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H.G.Muller

Joined: 10 Mar 2006
Posts: 12765
Location: Amsterdam

 Post subject: Re: Advantage for White; Bayeselo (to Rémi Coulom)    Posted: Sun Mar 04, 2012 10:44 am Thanks, Edmund! This is really interesting and important data. For one, it shows that the Sonas observation, that a linear model gives a better fit than Gaussian or Logistic, holds for computer games as well. A second point is that the draw probability vs Elo-difference looks like a parabola, i.e. it seems indeed proportional to the product score(deltaE)*(1-score(deltaE)). This indeed justifies the analysis of BayesElo, where a single draw is equivalent to one win + one loss (i.e. counts as 2 games). Some remarks: it seems the horizontal resolution of your graphs is higher than needed, considering the vertical spread of the data points. It would be better to increase the bin size by at least a factor 4 (or apply some other form of smoothing); this would reduce the vertical spread by a factor 2, without visibly increasing horizontal uncertainty. Perhaps you should use extra large Elo bins in the tails, where there you have only 2 or 3 data points per bin now, so that the percentages quantize to 50% or 33%, not contributing anything to visible estimation of how the curve looks. (Perhaps you should just combine bins until they have a certain minimum number of games, keeping track of average Elo (difference) as well as average score / drawRate. I get the impression that the draw vs. average Elo graph would be better fitted by a line with a break in it around 2950, first sloping up, and then saturating at about 42%. One would have to guard for systematic errors: the points at the high end of the average Elo scale are likely to be due to games with low Elo difference between the participants. And from the Elo difference graph we can see that the draw rate goes up if the Elo difference is small. So part of the increase of the draw rate could be due to that. So I think it would be useful to also calculate the variance of Elo difference as a function of average Elo. If there is significant variation of that across the scale, the contribution of variance to suppression of draws (as known from the second graph) could be used to correct the observed draw rate for sampling bias.
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Subject Author Date/Time
Edmund Moshammer Sat Mar 03, 2012 11:22 pm
H.G.Muller Sun Mar 04, 2012 6:56 am
Edmund Moshammer Sun Mar 04, 2012 8:49 am
Re: Advantage for White; Bayeselo (to Rémi Coulom) H.G.Muller Sun Mar 04, 2012 10:44 am
Lucas Braesch Sun Mar 04, 2012 11:06 am
H.G.Muller Sun Mar 04, 2012 11:29 am
Edmund Moshammer Sun Mar 04, 2012 2:42 pm
Edmund Moshammer Sun Mar 04, 2012 2:52 pm
H.G.Muller Sun Mar 04, 2012 3:26 pm
Edmund Moshammer Sun Mar 04, 2012 4:13 pm
H.G.Muller Sun Mar 04, 2012 4:33 pm
Edmund Moshammer Sun Mar 04, 2012 5:18 pm
Adam Hair Sat Jun 30, 2012 11:00 pm
Adam Hair Mon Jul 02, 2012 1:25 pm
Adam Hair Sun Jul 01, 2012 3:48 am
Adam Hair Sun Jul 01, 2012 8:47 pm
Edmund Moshammer Sun Jul 01, 2012 9:55 pm
Adam Hair Mon Jul 02, 2012 12:37 am
Adam Hair Mon Jul 02, 2012 1:27 pm
Marco Costalba Sun Jul 01, 2012 7:17 am
Lucas Braesch Sun Mar 04, 2012 8:53 am
Daniel Shawul Sun Mar 04, 2012 12:01 pm
Rémi Coulom Sun Mar 04, 2012 1:29 pm
H.G.Muller Sun Mar 04, 2012 2:20 pm
Rémi Coulom Sun Mar 04, 2012 3:52 pm
H.G.Muller Sun Mar 04, 2012 4:12 pm
Rémi Coulom Sun Mar 04, 2012 5:13 pm
H.G.Muller Sun Mar 04, 2012 5:27 pm
Rémi Coulom Sun Mar 04, 2012 5:32 pm
Daniel Shawul Wed Sep 12, 2012 12:18 am

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