TrueSkill Skill Rating System

The TrueSkill algorithm is described in the NeurIPS paper TrueSkill(TM): a Bayesian skill rating system, joint work with Ralf Herbrich and Tom Minka.

You can find more details on the TrueSkill page at Microsoft Research and the TrueSkill Wikipedia page. Also, Mike Moser’s excellent blogpost on TrueSkill explains all the underlying mathematics necessary to understand it.

TrueSkill is now textbook material, and, e.g., discussed in Kevin Murphy’s excellent textbook Machine Learning: A Probabilistic Perspective and in David Barber’s great book Bayesian Reasoning and Machine Learning

We later developed a generalisation of TrueSkill that makes it possible to track players’ skills through time, described in the NeurIPS paper TrueSkill Through Time. Most notably, it contains a plot of top chess players’ skill histories through time.