Author: martin fierz
Date: 00:51:15 08/05/03
Go up one level in this thread
On August 04, 2003 at 19:04:39, Dieter Buerssner wrote: >On August 04, 2003 at 18:36:27, Dann Corbit wrote: > >>If a player rated 500 points below a machine in real strength plays enough >>games, he will win one of them. > >If we can trust the statistics behind the ELO system. I am not sure, if it is >true for bigger rating differences (in the tails of the distributions). Also, to >my knowledge, the statistics does not say anything about the distribution of >wins/draws/losses. If you are expected to get 1% of the points, you could do it >by just drawing every 50th game and don't win any game. > >>It may take quite a lot of games. But this is not an opinion, it is a fact. > >I think, it is not a "pure" fact. It (the percentage of points, you reach, not >necessarily the number of wins) might be a fact, when we take the statistics >assumed behind the Elo system as a fact. But still my above point about >distribution of wins and draws would be valid. > >>This assumes simply playing games based on strength. If the human is clever at >>learning computer weakesses or playing anticomputer chess, it may tip the >>balance somewhat. >> >>Win expectency for a difference of 0 points is 0.5 >>Win expectency for a difference of 100 points is 0.359935 >>Win expectency for a difference of 200 points is 0.240253 >>Win expectency for a difference of 300 points is 0.15098 >>Win expectency for a difference of 400 points is 0.0909091 >>Win expectency for a difference of 500 points is 0.0532402 >>Win expectency for a difference of 600 points is 0.0306534 >>Win expectency for a difference of 700 points is 0.0174721 >>Win expectency for a difference of 800 points is 0.00990099 >>Win expectency for a difference of 900 points is 0.00559197 >>Win expectency for a difference of 1000 points is 0.00315231 > >I am no native English speaker. Win expectency sounds a bit misleading to my >ears, because it does not really mean, that you win that many games. > >BTW. I calculate slightly different numbers. The correct formula is: > > p = 0.5 - 0.5*erf(rating_difference/400.) > >With: > > x > - > 2 | | 2 > erf(x) = -------- | exp( - t ) dt. > sqrt(pi) | | > - > 0 > >Or for the numerically interested people, for rating_difference big, the form > >p = 0.5*erfc((rating_difference)/400.) > >would be better, when a "good" erfc-function is available (erfc(x) =: 1-erf(x)). >It would avoid to calculate the difference of numbers of equal size. > > >Regards, >Dieter there is this jeff sonas guy who sometimes is interviewed on the chessbase website. he's a statistician (?) and did some work on improving the rating system. among other things, i believe he also thought about the difference of having white/black and about how points are made - with wins or rather with draws. i.e. . you can read more about his theories on his site, www.chessmetrics.com, or in this chessbase article on dortmund: http://www.chessbase.com/newsdetail.asp?newsid=1094 cheers martin
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.