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EloStat, Bayeselo and Ordo
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Kai Laskos



Joined: 26 Jul 2006
Posts: 3360
PostPost subject: Re: EloStat, Bayeselo and Ordo    Posted: Sun Jun 24, 2012 9:46 pm Reply to topic Reply with quote
hgm wrote:
There are two separate issues here: the correctness of the model, ( Logistic, Gaussian, linear) and the correctness of the analysis once the model is given (to determine the parameters).

Yes, but if I am not wrong, the result here can be put on Edmund's plot, given the Bayeselo results and the true percentages, in the plot "White Score against Elo-delta". Your wondering of compression came from that plot.
Quote:


For a Logistic model with (small) draw margin m, the probability for a draw (L(x+m) - L(x-m) ~ d/dx L(x)) is proportional to the probability for one loss + one win (L(x) * (1 - L(x))). So one observed draw has the same effect on the likelihood of x (the rating difference) as one win + one loss.

With N wins and M losses the likelihood od x is L(x)^N * (1-L(x))^M, which is maximum when

(N*L(x)^(N-1) * (1-L(x))^M - M*L(x)^N * (1-L(x))^(M-1)) * dL/dx(x) = 0

or

N*(1-L(x)) = M*L(x)
N = (N+M) * L(x)
L(x) = N/(N+M)

i.e. the expected formula based on the fraction of wins.

But as draws count for win + loss, a 15-5 result based on 15 wins and 5 losses has L(x) = 0.75, while one based on 10 wins plus 10 draws would give the same as for 20 wins plus 10 losses, i.e. L(x) = 0.66.


That' fine, I already saw something similar, is the draw just proportional to 1 win and 1 loss, or exactly equal? Second, I don't think draws are equal to anything win-loss in statistical weight sense (be it for maximum likelihood method), one has to use some summed-up trinomial distribution giving the same percentage, with varying N,M, Draws.
My problem is a bit different, if you are right, then I don't know what "rating" is supposed to mean. In absence of any other information, what is the rating difference between two engines scoring +60 =30 -10 against each other? Is it hard and I cannot do that by hand?

Kai
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Subject Author Date/Time
EloStat, Bayeselo and Ordo Kai Laskos Sun Jun 24, 2012 1:27 pm
      Re: EloStat, Bayeselo and Ordo Adam Hair Sun Jun 24, 2012 4:38 pm
            Re: EloStat, Bayeselo and Ordo Kai Laskos Sun Jun 24, 2012 5:46 pm
                  Re: EloStat, Bayeselo and Ordo Edmund Moshammer Sun Jun 24, 2012 6:54 pm
                  Re: EloStat, Bayeselo and Ordo H.G.Muller Sun Jun 24, 2012 7:29 pm
                        Re: EloStat, Bayeselo and Ordo Kai Laskos Sun Jun 24, 2012 8:24 pm
                              Re: EloStat, Bayeselo and Ordo H.G.Muller Sun Jun 24, 2012 8:52 pm
                                    Re: EloStat, Bayeselo and Ordo Kai Laskos Sun Jun 24, 2012 9:46 pm
                                          Re: EloStat, Bayeselo and Ordo Miguel A. Ballicora Sun Jun 24, 2012 10:05 pm
                                                Re: EloStat, Bayeselo and Ordo H.G.Muller Sun Jun 24, 2012 10:44 pm
                                                      Re: EloStat, Bayeselo and Ordo Miguel A. Ballicora Sun Jun 24, 2012 10:58 pm
                                                            Re: EloStat, Bayeselo and Ordo H.G.Muller Mon Jun 25, 2012 8:35 pm
                                                                  Re: EloStat, Bayeselo and Ordo Miguel A. Ballicora Mon Jun 25, 2012 9:12 pm
                                                                        Re: EloStat, Bayeselo and Ordo H.G.Muller Tue Jun 26, 2012 6:44 am
                                                                              Re: EloStat, Bayeselo and Ordo Miguel A. Ballicora Tue Jun 26, 2012 3:48 pm
                                                                                    Re: EloStat, Bayeselo and Ordo H.G.Muller Tue Jun 26, 2012 4:21 pm
                                                                                          Re: EloStat, Bayeselo and Ordo Kai Laskos Tue Jun 26, 2012 9:11 pm
                                                                                          Re: EloStat, Bayeselo and Ordo H.G.Muller Wed Jun 27, 2012 5:29 am
                                                                                          Re: EloStat, Bayeselo and Ordo Kai Laskos Wed Jun 27, 2012 9:32 am
                                                                                          Re: EloStat, Bayeselo and Ordo H.G.Muller Wed Jun 27, 2012 11:26 am
                                                                                          Re: EloStat, Bayeselo and Ordo Kai Laskos Thu Jun 28, 2012 4:48 pm
                                                                                          Re: EloStat, Bayeselo and Ordo H.G.Muller Thu Jun 28, 2012 5:17 pm
                                          Re: EloStat, Bayeselo and Ordo H.G.Muller Sun Jun 24, 2012 10:36 pm
                                                Re: EloStat, Bayeselo and Ordo Kai Laskos Sun Jun 24, 2012 11:00 pm
                                                Re: EloStat, Bayeselo and Ordo Adam Hair Mon Jun 25, 2012 2:23 am
                                                      Re: EloStat, Bayeselo and Ordo H.G.Muller Mon Jun 25, 2012 8:18 pm
                                                            Re: EloStat, Bayeselo and Ordo Rémi Coulom Mon Jun 25, 2012 8:58 pm
                                                                  Re: EloStat, Bayeselo and Ordo H.G.Muller Mon Jun 25, 2012 9:09 pm
                                                                        Re: EloStat, Bayeselo and Ordo Rémi Coulom Mon Jun 25, 2012 9:16 pm
                                                                              Re: EloStat, Bayeselo and Ordo H.G.Muller Mon Jun 25, 2012 9:43 pm
                                                                                    Re: EloStat, Bayeselo and Ordo Rémi Coulom Tue Jun 26, 2012 8:07 am
                                                                                          Re: EloStat, Bayeselo and Ordo H.G.Muller Tue Jun 26, 2012 8:31 am
                                                                                          Re: EloStat, Bayeselo and Ordo Juan Molina Tue Jun 26, 2012 11:31 am
                                                                                          Re: EloStat, Bayeselo and Ordo H.G.Muller Tue Jun 26, 2012 12:22 pm
                                                                  Re: EloStat, Bayeselo and Ordo Kai Laskos Tue Jun 26, 2012 2:15 am
                                                                        Re: EloStat, Bayeselo and Ordo H.G.Muller Tue Jun 26, 2012 6:32 am
                                                            Re: EloStat, Bayeselo and Ordo Adam Hair Mon Jun 25, 2012 10:01 pm
                  Re: EloStat, Bayeselo and Ordo Sven Schüle Sun Jun 24, 2012 10:21 pm
                        Re: EloStat, Bayeselo and Ordo Kai Laskos Sun Jun 24, 2012 10:54 pm
                              Re: EloStat, Bayeselo and Ordo Sven Schüle Mon Jun 25, 2012 9:22 am
                                    Re: EloStat, Bayeselo and Ordo Rémi Coulom Mon Jun 25, 2012 1:51 pm
                                    Re: EloStat, Bayeselo and Ordo Kai Laskos Tue Jun 26, 2012 2:09 am
            Re: EloStat, Bayeselo and Ordo Adam Hair Mon Jun 25, 2012 1:26 am
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