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The Rating of Chess Players, Past and Present

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This work was written in 1978 by the Old Man himself, Arpad Elo. Chess players remember Elo as the cantankerous professor of physics from Marquette University, and as the inventor of the rating systems used by the United States Chess Federation (USCF) and the International Chess Federation (FIDE). Who better to explain the mathematics behind the rating system which, according to a letter Elo wrote to Chess Life several years ago, "is, after all, MY system". The explanations are semi-technical, but understandable by anybody with a mathematical inclination, regardless of their education in that field. There is even a chapter in which ratings are calculated retroactively, for grandmasters of bygone days. The book was written B.K. (before Kasparov), so of course Bobby Fischer comes out on top, with a rating of about 2780. His closest competitors are Lasker, Capablanca, and Botvinnik, each of whom peaked at about 2720. The average rating of tournament players in the U.S., by the way, is about 1500, several classes below the stars. Interesting reading.

Arpad Elo was a physicist who passed most of his life in the USA. He invented the rating system, the method to measure the strenght of chess level of the players. The Elo (rating) system, was incorporated by the International Chess Federation (FIDE), at the end of the seventies and now the rating of the players is the first measure that FIDE uses to classify the chess players.

Elo, in his book, defines the rating system, the formulas, the statistics and mathematics around it. He also analyse the performance of the best players of his time (and also the old players like Alekhine, Capablanca, Lasker), and make some points around the validity of the system. As usual with someone with mathematics preparation, Elo is very strict in his ideas and makes a good evaluation of the rating system in a whole.

In fact, he predicted the final result between Spassky and Fischer match (1972) exactly, using his formulas for that. I think this result validates correctly the good behaviour of the rating system

The only problem with the book is that it is not a very actual one. I mean, Elo talks about the first stage of the FIDE rating where there were no more than 300 players ranked. Right now the FIDE rating list has about 80,000 players classified.

On the other hand, Elo never predicted a phenomena is seeing today: rating inflation. Jeff Sonas, a mathematician who loves chess statistics has not also a good explanation to this problem.

In any case, Elo book is a must for who is interested in the mathematics of the Elo rating system.