Dr Ian Plummer
Technical
Where BR comes from
Some time ago I became aware of the article "New tabletennis rating system" (NTTRS) by David J. Marcus that appeared in The Statistician (2001) 50 Part 2, pp 191208. 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.
I also continued the gamebygame updating long used in our sport rather than to use the eventbyevent updating of NTTRS. I did program a version of BR in eventbyevent fashion, but when the resulting Percentage of Correct Predictions dropped to a level more or less halfway between that of BR and CGS, I became sufficiently discouraged to drop that idea.
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.
Author: Louis Nel
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