weighting population results

[Vern]

Background: Over on the PokerTracker forums we are discussing using actual population measured observations of stats to determine the average and standard deviation for players when making autorating rules. When taking these measurements of population though, what would be the appropriate way to weight results based upon hand count.

Example, I have two players in the database, one with ~10K hands and one with ~200 hands and I want to find the populations average VP$IP. Do I attribute greater weight to the first player because of the increased 'accuracy' of their observed stats being independant of the cards dealt?

From my perspective, when rating players, I think it would be more valuable to rate players after they attain a level of hands where I feel card randomness has become such a small fraction of the result that I can rely upon the result. In the example provided, 200 hands is more than enough to measure a player's VP$IP, but not measure their Won $ at Showdown to meet that standard.

I however am admittedly a stats novice, so I have posted here in hopes of enlightenment. Thanks in advance to anyone who takes the time answer.

Vern

[gaming_mouse]

The avg of the sample means is still the maximum liklihood estimate of the population mean (i'm pretty sure).

Weighting the value here wouldn't really make sense. You are essentially saying that having more hands on the first player makes it more likely that the second player is like the first player -- which just isn't true.

The difference in hands does, however, effect the overall accuracy of you estimate of the population mean. Remember that the variance of the sum of two indepenent random variables is the sum of their variances. So it would come into play when calculating a C.I. for your estimate, eg.