Re: Ribbit\'s Edits
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So the question for me is, does the SD calculated for every hand accurately model the SD of the big pots?
It should be fairly obvious that the SD in poker is highly dependent on the frequency and size of large pot events. As such, I think it's a reasonable parameter to use. Furthermore, it's fairly well established that SD is relatively easy to estimate.
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Focusing on the big pots is good, but you are looking at the wrong metric (and using the wrong type of statistics).
Let's look at two players. Both have the same number of "big" pots and all are of equal size. However, Player A has 65% of his big pots positive while Player B has just 35% of his big pots positive. Both will have roughly the same SD.
On another point, standard winrate analysis takes too much into account all the pots the player does not win or lose much on, i.e. most pots (99% or more).
A golden rule of statistical analysis is that you must take into account, i.e. not ignore, all variance possible. The variance associated with hands you don't play is clearly different from the variance associated with the big pot hands. It must be dealt with separately.
Going back to my highway example, I'll modify the situation. Let's make it a north-south 16 lane highway. You have a small number of cars traveling really fast going north, a small number of cars traveling south, and then you have a whole bunch of cars stopped or going really slowly. If you want to understand the net movement of cars over a whole week, but you only measure a 10 minute sample, I hypothesize that the most accurate thing is to break down the groups and analyze each separate group using more than just calculating average movement and variance (stdev). Then, and only then, can you come back and make a better guess at the population mean.
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