A Two Dimensional Measure of Performance in Chess

Abstract

A two dimensional measure of chess performance is presented and it is shown to have more information and a greater power of discrimination than scalar measures because it does not rely on scoring. The scoring procedure used by scalar measures to reduce chess game outcomes from a trinomial to a binomial variable causes some chess game outcome information to be irretrievably lost.

Keywords: chess, performance, rating, Elo, FIDE, playing strength, trinomial, statistics, numerical methods, Studentized Euclidean distance, probability vector, Monte Carlo simulation, bootstrap, uncertainty