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[ednever]

My understanding was your level was calculated bybyourvtrue skill estimate minus the uncertainty (which was some number of standard deviations)

Makes sense do far.

But I thought that standard deviation would just be a function of the number of games you played. It's inviously a lot more complicated than that.

I guess now if your performed was something like:

Play 10 games.
Lose five against a level 50, win give against a level 20, you would enc up with a lower st than if you...

Play 10 games.
Win 5 against a level 50, lose five against a level 20


Is that right?

I was looking up my own rank today (just hit lvl 35). I've "only" played 1200 or do games, but there are only about 4-5 people with high rank than me with lower st (which means I have very low "trueskill" for my level). All the people with lower st have played 3000-7000 games - ie lots more than me...

Do I have it right in my head now?

Ed

[Captain_Frisk]

I believe that officially - absent any DougZ modifications, that your std. deviation should only decrease as additional observations occur (http://research.microsoft.com/en-us/projects/trueskill/details.aspx) - as the system becomes more and more confident of your skill. 

You probably need to have taken a college level probability course to make sense of the research article linked above - and even then it's not a light read.

TLDR, the amount it decreases depends on the likelyhood of the outcome.  If you were expected to win, and did, your variance will drop (while your rating will increase slightly). If were expected to lose, and won - your variance will still drop, but not as much, but your mean skill rating will increase to compensate. 

DougZ has added a bit of rating decay - which increases your variance every so slightly every day.   This keeps people from perching at the top of the leaderboard, and serves to model the fact that knowledge about the game increases over time, and someone who hasn't played in a while may no longer actually be as skilled as they were the last time they played.

Among crazy frequent players - who also have a tendency to be near the top of the leaderboard, this has a tendency to reflect how often you have played recently.

Examples:
You have played ~220 games in the last 10 days - your variance: 6.9.  It looks like you're a relative newcomer who's playing obsessively, which is why you are higher on the leaderboard than the other players with a mean skill of 42.... because they don't play as often.

For some of the clowns near the top - who (with me excepted) play a decent amount

Headso ~ 350 games! ~ 5.7
WanderingWinder ~ 130 games ~ 6.5
Me ~ 100 games ~ 8.2

[qmech]

A quick summary of the Trueskill paper: for each player, have a probability distribution over skill levels representing our knowledge about that player's skill.  Whenever we witness the outcome of a game between two players we're tracking, perform a Bayesian update to give new, more accurate, distributions for those players.  This all turns out to be too hard, so we approximate by a normal distribution after each update.