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Subject: Re: A question about statistics...

Author: Ricardo Gibert

Date: 16:22:43 01/04/04

Go up one level in this thread


On January 04, 2004 at 14:57:59, Mike Byrne wrote:

>On January 04, 2004 at 13:46:48, Ricardo Gibert wrote:
>
>>On January 04, 2004 at 12:47:25, Peter Berger wrote:
>>
>>>On January 04, 2004 at 12:40:00, Ricardo Gibert wrote:
>>>
>>>>On January 04, 2004 at 12:29:15, Mark Young wrote:
>>>>
>>>>>On January 04, 2004 at 11:46:00, Roger Brown wrote:
>>>>>
>>>>>>Hello all,
>>>>>>
>>>>>>I have read numerous posts about the validity - or lack thereof actually - of
>>>>>>short matches between and among chess engines.  The arguments of those who say
>>>>>>that such matches are meaningless (Kurt Utzinger, Christopher Theron, Robert
>>>>>>Hyatt et al)typically indicate that well over 200 games are requires to make any
>>>>>>sort of statisticdal statement that engine X is better than engine Y.
>>>>>>
>>>>>>I concede this point.
>>>>>
>>>>>If you concede this point you don't understand. There is no magic number like
>>>>>200 or 2000. The score must be considered. Here is an example:
>>>>>
>>>>>A score of 17 - 3 in a 20 game match has a certainty of over 99% that the winner
>>>>>of the match is stronger then the loser.
>>>>>
>>>>>A 100 game match ending 55 - 45 only has a 81% chance that the winner of the
>>>>>match is the stronger program.
>>>>>
>>>>>A 200 game match ending 106 - 94 only has a 78 % chance that the winner is
>>>>>stronger then the loser.
>>>>
>>>>
>>>>Nothing you have said is really correct because you have ignored the significant
>>>>effect of draws in a match.
>>>
>>>The percentage of draws doesn't matter at all when it is about the conclusion
>>>which program is strongest based on the above match results.
>>>
>>>This has been shown by Remi Coloum and explained in multiple posts
>>>here(unfortunately the search engine hasn't found a new home yet).
>>>
>>>6-0 with 0 draws and 6-0 with 1000 draws has the exact same prediction value
>>>when it is about the question which engine is stronger based on a match result.
>>
>>In this case, the number of decisive games (w+L=6) and margin of victory (w-L=6)
>>is the same in both cases so the conclusion they have equal value is correct.
>>
>>    -------------------------------
>>
>>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.
>
>But if you team needed a half point for you  to win the Olympias, this is match
>up you wanted - a half point is a "shoo in" and you are the champs.  Sometimes a
>draw is more important than a win and (in the example I used) is just as good as
>a win.
>
>Let's call the losing program "drawmaster"
>
>
> 98% of the games will end in draw - a coinflip that lands on the edge?
>
>
>
>
>>
>>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.
>
>Let's call this losing program "win_or_die"
>
>>
>>The first match is very convincing in demonstrating superiority. It is just as
>>effective as +20-0=0 is as per Remi.
>
>You may think so, but at the the end of the day, Dr Elo will have program
>"drawmaster" rated exactly the same as "win_or_die" --- and ratings are what we
>were talking about here.  Which program you may want to use may be based on
>whether you need the win or a draw, if you need the draw , go with drawmaster,
>if you need the full point , your chances are better with "win_or_die" .

Ratings are not what I was responding to. Among the many erroneous things Mike
Young said, "A 100 game match ending 55 - 45 only has a 81% chance that the
winner of the match is the stronger program."  This is a very specific statement
dealing with whether a given player is better or not. Nothing to do with ratings
in that statement. He _cannot_ provide a figure like "81%" without consdiering
the percentage of games ending in draw. That's the type of mistake I directed
myself towards.

>
>
>>
>>The second match is very unconvincing in demonstrating my superiority. It showed
>>a game between us is a virtual coin flip.
>>
>>Draws matter a lot, but you need to understand just how. I'm very familiar with
>>what Remi has said on this and it was quite correct. The trouble is people
>>misunderstand what he has said.
>>
>>If you have understood the above, you will then understand that my remark to
>>Mike Young was right on the money.
>
>I understand the above, but you are mixing apples and oranges and in the context
>of the discussion taking place, your post was not on the money.   It's really a
>different subject (imo) and you just added unneeded confusion to a discussion.
>

I'm baffled as to why you think I'm mixing apples and oranges. I think you need
to read through the thread again more carefully. If you do, you will find I
cleared away some misconceptions rather than "...added unneeded confusion..."



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