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BGonline.org Forums
The FIBS rating formula : why sqrt(n) ?
Posted By: Fabrice Liardet
Date: Tuesday, 13 September 2011, at 7:44 p.m.
In a nutshell, the spirit of the FIBS rating formula (viewed as an extension of the classic Elo formula) is that if one multiplies the match length by n, it has the same effect on the match winning chances than multiplying the rating difference by the square root of n. I remember having read that it was a crude approximation in backgammon, because it was in fact precisely derived of the single-game model (where one wins only one point per game). Here is what Trice and Jacobs say about it in the Fish book :
Random walk theory suggests that the expected distance traveled from the starting point by a random walker is proportional to the square root of the number of steps he has taken. Applying this theory to backgammon matches means that if we quadruple the match length, we halve the rating difference needed to win in the same proportion.I am ready to take the random walk result on face value (I suppose it holds for n->infinity), but how does the conclusion follow ? Does that sqrt(n) somehow relate to the expected match length ? Am I being dense for not seeing even the beginning of it ?
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