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Subject: Re: A question about statistics...

Author: Ricardo Gibert

Date: 16:38:53 01/04/04

Go up one level in this thread

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.

>Bo Persson

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