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Joined: 06 May 2009
Posts: 1638
Location: Fuquay-Varina, North Carolina

Post subject: Re: EloStat, Bayeselo and Ordo    Posted: Mon Jun 25, 2012 10:01 pm

hgm wrote:
 Adam Hair wrote: I have to say I am a little lost. It makes sense to me that 2 draws could be replaced with a win and a loss, but not that one draw can be replaced with a win and a loss.

Well, this is what the Logistic model predicts. Because for the Logistic L(x)*(1-L(x)), which is the product of the probability for one win (L(x)) and one loss (1-L(x)), happens to be proportional to the probability of a single draw (which is given by the derivative of L(x)). Draws in this model are stronger evidence for equality of the players ratings than wins and losses, because they only occur with high frequency in a narrow range of rating difference, why the occasional win against a stronger opponent still occurs for much larger rating differences.

Now for other rating models it is in general not true that F*(1-F) ~ F'. (And in such models F' might not even model the draw rate. For instance, in the Gaussian model there is no exact equivalence between a draw and any number of wins + losses, even for fractional numbers. But in the limit of a large number of games, the likelihood for N draws approaches that of 0.9N wins plus 0.9N losses (IIRC). So one might say that each draw counts for 1.8 games there.

So it all depends on which power of F*(1-F) is proportional to F' (expanded as secod-order power series).

Now the assumption that this power is 1, as the Logistic has, was actually supported by real data, where win probability times loss probability gave a curve that fitted the draw probability very well.

Thanks H.G.. I think you have given me enough of an explanation for me to work out my misunderstanding (along with some additional reading and pencil/paper work).
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Subject Author Date/Time
Kai Laskos Sun Jun 24, 2012 1:27 pm
Adam Hair Sun Jun 24, 2012 4:38 pm
Kai Laskos Sun Jun 24, 2012 5:46 pm
Edmund Moshammer Sun Jun 24, 2012 6:54 pm
H.G.Muller Sun Jun 24, 2012 7:29 pm
Kai Laskos Sun Jun 24, 2012 8:24 pm
H.G.Muller Sun Jun 24, 2012 8:52 pm
Kai Laskos Sun Jun 24, 2012 9:46 pm
Miguel A. Ballicora Sun Jun 24, 2012 10:05 pm
H.G.Muller Sun Jun 24, 2012 10:44 pm
Miguel A. Ballicora Sun Jun 24, 2012 10:58 pm
H.G.Muller Mon Jun 25, 2012 8:35 pm
Miguel A. Ballicora Mon Jun 25, 2012 9:12 pm
H.G.Muller Tue Jun 26, 2012 6:44 am
Miguel A. Ballicora Tue Jun 26, 2012 3:48 pm
H.G.Muller Tue Jun 26, 2012 4:21 pm
Kai Laskos Tue Jun 26, 2012 9:11 pm
H.G.Muller Wed Jun 27, 2012 5:29 am
Kai Laskos Wed Jun 27, 2012 9:32 am
H.G.Muller Wed Jun 27, 2012 11:26 am
Kai Laskos Thu Jun 28, 2012 4:48 pm
H.G.Muller Thu Jun 28, 2012 5:17 pm
H.G.Muller Sun Jun 24, 2012 10:36 pm
Kai Laskos Sun Jun 24, 2012 11:00 pm
Adam Hair Mon Jun 25, 2012 2:23 am
H.G.Muller Mon Jun 25, 2012 8:18 pm
Rémi Coulom Mon Jun 25, 2012 8:58 pm
H.G.Muller Mon Jun 25, 2012 9:09 pm
Rémi Coulom Mon Jun 25, 2012 9:16 pm
H.G.Muller Mon Jun 25, 2012 9:43 pm
Rémi Coulom Tue Jun 26, 2012 8:07 am
H.G.Muller Tue Jun 26, 2012 8:31 am
Juan Molina Tue Jun 26, 2012 11:31 am
H.G.Muller Tue Jun 26, 2012 12:22 pm
Kai Laskos Tue Jun 26, 2012 2:15 am
H.G.Muller Tue Jun 26, 2012 6:32 am
Re: EloStat, Bayeselo and Ordo Adam Hair Mon Jun 25, 2012 10:01 pm
Sven Schüle Sun Jun 24, 2012 10:21 pm
Kai Laskos Sun Jun 24, 2012 10:54 pm
Sven Schüle Mon Jun 25, 2012 9:22 am
Rémi Coulom Mon Jun 25, 2012 1:51 pm
Kai Laskos Tue Jun 26, 2012 2:09 am
Adam Hair Mon Jun 25, 2012 1:26 am

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