Where BR comes from
Some time ago I became aware of the article "New table-tennis rating system" (NTTRS) by David J. Marcus that appeared in The Statistician (2001) 50 Part 2, pp 191-208. The system described there looked impressive, but somewhat difficult for a newcomer to digest and also rather challenging to program. So it was not until the Ranking Review Committee of the WCF was formed late in 2005 that I finally got around to a serious study of this article. As I got to understand it better, my admiration increased. I have come to look upon it as the most significant contribution to the literature of ranking systems that I have seen. Its approach combines realism with elegance. No other system that I encountered seemed theoretically as soundly based.
So I would like to express my profound indebtedness to that inspiring article. The system BR has its roots in NTTRS, but deviates from it in a few ways. Whereas in NTTRS player performance is represented as a discrete probability measure that need not be normal, I decided to put (smooth) normal probability density functions (Bell Curves) in this role, at least for the rating of Recent Performance. A practical consequence is that player data can be represented as just two numbers (Mean and SD) instead of a list of some 300 real numbers (as in NTTRS). A Bell Curve can be visualized by everybody, while only a small minority would be comfortable with the measure theoretic concept.
The rating developed here for Performance over a Period is new – not done in NTTRS or anywhere that I know of. The nature of the problem forced me to define the rating (PP Grade) in terms of a (Dirac) probability measure which is not a Bell Curve. Fortunately, the Dirac measure becomes represented as a single real number, which is the kind of rating the croquet public is used to, albeit from a different point of view.
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