expectation about the true value, you can form a Bayesian confidence interval. This will typically center around (x + a) / (n + b) where x is your number of successes, n is your number of trials, a/b is your expected true proportion before you made the observations and the size of a and b indicate how much weight you put on your prior belief (big numbers mean you were pretty sure the true probability was near a/b and the sample evidence doesn't weigh much in your beliefs, small numbers means you had only a weak prior assumption and even a small sample can change your beliefs significantly).
The reason is that the closer a true proportion is to 0.5, the larger the standard deviation of observed proportions. For example, suppose you observe 3 successes out of 10 trials. If the true probability of success is 0.2, you have a 20% chance of observing 3 out of 10. You have the same 20% probability if the true probability of success is 0.41476. Therefore, if you're creating a confidence interval for the two proportions, it makes sense to center the interval not on the observed proportion (0.3 in this case), but on something closer to 0.5. This is true whether or not you expect the true proportion to be close to 0.25 or 0.5 or anything else.
Thanks for the explanation. Now that I know this the .5 doesn't bother me
Quote:
If you do have an expectation about the true value, you can form a Bayesian confidence interval. This will typically center around (x + a) / (n + b) where x is your number of successes, n is your number of trials, a/b is your expected true proportion before you made the observations and the size of a and b indicate how much weight you put on your prior belief (big numbers mean you were pretty sure the true probability was near a/b and the sample evidence doesn't weigh much in your beliefs, small numbers means you had only a weak prior assumption and even a small sample can change your beliefs significantly).
From what I had found I think Bayesian confidence intervals are what I want, but unfortunately I couldn't find a way to calculate these in Poker Tracker.
If this still bothers you though why don't you consider just using a confidence interval. As long as the vpip isnt close to 0 or 1 that should work just as well.
Something like preflop 3bet% that can have values somewhere around 4% were one of the reasons for choosing the Wilson Score Interval. From what I read, it seemed to be preferred for small sample sizes or extreme values.
But, I guess there's no reason I have to use the same formula for all stats.
I've been experimenting in Poker Tracker using the Wilson Score Interval formula to show ranges on my HUD instead of the actual percentages. My reasoning is that it provides a more accurate indication of how significant the sample size on an opponent is.
For example, someone with a 30 VPIP of 10 hands of data might be shown with a VPIP of 20-40, where as someone with 2k hands might be 28-32 (I haven't calculated what would actually be shown - yes, I'm lazy)
My only issue with this is the one as stated on Wikipedia, being that the central point is a weighted average of .5 and the actual proportion (with the weight of .5 being reduced as the sample size increases). I would prefer that, instead of using .5, the average of the stat is used instead (e.g., something like .25 for VPIP).
Is there a way to modify the Wilson Score Interval to achieve this?
I did try messing with the numbers a little, but this usually resulted in impossible ranges (e.g., negative numbers).
This interests me, but how do you get the HUD to display ranges?
This interests me, but how do you get the HUD to display ranges?
You need to create custom stats.
For example, I have custom variables var_vpip_upper, var_vpip_lower that use the Wilson Score Interval to calculate the upper/lower bounds. Then a custom statistic where this is the format expression:
