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# Microsoft TrueSkill and the Art of Gaming Statistics

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## Matchmaking and Team Skills

With comparison of players’ relative skills and consistencies, it’s possible to determine the probability that a set of players will have an entertaining match. That is to say, their actual skills are comparable. By using Bayesian inference to compare two players’ skills and uncertainty ratings, the probability that a set match between them will end in a draw is calculated. The higher the probability of a draw, the closer the match will likely be, and thus more entertaining. Draws are not always possible depending on the type of game being played, but the same calculations can be used for effective matchmaking.

These calculations can also be used to create effective teams and interesting matches in team-based games. Individual teams can be formed in the same way overall matches would be made, and those teams can then be compared in the same way that two players would be compared. Comparison of teams is made easy by TrueSkill, with the ranking of a team considered to be the average skill and uncertainty ratings of its players. In this way, a team with very high-ranked players combined with very low-ranked players would be considered a fair match for a team comprised of all average-ranked players.

Thore and Ralf confess, however, that this approach may not always be applicable:

Our assumption is indeed that the skill of a team can be calculated as the sum of the skills of the team members. This is in many ways the simplest assumption possible and leads to an efficient update algorithm for the player skills. However, we are fully aware that this assumption may not be valid for all types of team games. Take, for example, a Team Sniper game in Halo 2. It would be very well possible that the game outcome is determined by the skill of the best sniper in each team, not by the sum of the skills in each team. One can also think of games where the weakest player dominates the outcome. Think, for example, of a team racing game in which the last team member to cross the finishing line determines the outcome. Clearly, your weakest player would determine the fate of the team. However, these are all game type–specific decisions. TrueSkill, in contrast, aims at providing a unified ranking and matchmaking for all games. In the future, we may think of adapting TrueSkill to specific game types.

In addition to adapting TrueSkill for individual types of video games, the system’s creators believe that it could be applied outside of the video game world to more types of rankings.

The mathematical backbone of TrueSkill is very generally applicable can be used in a variety of problems, including:
• Ranking of Web pages
• Ranking of content
• Ranking moves in Go
We are currently exploring the possibilities in all these areas. For example, over the last six months we have developed an engine to play the ancient oriental game of Go by learning from expert games. Using the TrueSkill technology, the system achieves a playing strength of roughly 10–12 kyu (medium amateur level) but can play as many as 1000 moves per second.