Author: blass uri
Date: 00:42:39 02/24/00
Go up one level in this thread
On February 23, 2000 at 20:18:50, Dann Corbit wrote: >On February 23, 2000 at 20:10:17, blass uri wrote: >>On February 23, 2000 at 19:54:40, Dann Corbit wrote: >> >>>On February 23, 2000 at 19:49:38, blass uri wrote: >>>[snip] >>>>I know that the theory is based on mathematics but it is possible to do a >>>>different theory that say that >>>> >>>>if people with 2400 earn 36% of the points against people with 2500 >>>>and people with 2300 earn 36% of the points against people with 2400 >>>>then >>>>people with 2300 earn 26% of the points against people with 2500 >>>> >>>>I see no reason to assume that 24% is correct and not 26% or 22% unless 24% is >>>>based on practical results of games and I know that the probabilities are not >>>>based on practical results of games(I know that the probabilities are based on >>>>the assumption that the ability of players has a normal distribution with 200 >>>>wlo standard deviation) >>>> >>>>The only way to have a better guess about the probabilities is to count results >>>>of games between people with 100 elo difference and between people with 200 elo >>>>difference but I do not know about somebody who did it. >>> >>>The way the ELO figures are computed is from actual games. Since the games are >>>used to compute the curves, the results are accurate. Of course, they do >>>require a huge number of trials to get an accurate figure. >>> >>>In other words, the actual games themselves determine the ELO, not the other way >>>around. >> >>Suppose that a wins against b 64:36 >>b wins against c 64:36 >> >>The question is what is the expected result of a against c based only on this >>information. >> >>If it is not 76:24 then the rating is based on wrong assumptions. > >You cannot extrapolate a single performance based upon ELO. It is how we can >expect a large body of data to behave. It is like trying to predict a coin toss >sequence. You won't predict a single sequence. But you can predict averages >over millions of sequences. When I ask what is the expected result I mean to the average. You can take a big data of games between players when the difference in rating is a constant x choose x such that the average result is 64:36 Now the question is if the average result when the difference is 2x is 76:24 I do not think that this question was tested. > >>I do not know about investigation of the results between a and c >> >>It is possible to find the differnece in elo rating that produce practically >>64:36(suppose it is 100 elo) >>now it is possible to check if differnece of 200 elo gives result that is >>practically different then 76:24 > >It's been tested if that is what you are wondering. If the model were wrong, >it's self adjusting anyway. I agree it is adjusting to have smaller errors but suppose we have a world with and suppose that we have a world that a wins b 64:36 b wins c 64:36 and a wins c 100:0 What is the rating of the players. it is dependent on how many games a is playing against b and how many games a is playing against c and how many games b is playing against c. > >Apparently, it is not terribly useful for extreme ELO differences, but it works >well withing spans of a few hundred. I agree the difference between the probabilities based on the elo rating and the practical probablities is not very big but I do not know if people try to find the difference. 1)The best guess about the probabilities should not be based only on the difference in rating(if you know from the past that one player is unstable you can guess that he has a bigger probability to win a player with 200 elo rating higher than him(her) and a bigger probability to lose against player with 200 elo rating lower than him(her)) 2)If you try to find only the best guess based only on the difference between the players I do not think that it is possible to do a model when 64:36 is the best guess for 100 elo difference and 76:24 is the best guess when the difference is 200 elo. I agree that the difference is not very big but there is a difference because I know that the 64:36 and 76:24 is not based on practical games but on some assumptions(about normal distribution). Uri
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