The Fibs Rating Formula

[nabla]

Hello, I don't know whether I am posting this in the right forum, but I did not find any other in which this seemed to fit. At least the topic is related to the FIBS server.

Recall that the FIBS rating formula is based on the classic Elo formula, used since a long time in all chess rating lists, with two twists taking in account the match length. The twists consist in
1) Before evaluating the Elo formula, multiplying the rating difference by the square root of n, where n is the length of the match.
2) After getting the resulting rating gains and losses by the Elo formula, multiplying those gains / losses by the square root of n - I will not discuss this point which is only a change of coefficient.

I have read in this rec.games.backgammon message that point 1) was mathematically proven to be fair for cubeless matches to n points (the author then states that it might not fair for matches with the cube, but the initial assumption remains).  
But I couldn't find a proof of this fact either by myself, either on the Internet. Does anybody know a proof or at least a authoritative source for this fact ?

[spielberg]

Gosh - this is a very very hard question but :

It may be shown that in chess it is always best to play a "perfect game" assuming your opponent will do the same.

This is certainly not the case for backgammon which in this case is a more complex game than chess.


Therefore while the ELO formula provides a rough guide to winning probabilities in mathematical terms it is, strictly, an approximation rather than a valid model for backgammon.

[nabla]

IMHO the Elo model is valid for backgammon, but you have to accept that an equivalent skill difference will result in a smaller rating difference, because of the greater luck factor (nevertheless, even in chess, a much weaker player can defeat a much stronger player from time to time).

But my question was independent of the game played : why is that true that playing n-point matches instead of single games requires to multiply the rating difference by exactly the square root on n ? The person who invented the FIBS rating formula probably knows the answer !

[socksey]

I doubt that.   Take into account:  

http://www.alef.co.uk/fibs/archive/dysfunction.html

and I'm sure you will agree with me!   <_<

socksey



"And those who were seen dancing were thought to be insane by those who could not hear the music." - Friedrich Nietzsche

[nabla]

Shshshsh, don't tell that I am conducting a new experiment !