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Leaderboards
Q: If the skill of every player is represented by two numbers, how is it possible to rank players in a leaderboard?
A: The TrueSkill ranking system uses the so-called conservative skill estimate which is the 1% quantile of the belief distribution: it is extremely likely (to be precise, with a belief of 99%) that the players actual skill is higher than the conservative estimate. Have a look in the detailed description.
Q: How can I become the top player in a leaderboard?
A: It's simple: Win games! The TrueSkill ranking system matches you with people of similar skill so winning against them will always bring you up the leaderboard.
But, more seriously, in order to become a level 50 player in an 8-player-Free-for-All game mode you will only need to win 8 (tightly) match-made games in a row! If you do not believe that, try out our interactive rank calculator: Always make sure that Alice wins the game and all other 7 players have the same μ but a σ of 1 (you can use the After->Before button). After 8 games you should see that Alice's μ is 56.995 and the σ is 1.901; hence, the conservative skill estimate would be Level 51! It may take a bit longer in reality because in these calculations it was assumed that there are always enough players of every playing strength available.
Q: Who is the better player: Someone with a large μ and a large σ or a small μ and a small σ?
A: The answer to this question is not straightforward. For someone with a large σ the TrueSkill ranking system is still uncertain about the skill. Thus, the player with the large μ and a large σ may be better. The best way to find out is to ask the player with the large σ to play more.
Q: I am a level 30 player with a σ of 5 and my friend is a level 28 player with a σ of 2? Why does the TrueSkill ranking system claim that my friend is better; at the end of the day, my level is higher?
A: That is correct. But, you have not played enough games yet for the TrueSkill ranking system to confidently know that you are better; so conservatively speaking, your level is probably 15 = 30 - 3 * 5 whereas your friend's conservative estimate is level 22 = 28 - 3 * 2.
Q: A couple of days ago I managed to get into the top 350 (in PGR 3 online career) after winning probably 25 of 30 races and that brought me up about 120 spots. Now tonight I have had 5 races: 2 wins,1 second,5th (got spun twice) and a 4th on one of the Vegas tracks. Because of this pathetic record (that is how the TrueSkill formula sees it) I have gone down 115 spots. How is it fair that 2 bad races basically dropped me down almost as many points as 25 wins out of 30 races took to gain all those places ?
A: There are two reasons that can cause this problem (although the latter is probably more responsible for this "phenomenon"):
- Ranks displayed in PGR 3 are the position in the total leaderboard. That means, if you are rank 659 then there are 658 gamers with a higher skill (estimate) than you. This number can vary without a gamer actually having to play a game; for example, if some (legitimate) "Gotham star" gets to the top 100 players in the world whilst you are not even racing, then your rank goes down to "660" without you doing anything wrong. This "rank" can never be guaranteed to be "stable".
- Roughly speaking, the change in your skill estimate depends on how "surprising" the game outcome is. If you happen to be (among) the player(s) with the highest skill in each of the games you played, then the 25 wins were not surprising and hence none of these games provided a significant increase in your skill estimate. However, if coming 5th was a rather unlikely outcome in the game were you actually did come fifth, then your skill needs to be adapted significantly. Another way of seeing the issue is that TrueSkill does take the strength of the opposition into account. One cannot simply compute the win ratio and equate this with skill; if all wins happen in the (sometimes) unavoidable unbalanced games then a win is not really testament to your (even) high(er) skill!
Q: Well there must be a bug in the system cause I jumped into a 4 person race with 3 lower ranked individuals, won the race and my position in the league I was in dropped about 50 spots.
A: Surprisingly, this is not a bug and it happens when players with very small σ but widely varying μ get matched together (thanks to rugdivot for figuring this out). For example, try
this
link.
So, what is going on here? Between any two games of a gamer, the TrueSkill ranking system assumes that the true skill of a gamer, that is, μ, can have changed slightly either up or down; this property is what allows the ranking system to adapt to a change in the skill of a gamer. Technically, this is achieved by a small increase in the σ of each participating gamer before the game outcome is incorporated. Usually, a game outcome provides enough pieces of information to reduce this increased uncertainty. But, in a badly matched game (as the one described above) this is not the case; in this case, nothing can be learned about the winner from the game outcome (because it was already known before the game that the winner was significantly higher ranked than the other gamers he has beaten). So, conservatively speaking, the winner's skill might have slightly decreased! Note that this can only happen if the gamer is not matched correctly so that he can "prove" to the TrueSkill ranking system that his skill has not changed.
Q: Is it at all possible to view the TrueSkill rating of an individual Xbox Live Gamertag? Is there a website that I can go to, to see the ratings of people's
gamertags?
A: Most Xbox 360 games have a leaderboard function where you can find your TrueSkill; in fact, starting 23rd May 2006 some games have also provided web access to gamers' TrueSkill rating. However, there are a few exceptions, most notably with the game Call of Duty 2. At the moment, there is no way to find out about your TrueSkill in this game.
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TrueSkill™ Frequently Asked Questions 