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Heh, well, what I did is a little complicated, but I think it's about the best you can do for a set of bots that each have their own distributions. Basically I run 1,000 or whatever random simulations of the overall score, based on the averages / standard deviations of each individual bot's score distribution. Then I can take those "overall score" samples, supposedly generated from the same distribution as the real scores, and use them as additional samples to calculate the confidence interval of the overall score. It's a fairly basic Monte Carlo method.