TrueSkill

microsoft.com/en-us/research/project/trueskill-ranking-system

A Bayesian skill rating system developed by Microsoft research.

Summary:

• ELO uses point estimation, producing a single skill value, whereas TrueSkill uses interval estimation, giving a range of skill. The skill estimate is represented by the mean, and its certainty by the standard deviation. The standard deviation narrows as more games are played. (In other words, playing more games increases certainty in the skill estimate.)
• An obvious result (the expected winner wins) has a small effect on ratings; an unexpected result (the expected loser wins) has a large effect.
• Rating calculations can vary with a game’s characteristics:
  • Beta: A value that varies with how strongly skill correlates with winning and losing in the game.
  • Dynamics Factor/Tau: The amount of “noise” added to keep the standard deviation from converging to zero as games are played.
  • Draw Probability: The probability of a draw. A draw in a game with a high draw probability is an “obvious result.” Conversely, a weak team beating a strong team despite a high draw probability is a “very surprising result.” In ELO, drawn games cannot affect ratings. But a draw itself is important information, especially when draws are unlikely.
• Calculations also account for practical situations:
  • Partial Play: Players who influenced the outcome only slightly because they joined midway, left midway, took a break, and so on.
  • Partial Update: Cases where we want this game’s result to affect ratings only partially, for reasons such as an “unstable network.”
• Unlike ELO, it can calculate ratings for each participant in team matches with various team configurations.
• It can predict how good a team configuration is (that is, how evenly matched the game will be): Match Quality.