Author: Mike Byrne

Date: 18:04:53 01/04/04

Go up one level in this thread

On January 04, 2004 at 19:38:53, Ricardo Gibert wrote: >On January 04, 2004 at 17:15:33, Bo Persson wrote: > >>On January 04, 2004 at 13:46:48, Ricardo Gibert wrote: >> >>> ------------------------------- >>> >>>In the examples given before, the number of decisive games depends on the number >>>of draws e.g. +17-3=0 and +14-0=6 are not of equal value since the number >>>decisive games are not equal. >>> >>>Let's take a more obvious example. Let's say we play a 1000 game match and I win >>>by +20-0=980. I only score 51%, but if we then play a short match, your chances >>>of winning such a match is virtually zero, since the longer match has clearly >>>demonstrated you couldn't win a game if your life depended on it. >>> >>>Now compare this with the alternative possibility. We play a 1000 game match and >>>I win +510-490=0. Again 51%. Now we play a short match afterward, the match >>>outcome will be very nearly a virtual coin flip. >>> >>>The first match is very convincing in demonstrating superiority. It is just as >>>effective as +20-0=0 is as per Remi. >> >>No, it's not! >> >>+20-0=980 shows that you on average can win one game out of 50. What does that >>tell us about your chances in a 20 game match? >> >>I would bet my money on +0-0=20 > >So would I, but that does not change the fact that the player scoring +20-0=980 >is the superior player with respect to his opponent, which is what I was talking >about. He is not superior by much at all, but you are just as certain of this >superiority statistically speaking as you would be if he had scored +20-0=0. >Obviously the latter score suggests a higher magnitude of superiority, but I'm >not addressing the issue of magnitude. I am addressing the question of whether >he is superior or not. > >As an example, take Mike Young's statement, "A 100 game match ending 55 - 45 >only has a 81% chance that the winner of the match is the stronger program." He >is addressing the question of whether is superior is superior or not. He is not >addressing of how superior the winner is. He sets a specific figure of "81%" >without considering the percentage of the games ending in a draw. This cannot be >correct and I demonstrated that. Elo's confidence level with respect to ratings is mathethmatically defined and it does not matter whether the scores are 1-0, 0-1 or 0-0-2 - they will compute the same mathematically. Mark Young's statement is correct (although I did not do the math) but if he did and it is correct - then the 81% is correct and both examples, it will compute the same. If you have a different formula than Elo's that's fine - but this discussion was in the context of using ELOSTAT or such such program based on Elo's work -- it was not really a debate of Elo vs whatever rating system you are using. Of course it has been 20 years since I have looked at this and maybe the acceptbable theory is now different. But Elo's theory and rating systemn is fine my purposes and most others. > >> >> >>Bo Persson

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