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# Microsoft TrueSkill and the Art of Gaming Statistics

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## Determining TrueSkill

The main question in a video game ranking system is the ultimate skill of the player, but Microsoft’s TrueSkill system is one of the few to attempt to factor in a very important figure: uncertainty. Uncertainty, of course, is a very difficult thing to quantify, but TrueSkill does it in an interesting way: by using Bayesian inference. Put very briefly, Bayesian inference is a means of deducing the likelihood of a given event to a certain probability. Uncertainty in this application refers to the consistency of a player’s performance. Players’ skill ratings are tracked separately from their uncertainty, and although the skill rating will go up by defeating high-ranking players and go down for losing to low-ranking ones, if they frequently do, both their uncertainty will only increase.

More likely, after a few games some conclusions can be drawn about a certain player’s skill. By competing in large games with a high number of opponents a player’s uncertainty can decrease rather quickly, but the placement within online matches helps to determine that.

For instance, if you’re in a free-for-all game with 64 players, all with identical skill and uncertainty ratings, and you place higher than 32 but lower than 31, the system can be fairly confident that your overall skill is somewhere in the middle when compared with the group of competitors. You will, therefore, have your uncertainty rating reduced by a relatively large amount.

However, if you come in first, your uncertainty will remain higher simply because you may have grossly outclassed the second-place competitor or barely eked out the win, but there is no one else in that particular match to compare your performance to, and so there is no way to quantify your performance reliably.

In this case, your skill rating would increase the most of all competitors, but your uncertainty would still remain somewhat high. Having a high skill rating is of primary importance, of course, but a high uncertainty could result in you being unjustly lowered on the game’s overall leaderboard. TrueSkill leaderboards are calculated so that a player’s uncertainty factor is multiplied by a constant and then subtracted from the overall skill rating. By increasing or decreasing the value of that constant, the leaderboard can be adjusted to give more or less importance to consistent performance.

By participating in large online games and by performing consistently, the system can generally identify your skill (or lack thereof) very quickly. If you have the abilities, you can move to the top of the leaderboards in just a few hours, whereas other games require hundreds of online matches before you could even consider approaching the top. According to Thore and Ralf, this has caught some gamers off guard:

...we have mainly gotten positive feedback from people who were amazed how fast the system found out about their skill. In fact, one gamer was "complaining" that he was featured on Gotham TV after only two hours of playing (which means that he was already rated among the Top 100 players in PGR 3); to us, this is testament that the system works as expected.