Author: Robert Hyatt
Date: 07:06:08 11/25/03
Go up one level in this thread
On November 25, 2003 at 05:52:13, Rémi Coulom wrote: >On November 24, 2003 at 16:23:39, Robert Hyatt wrote: > >>On November 24, 2003 at 14:28:44, Rémi Coulom wrote: >> >>>On November 24, 2003 at 14:07:27, Robert Hyatt wrote: >>> >>><snip> >>>>Draws count. That's why the Elo formula specifically includes draws in the >>>>calculation... >>> >>>I considered only the problem of estimating the likelihood that one player is >>>better than the other. Not the estimation of the difference in strength. >> >>Fine, but remember my example. Two _identical_ players. Me and a clone of >>me. We play 500 draws, then I get sick and my clone wins 6 games. I recover >>and we play another 500 draws. Is my clone better? Elo says "no". Or >>"barely". IE we may be separated by .01 rating point after that second set >>of 500 draws. Concluding my clone is "better" is simply wrong here. If >>everything were uniform, and games are 100% independent events, maybe that >>works. But humans don't play 1006 independent games. We get sick or distracted >>or whatever. >> >>The 1000 draws cover that case if you don't ignore them. >> >>> >>><snip> >>>>If all you care about is "who is better" then omitting the draws makes >>>>some kind of sense, but it doesn't give any idea _how_ much better one >>>>is than the other. >>> >>>So we agree. I did not care at all about how much better one is than the other. >>> >>>Rémi >> >>I'm not sure we agree yet. See my example above. Is my clone better? I >>think not. > >Your clone is not better. What I say is not that your clone is better. What I >say is "assuming the games are independent, and considering the results only, it >is more likely than your clone is better". I understand your statement. I simply don't agree that every game is an independent event, played under the same circumstances. Illness is a good example. Distractions are another. And, there is the random chance of something really bad happening. IE the 1984 US Speed Chess Championship where Cray Blitz simply destroyed everyone, until it played a 1900 player and self-destructed to avoid a mate that the opponent didn't see and couldn't see in the time given. In fact, GMs watching the game couldn't see the mate. Suppose that was the only decisive game in a match. Was the 1900 player actually better? Every now and then a chess game is won by a "coin toss" type of event, where you happen to stumble into a won game without playing better than your opponent. With 1000 draws, and 1 win, I would _never_ conclude that the player with 1 win is better. Not even .1 x 10^-100 better. Even computer vs computer sees an occasional coin-toss game... > >The assumption that games are independent is not completely in contradiction >with the possibility of being distracted or sick. If you consider that the >probability of being distracted or sick is the same for both players, and that >it does not depend on his state in the previous game, then my math still holds. >Two players of equal strength do not necessarily draw every match they play. > >6 games in a row being lost because your sickness may span over more than one >game does break my hypotheses, though. That was my basic idea... I played in more than one tournament, not feeling well, for reasons that I don't even understand today. :) I've seen 2200+ players do poorly and later discover they are going through a divorce, or a death in their family, or whatever... However, your hypothesis is fine, so long as the "independence" is clarified to be random games here and there. Unfortunately, as always, humans tend to break any good plan. :) That is harder to justify when talking about computers of course, but there are bad hardware days. I've had 'em. :) > >> >>I would be much more convinced if my clone won N in a row, rather than >>drawing a huge number, then winning M, then drawing a huge number again. > >I understand your reasoning, and agree with you. That's because in your case you >do not assume that the games are independent. > >Rémi
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