Predicting the Outcome of Chess Games based on Historical Data

This report describes an approach used in the competition “Chess Ratings – Elo versus the Rest of the World” that took place between August and November 2010. Using the Bradley-Terry model as starting point, we postulate that the strength of each player can be approximated by the expected score against a common but unknown reference player, whose strength is never actually computed. This approach provides an iterative procedure for computing the strength of each player based on the strength of its opponents and on the average score against those opponents. To ensure convergence and to better fit the model to the training data, the approach can be tuned with several parameters such as a prior for the average score against opponents, a prior for the average strength of opponents, and a time factor to gradually reduce the weight of past games. In this competition, the approach was tuned in order to minimize a month-aggregated RMSE of game predictions.