Author: Dieter Buerssner

Date: 11:03:05 01/06/04

Go up one level in this thread

On January 05, 2004 at 18:11:25, Peter Fendrich wrote: >The rest is basic formulas for >the standard deviation. Actually, I am puzzled about these basic formulas for the standard deviation. Somehow I don't get it (in German, ich vermute, ich sitze auf der Leitung). Anyway, I made a few experiments. I did some Monte-Carlo simulation of matches (its easier, than to figure out the mathematics - actully I can figure it out with only wins and losses, but not with draws, too). When I assume, that white wins/draws/losses and black wins/draws/losses for the player have the same probabilties, and I fit the data m vs. p(m) with a Gauss-function I get exactly sigma = s/sqrt(n) with your formula. s=sqrt((W*(1-m)^2 + D*(0.5-m)^2 + L*(0-m)^2)/(n-1)) Not too surprising the function fits perfectly, with the deviations randomly distributed and of an order of magnitude as one can expect from the Monte Carlo method (proportional to 1/sqrt(N), N number of matches used in the simulation). When the Monte-Carlo method simulates 1 million games, there are about 4 significant figures, that are the same from the fit and the formula. However, the function m vs. p(m) looks different, when I assume different w/d/l probabilities for white and black. So, we not only have W, D, L, but wW, wD, wL, bW, bD, bL and say nb, nw, mb, mw (typically nb=nw). Can you also give a formula for this scenario for s? What do you think of the margins given by Elostat - something seems wrong there in the case of the W=20, D=980, L=0. Regards, Dieter

- Re: A question about statistics...
**Peter Fendrich***16:03:58 01/06/04*- Re: A question about statistics...
**Dieter Buerssner***09:23:00 01/07/04*- Re: A question about statistics...
**Peter Fendrich***05:53:58 01/09/04*- Re: A question about statistics...
**Dieter Buerssner***10:26:17 01/09/04*- Re: A question about statistics...
**Peter Fendrich***05:05:34 01/12/04*

- Re: A question about statistics...

- Re: A question about statistics...

- Re: A question about statistics...

- Re: A question about statistics...

This page took 0.17 seconds to execute

Last modified: Thu, 07 Jul 11 08:48:38 -0700

Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.