[BruceZ]

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And since you were picky about me using a 2-sided t-test (my range, btw, was from a 1-sided t-test but I used a conservative 20BB estimate just to impose more restriction),

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I actually figured out that was probably what you did after it was too late to take down my post. Many people fail to make this adjustment correctly, and for them this isn't picky. It is fundamental and significant.


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I will be picky about you referring to it as my 1-sided Confidence Interval. T tests might have a nice CI representation but the test itself is against a 5% upper tail critical region.

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There is a fundamental equivalence between hypothesis testing and confidence intervals (DeGroot p. 482). The null hypothesis that the win rate is negative is called a 1-sided alternative, as opposed to a null hypothesis that the win rate lies between two bounds, which would be a 2-sided alternative. Rejecting the 1-sided hypothesis at the 5% level is equivalent to saying that the interval from 0 to +infinity is a 95% confidence interval for the win rate. This is what I meant by 1-sided confidence interval, so that 0 corresponds to 1.65 SD below the mean, and 95% corresponds to the area under the bell curve from 1.65 SD below the mean to +infinity, instead of the mean +/- 2 SD for a 2-sided alternative.