Henry Baker: 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.
--not so. Elo's system in his book (which I read prior to writing my 1984 BS thesis) based on Gaussian, the others based on logistic. But these functions employed in the rating formulas, not as probability distributions of rating distribution. My 1984 bachelor's thesis at MIT, which my paper #20 was based on, shows Elo was wrong to do what he did, and logistic is superior to Gaussian where he used it, at least in the sense I proved "minimatch self-consistency" results for logistic (my "WM^n model") while Gaussian has no such. If Glickman claims otherwise it is perhaps because he never read Elo's book, or for some other reason, I have no idea. However, it appears in the meantime that the world in general has somehow realized that Gaussians suck (presumably due to experiments, since few members of the world showed any signs of reading my BS thesis), and most (all?) rating agencies have switched away from Elo's original system and to a logistic-base system.
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
"Zermelo's 1928 paper on measuring participants' playing strengths in chess tournaments is a remarkable work in the history of paired comparison modeling."