TrueSkill is a skill-based ranking system developed by Microsoft for use with video game matchmaking on the Xbox network.
Unlike the popular Elo rating system, which was initially designed for chess, TrueSkill is designed to support games with more than two players.
[1][2] In 2018, Microsoft published details about an extended version of TrueSkill, named TrueSkill2.
[3] It is based on a Thurstonian model with a Gaussian score distribution.
(mu, representing perceived skill) and a variance of
(sigma, representing how "unconfident" the system is in the player's
Unbalanced games, for example, result in either negligible updates when the favorite wins, or huge updates when the favorite loses surprisingly.
Factor graphs and expectation propagation via moment matching are used to compute the message passing equations which in turn compute the skills for the players.
[1][2] Player ranks are displayed as the conservative estimate of their skill,
This is conservative, because the system is 99% sure that the player's skill is actually higher than what is displayed as their rank.
This explains why people may gain ranks from losses.