# Computer Chess Club Archives

## Messages

### Subject: Re: Simulating the result of a single game by random numbers

Author: Andreas Herrmann

Date: 15:56:54 07/03/01

Go up one level in this thread

```On July 03, 2001 at 15:08:42, Christoph Fieberg wrote:

>Description of the program I developed for simulating the result of a chess game
>of two rated players.
>
>The result of the game depends on the performance factor and a draw factor.
>
>1.) Performance factor
>
>The performance factor depends on the rating difference and on the advantage
>playing the white pieces.
>
>In order to determine the performance factor I analyzed nearly 100.000 games of
>games with both players 2500+. The distribution for 1-0, Draw, 0-1 was (rounded)
>31%-50%-19%. White had a success-rate of 56% (= 31 + 50/2) and Black of 44%. [I
>would be happy if this distribution could be validated by others. It has to be
>noted that this is an average distribution for players 2500+. On the top level
>the success-rate is lower due to a higher number of draws.]
>
>The average opponent for White and Black had the same rating and therefore the
>advantage playing white (if both players have the same strength) is 12%-points
>(56-44) what can be expressed as 42 Elo-points (see formula below). Thus, for
>calculation purposes White has to be added 21 Elo and Black substracted 21 Elo
>in order to consider the advantage playing white.

Before some month i calculated an average advantage of 26 ELO (instaed of your
42) for white (from many thousands of real computer games).
games, where someone calculated a value of 32 ELO. Sorry, today i don't know
where it was. I think also, that in human games is the opening advantage a
little higher than in computer games.

>
>The following formula (I think used by FIDE) allows to calculate the performance
>based on Elo-difference and vice versa. It is:
>
>Performance (%) = (1 / (1 + (10 ^ (-difference / 400))))
>

Use the above formula only for performance values between 15% and 85%, because
lower and higher values got "wrong" results. Better is using an internal ELO
table with all values from 1% to 99%. Values between the full percent values,
can be interpolated.
Before some years i also used your above formula in my rating program. But now i
use an internal table, because the calculated values are more exact.

Yesterday i had the idea, to make such a tournament simulator.
Here my first ideas:

Input values to the program:
- number of players
- ELO and name of each player
- tournament mode (swiss, round robin ...)
- rounds to play
- ELO advantage for white (for excample 26)
- average draws in percent (normally about 14%, calculated from many thousands
of computer games)
- number of tournaments

Outputs:
- ev. each tournament result in a file
- for each player: all reached places
...

Andreas

http://www.wbholmes.de

```