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Rollout

Posted By: Bob Koca
Date: Sunday, 9 November 2008, at 7:10 p.m.

In Response To: Rollout (Stick)

68 - 95 - 99.7 are approximations for 1, 2, and 3 standard deviations.

The interpretation of exactly what it means is more subtle than people think but thinking like Stick did is for practical purposes close enough. A correct interpretation would be: Assuming that the plays are actually equal there is a probsability P that the results would not favor by chance one play by as much as the RO did. The value P is obtained from P(absolute value of X < JSD) where x has a N(0,1) distribution.

Here is an example where Stick's interpretation would send you wrong. Suppose that you are quite sure that play A is better than play B but check it anyways. The RO supports this and quickly goes to 3 JSD. This means that if the 2 plays are actually equal there is 99.7% chance that the difference is not due to chance. But you should think there is better than 99.7% chance that play A is better. Look into Bayesian statistics for more on that point.

UBK

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