Author: Bas Hamstra
Date: 14:02:01 05/25/04
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On May 25, 2004 at 16:39:38, Andrew Wagner wrote: >On May 25, 2004 at 15:49:22, Bas Hamstra wrote: > >>Supposed you played a huge automated tournament, and ratings were automatically >>calculated (like in Arena) and displayed for all participants. Then, would it be >>possible to derive/calculate the sigma, 2*sigma, 3*sigma rating >>rating-intervals? If so how? >> >> >> >>Ciao, >> >>Bas. > >Hi. I'm not sure what you mean by 2*sigma and 3*sigma. The are not statistically >significant, so far as I know. Variance is sigma^2 (i.e. sigma * sigma). The >formula for this is: sum((x - average)^2)/N. So, let's take a few ratings for an >example: >2400 >2432 >2414 >2443 > >The average is 2422.25. Therefore, we have (22.25^2) + (9.75^2) + (8.25^2) + >(19.75^2) in the numerator. That's 1048.25. And our N here is 4 because we have >4 ratings, so our answer is 1048.25/4 or 262. That's the variance. Taking the >square root, we get 16.2, which is sigma (standard deviation). Hope that helps. >Andrew What I mean is in a "normal" distribution you can expect values to lie in the interval [Mean-sigma, Mean+sigma] with 65% confidence. For +- 2*sigma borders the confidence is 95% and for 3*sigma it's 99.7%. What I like to calculate is after a tournament with n participants, over a certain number of rounds, with 95% confidence: what is the rating interval of program A, program B, etc.
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