Rating Systems for Gameplayers, and Learning

| This report studies rating systems: systems that produce quantitative measures, called \rat-ings," of the ability of players in a league, based on game results. By \quantitative", it is meant that win odds for a game between two players in the league may be estimated from their ratings. We consider both`static' and`dynamic' systems. The latter update the ratings after each game. Attention is given to noise in rating systems and to the distribution of ratings in the player population. Some real-world data is also included. This subject may be of interest