Skill ICM Model

[sledghammer]

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I have run into one small problem with the equation thus far but it has to do with the distribution of proportions. I'll have the kinks worked out in a day or two hopefully.

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I think your problem right now is that you are using standard deviation of the binomial win column, and it isn't close to normally distributed. Ordinarily that wouldn't be a problem (because your dataset is so large), but the positive events(wins) are so rare that your large sample size might not be able to make up for it. Might not be a problem since it seems you got reasonable numbers.

A way to get a confidence interval without finding the actual variance is to run a simulation. Take your tournament player # column, invert it and multiply that by your winratio to get your win chance for each tournament. Then run a simulation that goes through and sees how many tournaments you win, given each win chance. Find the resulting winratio for each. Run the simulation 10k times at least, and see what the distribution of your winratio's looks like. Cut off the bottom and top 2.5%, and you have your CI for winratio.

I tried to come up with a non-empirical way to find it, using pk(1-pk) [where p is even win chance, k is winratio] for the variance of each row, and then combining them into a final variance, but I ran into some problems.