Understanding distributions of chess performances

Abstract. This paper studies the population of chess players and the distribu-tion of their performances measured by Elo ratings and by computer analysis of moves. Evidence that ratings have remained stable since the inception of the Elo system in the 1970’s is given in several forms: by showing that the population of strong players fits a simple logistic-curve model without inflation, by plotting players ’ average error against the FIDE category of tournaments over time, and by skill parameters from a model that employs computer analysis keeping a nearly constant relation to Elo rating across that time. The distribution of the model’s In-trinsic Performance Ratings can hence be used to compare populations that have limited interaction, such as between players in a national chess federation and FIDE, and ascertain relative drift in their respective rating systems