Rating competitors in games with strength-dependent tie probabilities

Metro Toronto Convention Centre 

Competitor rating systems for head-to-head games are typically used to measure playing strength from game outcomes. Most implemented rating systems assume only win/loss outcomes, and treat occurrences of ties as the equivalent to half a win and half a loss. However, in games such as chess, the probability of a tie (draw) is demonstrably higher for stronger players than for weaker players, so that rating systems ignoring this aspect of game results may produce inaccurate strength estimates. We develop a new rating system for head-to-head games that explicitly acknowledges a tie as a third outcome, with the probability of a tie depending on the strengths of the competitors. Our approach relies on time-varying game outcomes following a Bayesian dynamic modeling framework, and that posterior updates within a time period are approximated by one iteration of Newton-Raphson evaluated at the prior mean. The approach is demonstrated on a large dataset of chess games played in International Correspondence Chess Federation tournaments.