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win probability for a PR difference and match length

Posted By: Rick Janowski
Date: Thursday, 20 September 2012, at 2:14 p.m.

In Response To: win probability for a PR difference and match length (niuniuch)

The Elo-based rating system for backgammon was derived by Larry Kaufman and Kent Goulding in the late 80s utilising the Elo-based chess rating system as a model to work from (full background given in one of the 1991 articles in Inside Backgammon). Later the methodology derived was adapted by FIBS and subsequent online backgammon servers. The website Backgammon Galore gives a very good FAQ on backgammon rating systems (http://www.bkgm.com/faq/Ratings.html#rating_formula).

The backgammon system utilises a fairly simple "logistic curve" equation which gives very close results to adapting a full statistical "normal distribution" which I believe is used in major chess systems (relative errors are negligible). Moreover, the "equation" enables a fairly straightforward expression to be derived for odds or winning chances. The backgammon system effectively equates a 25-point backgammon match to a single game of chess. For different length matches, an expression for the relative value of a win is derived from "random walk" theory. Although the use of this this theory is probably reasonable and certainly fairly practical, it doesn’t take into account varying gammon prices, cube efficiency or, most importantly in my view, the crawford game effect). I investigated an alternative approach by observing winning chances at even match scores for opponents with significant skill differences, using the Jake Jacobs derived "Fish" METs. What I found was that there is reasonably good correlation between the two approaches for match lengths of 7 and above.

To utilise performance ratings in a an Elo-based Backgammon Rating System, it is possible to utilise the empirical relationship derived by Xavier of 3 pr difference = 100 Elo difference. My tests on a considerable amount of data from IIBGF tournaments last year showed excellent correlation with this relationship for all Elo ratings above 1500.

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