# Computer Chess Club Archives

## Messages

### Subject: Some thougths about statistics

Author: Martin Schubert

Date: 01:25:32 02/24/00

Go up one level in this thread

```On February 23, 2000 at 18:17:29, Dann Corbit wrote:

>On February 23, 2000 at 16:33:18, blass uri wrote:
>[snip]
>>I think that the probabilities are based on wrong assumptions.
>>
>>Suppose people with 2400 earn 36% of the points against people with 2500 and
>>people with 2300 earn 36% of the points against people with 2400.
>>
>>what will be the result of people with 2300 against people with 2500?
>
>24%
>
>>I have no reason to believe that it is the number that the theory suggests
>>because the theory was based on some assumptions and not on investigation of
>>games and I have no reason to assume that the assumptions are correct.
>
>The theory is based on mathematics.  It is simply turning physical measurements
>into probability estimates for outcomes.

You say, the theory is based on mathematics. I have one question: under which
conditions holds this theory. Do they really hold?
In statistics you usually have conditions like "identically independent
distributed".
"Independent" means, that if you repeat an "experiment", the result of an
"experiment" doesn't depend on the results of the "experiments" before.
IMO, this conditions doesn't hold. Because of the booklearning. So the result of
one game depends on the results of the games before. Maybe the differences
aren't big, but has anybody still examined this?

"Identically distributed":
This means IMO the rating of each program is always the same. Is that true?
Program A wins (most times) against Program B, Program B wins against Program C,
Program C wins against Program A. So which program is the best? So the ratings
depends on how many games of each pairing are played. If you play 100 games A-B,
50 B-C and 50 A-C, so you get the best rating for A, etc.
Maybe there is one program, which usually clear defeats weak programs. Another
program is as good as the first, has problems to get a good score against weak
programs. (Doesn't Tiger have problems, that it too often draws against weaker
opposites?)
So if you test against old programs on old machines, some programs have an

My problem with the ratings is: For each programs you get a rating. But
statistically it means noting. As long as the preceding conditions do not hold.

Greetings, Martin Schubert

```

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