Pierre Dangauthier, Ralf Herbrich, Tom Minka, Thore Graepel
We extend the Bayesian skill rating system TrueSkill to infer entire time series of skills of players by smoothing through time instead of (cid:12)ltering. The skill of each participating player, say, every year is represented by a latent skill variable which is a(cid:11)ected by the relevant game outcomes that year, and coupled with the skill variables of the previous and subsequent year. Inference in the resulting factor graph is carried out by approximate message passing (EP) along the time series of skills. As before the system tracks the uncertainty about player skills, explicitly models draws, can deal with any number of competing entities and can infer individual skills from team results. We extend the system to estimate player-speci(cid:12)c draw mar- gins. Based on these models we present an analysis of the skill curves of important players in the history of chess over the past 150 years. Results include plots of players’ lifetime skill development as well as the ability to compare the skills of di(cid:11)erent players across time. Our results indicate that a) the overall playing strength has increased over the past 150 years, and b) that modelling a player’s ability to force a draw provides signi(cid:12)cantly better predictive power.