# Computer Chess Club Archives

## Messages

### Subject: Re: A question about statistics...

Author: Sandro Necchi

Date: 01:13:21 01/06/04

Go up one level in this thread

```On January 04, 2004 at 19:22:43, Ricardo Gibert wrote:

>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.

Well, if referred to 2 chess programs playing each other, this figure may be
optimistic/not true.
A better figure based on not to many games (<300) would be better with at least
6 different opponents.
There are cases where a program performs quite well against another one, but
does not so well against other programs. The result could change the final
figure more than you think.

Sandro

>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..."

```