Author: Dieter Buerssner
Date: 14:48:25 10/06/03
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On October 06, 2003 at 16:43:28, Dann Corbit wrote: >On October 06, 2003 at 16:39:07, Dieter Buerssner wrote: > >>Don't be too optimistic. I calculate a different number. For a rating difference >>of 2800 points, I calculate the average points expected in one game for the >>weaker player as: >> >>p = 0.5*erfc(rating_difference/400.) >> 2.0919128E-23 >> >>So, you should never lose and not allow one single draw in over 2e22 games. Good >>luck! :-) >> >>I guess, Dann used some approximate formula, that will only work well with >>rather moderate rating difference. > >I used the USCF formula. I think, you used 1-1/(1+10^(-rating_difference/400)) This formula is an approximation of the error function, that will not work well with a large rating difference. http://www.fide.com/official/handbook.asp?level=B0214 mentions the formula, but also states, that it is only an approximation. If we look at the table given at http://www.fide.com/official/handbook.asp?level=B0210 For example for rating difference of 444 I calculate 0.07 with your formula, while the table gives 0.06, and my formula with the error function as well. For 677 I get 0.01 while your formula gives 0.02 (the difference is larger than a small rounding effect - actually I get under 0.01 vs more than 0.02). The larger the rating difference, the larger will be the relative error of the approximate formula. I have no idea how USCF handles it in detail, but the formula with the error function should be mathematically correct, if I have not made any stupid error. I can reproduce all numbers that I tried in the FIDE table. However I did not find the exact formula at the FIDE site. Perhaps they find it too obscure to mention. For very large rating difference my implementation of erfc might not be very accurate. Users of Mathematica/Maple/... could probably easily check it. Regards, Dieter
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