I didn't followed this discussion, I just assumed the logistic distribution out of my ignorance. The curve being empirical, and the common cases used being logistic and Gaussian model, I saw no problem with that. I don't believe that 5 Elo points difference are meaningless, I mean, if the differences are 340 points and 345 points, then the difference of 5 points of differences is probably meaningless. But 5 points absolute difference must look similar in Gaussian model or logistic. I don't think the problem was about the shape of the logistic, Gaussian model, whatever very similar empirical curves.lkaufman wrote:FIDE ratings may use the normal distribution rather than the Logistic, I'm not sure, but the differences are insignificant except for extreme elo differences. But they consider only the player's score against the given opponents, not how it was composed of wins and draws, so it therefore follows that for FIDE one win plus one loss is identical to two draws. If the model behind BayesElo implies that one win plus one loss is the same as one draw, that is a HUGE difference. Ironically, if FIDE were to switch to counting draws twice to conform to BayesElo, the effect would be to favor top players who had less draws. These days, many events award prizes based on effectively giving each player only 1/3 of a point for draws. So a revised Bayes-Elo like FIDE rating system would accidentally work to favor the strong players who made less draws, the same ones favored by this prize-distribution! Of course it would have the opposite effect for tail-enders, but their ratings are generally considered less important.hgm wrote:This sounds reasonable. But I thought FIDE ratings were based on a Gaussian model, and I never calculated how it would work out for that. But it canot be excluded draws should have a different weight from wins or losses.lkaufman wrote:It suddenly occurred to me that if BayesElo is correct, then when doing normal sequential ratings (like USCF or FIDE) wouldn't it be correct to rate each draw twice, or alternatively to only half-rate wins and losses? That doesn't sound right, but it would seem to be logical if the underlying assumption of BayesElo is right. Only in that way would one draw = one win plus one loss.

Of course Sonas showed that the FIDE model is no good at all, so it could use a lot more changes as just the draw weight.

This idea of double-rating draws is not of just hypothetical importance to me. As a member of the USCF rating committee, I am in a position to propose the idea for serious consideration. But one thing about it bothers me. Let's say K (the limiting value of a loss against a very weak opponent) is 32. Normally a huge upset win would get 32 and a huge upset draw would get 16, but if we give draws double credit they also get 32, which is absurd. So maybe double credit for draws just works if the players are closely matched, and the multiplier gradually decays to 1 as the rating spread increases. Does this sound right to you? Can you make a better proposal for modifying sequential ratings in the spirit of BayesElo?

Kai