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Subject: Re: ELO variance

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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