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A Definitive Analysis of the Trueskill System (How Your Skill Level Works)

#1RepthPosted 11/26/2007 8:36:15 AMmessage detail
This is a mini-guide based on the original true-skill explanation of El Kafungus of Bungie.net. His original explanation may be accessed here: http://www.bungie.net/Forums/posts.aspx?postID=14414600

Note that I do not take any credit for this as my own work, it is only a summary of El Kafungus's explanation.

What is the trueskill system and how does it work?
Well, the trueskill system is a skill rating system that is used for many games on XBox Live and more than likely PC. If you haven't already guessed, the reason I bring it up is because Halo 3 uses the trueskill system.

The trueskill system works on two basic valus, your uncertainty value (sigma) and your actual skill (mu). I will refer to them as sigma and mu from now on.

Your sigma is basically how the game accounts for luck; it is the numerical representation of what your skill could be. Play consistently for a low sigma, or play inconsistently for a high sigma.

Your mu is the actual representation of your skill. Win games to raise it, lose games to lower it.

The mathematical relation of mu and sigma is (mu) - k(sigma) where k is a constant assigned by the developers. This means that your skill is actually higher than the number you see, but the game does not give you the benefit of the doubt.


These are the basics of the trueskill system, and so I do not deter people from reading by creating a wall of text, I will include the "What does this mean to me?" section in the next post.
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iRepth
#2Repth(Topic Creator)Posted 11/26/2007 8:36:40 AMmessage detail
What does it mean to me?

Why don't I level up after winning X games in a row?

Mu increases after a win. Always. The increase is proportional to the winner's Sigma and the Mu difference between the winner and the loser. So, if your Sigma is high, you will proceed faster through the ranking system (in BOTH directions). If your Sigma is low, you will both gain and lose rank more slowly.


So, I want a high Sigma value?

While it sounds as though a high Sigma value is desirable, it CAN be a double edged sword. A high Sigma can mean you increase by one level for every win. It also means you decrease by one level for every loss. In addition, a high Sigma means that your skill ranking will be significantly lower than your actual skill owing to the conservative nature of the Ranking = mu - (K * Sigma) ranking equation.

Also, Sigma value starts out VERY high. So, if this is your friend's first time in a particular ranked hopper, and he wins consistently, his rank will rise meteorically due to his high Sigma.



Why do I win 10 games and not level up, then delevel when I lose 2? Help!

There are several possible explanations for this. The easiest one, and the one that fits the Trueskill system EXACTLY as explained by Microsoft, is that losing against a team that is X (I believe 6 or more, but experimentation is needed to determine the true value) skill points below you can cause you to lose as much as 5 times the Mu value that winning against even level teams gains you. Of course, winning against a team that has X more skill levels than you can net you as much as 5 times the Mu gain. The reverse is true as well. Winning against a weak team can count as little as 1/5th of an even skill win.

Second, and this is enlightened conjecture, your Sigma value was low at the beginning of your streak, and since your win streak is raising it, the conservative ranking system (Remember, Rank = Mu MINUS (K times Sigma)) is kicking in to reduce your apparent skill level. Your real Mu is higher, but your higher Sigma is having a negative impact.


Some Myth Busting

Trueskill DOES NOT take into evaluation performances inside the game. The ONLY statistics that Trueskill takes from a game are the Mu and Sigma values of all the players, and how you placed.

This means that out of all of these statistics:
Getting the MVP
Having a High K/D ratio
Getting the most medals
Skill levels of those you killed / killed you
Weapons you used
Headshots
Captures, detonations, stops, ousts, etc.

NONE of them matter when calculating the Mu increase/decrease. Any link between any of these and the skill ratings are purely correlative and not causative.


Up next: summary.
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XBL GT:
iRepth
#3Repth(Topic Creator)Posted 11/26/2007 8:37:40 AMmessage detail
Summary (if nothing else, read this!)

If you're worried that you're not getting your fair shake in the ranking system, look at the last 50 games that you've played in that hopper. (If you haven't played 50 games, play more. The system needs more data.)

Take your win/loss average. If it's 65% or above, and you've been in that playlist for a while, you've probably increased in level 2 or more times over the last 50 games (or you will in the next 20 or so). Otherwise you are going to be hovering around the same level or dropping in rank.
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XBL GT:
iRepth
#4SSJ_MCPosted 11/26/2007 8:49:01 AMmessage detail
Nice job, Repth. I requested this to be stickied.
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#5reviewmonsterPosted 11/26/2007 8:52:26 AMmessage detail
I would request to be sticked, but I don't think I have the ability.

:(


IT'S STICKIED IN MY HEART.

and thats all that matters.
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#6AngelsNAirwav3sPosted 11/26/2007 8:52:35 AMmessage detail
sticky
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#7gboymagikPosted 11/26/2007 8:55:25 AMmessage detail
how do u request for sticky? or what level do you have to be
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#8TaOpOcLPosted 11/26/2007 9:06:58 AMmessage detail
This should be stickied. For reals.
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#9king_mickeyPosted 11/26/2007 9:11:03 AMmessage detail
For those who want the sticky (and don't know how to yet...)

http://boards.gamefaqs.com/gfaqs/detail.php?board=926632&topic=39792811&message=436150348

Scroll down and you'll see "Request Sticky Topic" or something.

Make sure you state a good reason if you the topic stickied.

I'm not sure if the feature is restricted against new users :p
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#10Orange_ApplePosted 11/26/2007 9:15:55 AMmessage detail
sticky requested
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http://boards.gamefaqs.com/gfaqs/genmessage.php?board=926632&topic=38697301 (For those who want to play some Customs)
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