There is a desire to provide a way to determine relative skills of players of games such as computer games, chess, tennis and any other suitable type of game. Our earlier Bayesian Scoring system is implemented in Xbox Live (trade mark) and is currently commercially available under the trade name TrueSkill (trade mark). Here we build on our earlier work and use a new method of computation to enable processing times to be significantly reduced. Message passing techniques are adapted to enable computation of updated skill beliefs to be obtained quickly even in the case of multiple teams of multiple players.