Computer Chess Club Archives




Subject: Re: A question about statistics...

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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