My results from several hours of Googling: 1. Huge amount of research on chess ratings. scholar.google.com "chess" "Elo" 2. Elo model was invented by Zermelo 1928 and Bradley&Terry 1952, rediscovered by Ford 1957. Bradley, Ralph A. and Terry, Milton E. (1952). The rank analysis of incomplete block designs. I. The method of paired comparisons. Biometrika, 39, 324-45. Elo, Arpad E. (1978). The rating of chessplayers, past and present. Arco Publishing: New York. https://en.wikipedia.org/wiki/Elo_rating_system Ford, Lester R. Jr. (1957). Solution of a ranking problem from binary comparisons. American Mathematical Monthly, 64(8), 28-33. As best I can tell, the Elo model is based on the "logistic" distribution rather than the Gaussian distribution. They look very similar, but the logistic has slightly fatter tails. sech((x-mu)/(2s))^2/(4s) Just remember "sech-mate" ;-) Its cdf is the hyperbolic tangent function! https://en.wikipedia.org/wiki/Logistic_distribution The best discussion of ZermElo I was able to find is: "Introductory note to 1928" Mark E. Glickman 10 pages "Zermelos 1928 paper on measuring participants playing strengths in chess tournaments is a remarkable work in the history of paired comparison modeling." http://www.glicko.net/research/preface-z28.pdf At 05:23 AM 9/5/2014, Henry Baker wrote:
I found this (somewhat old) picture of the distribution of chess ratings:
http://zwim.free.fr/ics/rating_distribution.gif
It isn't exactly Gaussian, but it seems to have Gaussian qualities.
1. Has anyone done research on the distribution of chess ratings?
2. What is the _interpretation_ of chess ratings? I.e., if A has chess rating Ar and B has chess rating Br, what is the probability that A beats B?