TrueSkill

TrueSkill is a Bayesian rating system designed for multiplayer video games, developed by Microsoft Research and deployed on Xbox Live to rank players and support matchmaking. It generalizes the Elo rating approach to handle multiple players and varying team sizes, updating skill estimates as players compete and their performance becomes known.

In TrueSkill, each player's true skill s_i is modeled as a Gaussian distribution with mean mu_i and standard deviation sigma_i, reflecting both an estimate of skill and uncertainty. For a game, a player’s in-game performance is assumed to be p_i ~ N(mu_i, sigma_i^2 + beta^2), where beta represents variability in performance across matches. The observed match outcomes define constraints on these performances, and Bayesian inference yields posterior distributions over the players’ mu_i and sigma_i. In practice, efficient approximations are used to update a player’s means and uncertainties after each match.

The system supports teams of any size, treating each team’s performance as a sum of individual performances and comparing teams to determine outcomes, including draws. After a match, the algorithm increases the winning players’ mu values and decreases losers’ mu values, while typically reducing sigma values to reflect growing confidence as more data accumulates. This probabilistic framework allows TrueSkill to handle uncertain results and evolving rosters.

Compared with Elo, TrueSkill explicitly accounts for uncertainty, supports variable team composition and multi-player games, and accommodates draws. It has been influential in matchmaking design and ranking systems beyond Xbox Live, with numerous research publications detailing its mathematical foundations and practical implementations.