[Math] Explanation of the TrueSkill bayesian ranking algorithm in a two-person game, like Tennis

algorithmsbayesian

TrueSkill is mostly used for ranking and matching players on Xbox Online Games, it is a general rating model that could be applied to any game, including Chess, Tennis or Football.
It models every player with a single skill variable $s \sim N(x\mid m, v)$, which indicates how good player is on tennis. The expected skill value $m$ is accompanied by a level of uncertainty $v$, which tells us, how confident we are about the player’s skill estimation. Usually, the skill uncertainty decreases after observing the result of a game and it increases over the time, when player is not playing any games. Regarding to the expect skill value $m$, it moves up for a winner of a game and it shifts in an opposite direction for a loser.

Consider two tennis players $p_1$ and $p_2$ playing a tennis game and assume that we are provided with the probability distributions of skill and performance variables for both players at the beginning of the game. How would we ask for the probability of winning the game by player p1 and we would like to know the skills for both players given player p1 is a winner. Which informations are needed? For example – the won matches in whole career or won gamepoints? I don't really understand, how I could use this ranking algorithm in a two-person game, like tennis (or any other sport, where there are two teams).

Best Answer

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

The answer would be game points do not matter. The model is only based on wins and losses. Won matches over time would assist the model in getting a more accurate picture. See FAQ in the above link for team games.

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