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  • Subject: In depth explanation of the Halo 3 skill ranking system.
Subject: In depth explanation of the Halo 3 skill ranking system.
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I am NOT an employee of Bungie nor one of Microsoft, and my views and opinions do not necessarily reflect those of either of the aforementioned entities.
Also, thanks for sticking this Bungie, I hope it is useful.


There is one caveat to consider before we get under weigh. Bungie is not likely, nor or ever, to release the true inner workings of the Halo 3 ranking system, but as it is based somewhat on the Microsoft Trueskill system, this is a fair approximation of the way skill ranking works in Halo 3.

What is the Trueskill system?
The Trueskill system is a player skill rating system for Xbox Live. Halo 3 uses a version of the Trueskill system in order to make the matches fairly even.



How Does Trueskill Work?
Trueskill assigns skills on a normal distribution (bell curve, Gaussian). The Trueskill system has two main variables to consider. They are your player skill level (Mu) and your uncertainty factor (Sigma).

Mu is an approximation of your skill level based upon past performance. Win games to raise Mu, and lose games to lower Mu.

Sigma is the numerical representation of the range in which your true skill could lie. Play really consistently, and you have a low Sigma. Play streakily, and you have a higher Sigma.

After a win, the Trueskill system adjusts your skill ranking based upon the Mu and Sigma of all the players in the game. We'll go deeper into how much it is adjusted later.

Trueskill systems use a conservative ranking Ranking = mu - (K * Sigma) so your skill is likely to be higher than the actual number represented in your Halo 3 highest skill level. K is a constant assigned an arbitrary value by the developers of the game.



Why don't I level up after winning X games in a row? / Why does my friend go up three levels a game and I don't?
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.



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.

For example. When I play Team Slayer with my buddies on my alternate gamertag, much of the time I end up carrying the team. I created this tag to play with my buddies, and as such, have only ever played on that party with that tag. I ranked up to the level of my friends within 20 or so games, while it had taken them 50 to 100 games to reach their level. My friends thought that it was because of my frequent MVP status and my high K/D ratio that I leveled up so fast.

Wrong. I leveled up fast because A) I initially had a very high Sigma, making my Mu more variable after each win, B) Starting out at a 1 and playing people in the mid teens gave me a considerable boost every time I won, and C) We won more frequently than they had in the past.



Summation
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.



Addendum, Opinion, and Technical Notes
In strict Trueskill systems, Sigma only decreases. I believe the "momentum" system in Halo 3 means that Sigma can be increased through consistent winning or losing. This is total conjecture, but I think that Sigma in Halo 3 matchmaking hoppers is proportional to the absolute value of the win/loss ratio of your last X number of games. The formula probably looks a little like: Sigma = C ( | wins - losses | ) where C is an arbitrary constant. This would explain why when some people go on a win streak with two or more different parties, their skill goes up faster than their teammates' skill.

I also believe that the system is weighted so that the peak of the normal distribution is around level 20, not level 25. That means it will take more wins to level through 1-25 than it will 25-50. Which makes a bit of sense, if you don't want the highest levels too terribly crowded.

The higher the Sigma of your opponents, the less Mu you gain from beating them.

Predictable outcomes (e.g. win against a lower ranked opponent) are treated as statistically less significant. Upsets are given more weight. So, winning against lower ranked opponents doesn't do much for your Mu rating. Neither does losing against higher ranked ones. But beat a team that's 6 or more ranks above you and at least someone on your team will rank up.

Trueskill ratings have no discernable correlation from hopper to hopper. When you play on a hopper you've never played on before, you are starting with a fresh Mu and a high Sigma.

Team Mu and Team Sigma are the summation of the Mu and Sigma values of all the players on the team. When calculating the skill of an opponent in a team game, the system uses the Team Mu and Team Sigma values in calculation wherever rational.

*Removed equations for space. They can be found in the link below.*

The rest of the equations and a less Halo 3 centric analysis of the Trueskill system can be found here.

_________________________________________________________
Important additions, Appendices, and Member Questions Answered
_________________________________________________________

In-depth response to a post LoveNub made later in this thread. Should clear things up for some.

More data analyzed, and a request for help with research

Kudos to Jay120171 for finding the post detailing the Mixed Party Bug in matchmaking.

"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.

mo0vaf00 writes: (edited to clarify intent)
So is there some kind of value that requires you to be inconsistent to rank up? If I win 1 game going even and win the next going +10 do I have more of a chance of ranking up than just winning 2 games getting the same score?


This conclusion is popping up fairly frequently. The answer is no. The system does not look at "In Match" statistics. At all. These stats are all included in a list above. The game only looks at your wins and your losses, and the strength of the opponents you play against.

Also, the system does not "reward" you for having a high Sigma value. There is ONE positive associated with high Sigma, and there are TWO negatives.
Positive: Your level can move up faster through winning.
Negative: Your level can move down faster through losing.
Negative: The conservative ranking system ranks you lower when your Sigma is higher.

Higher Sigma simply means your level is more fluid. Sigma is good to have high when you are still reaching your appropriate skill level, but good to have low once you've reached it and are working on improving.


[Edited on 11.24.2007 11:54 PM PST]

  • 11.12.2007 1:22 PM PDT

Very nice post and informative. I saw your link in another thread we were in together but I wanted to comment here and give your thread a little bump. I know there are some people who would really like to read this and some who really should read it.

  • 11.12.2007 2:35 PM PDT
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Very well thought out, and very well organized. While I already had a decent grasp on this from Microsoft's website, tis could be the proverbial Halo ring against all 'My rank isn't moving' threads.

P.S. You can has Recon.

  • 11.12.2007 2:38 PM PDT

you say K/D etc doesnt matter. How come in a weekly update they mentioned something like: "if you start getting more headshots your rank will go up more" or something along those lines.

Also, the consistancy thing. Is it based only on wins and losses? Or is it based on how well you perform. If I CONSISTANTLY go +10 in TS that lowers my sigma since im consistent and makes it take more wins to level??

  • 11.12.2007 2:49 PM PDT
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Cheers for the write up. Tis a shame this thread will probably die as the majority of users on this site won't understand it. But cheers anyway.

[Edited on 11.16.2007 5:54 AM PST]

  • 11.12.2007 3:02 PM PDT

Posted by: Rankith117
you say K/D etc doesnt matter. How come in a weekly update they mentioned something like: "if you start getting more headshots your rank will go up more" or something along those lines.

Also, the consistancy thing. Is it based only on wins and losses? Or is it based on how well you perform. If I CONSISTANTLY go +10 in TS that lowers my sigma since im consistent and makes it take more wins to level??
That particular comment only meant if you get better you will rank up. Getting more headshots was simply a way of expressing an increase in skill. Achronos has posted all over the forums in a number of threads correcting that statement. This is just one such post by him on the issue but there are many more if you look for them.

As for the second question: It's consistency in the wins and losses. Performance during the game is not a factor at all for any of it.

[Edited on 11.12.2007 3:14 PM PST]

  • 11.12.2007 3:11 PM PDT

GOAT

Its stickied now.

Good Job!

  • 11.12.2007 3:55 PM PDT
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Psalm 32:10

Many are the woes of the wicked,
but the LORD's unfailing love
surrounds the man who trusts in him.

Good stuff man.

  • 11.12.2007 4:01 PM PDT
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Talk to the Soul | ~B.B. | Know Your Duardo |  | Hero | ISFJ | 77135 | 94371

"It's not who I am underneath, but what I do that defines me."

Nice job. Well done.

  • 11.12.2007 4:06 PM PDT
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Excellent post sir.
I hope this will make some of the other unintelligent people on this forum stop complaining.
But...probably not, as they're unintelligent, hah.

  • 11.12.2007 4:08 PM PDT
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and sometimes i'll even win 7 in a row and get mvp out of three of those and still not go up in one of those matches.

  • 11.12.2007 4:12 PM PDT

Sup (H) =]

Great, Finally a in-depth definition of how the Ranking System works :)))

  • 11.12.2007 4:43 PM PDT

#2 Supporter Halocharts, #11 other account.
"Ordinary love is selfish, deeply rooted in desires and satisfactions. Divine love is without condition, without boundary, without change."
You are all loved beyond measure.
I, like you, am a light-sound-vibration complex that resonates with others. I have hopes and dreams and ambitions, just like you! I AM, and so are you! Yes, we are one and the same, you and I.

Posted by: zz BIG Biv yy
and sometimes i'll even win 7 in a row and get mvp out of three of those and still not go up in one of those matches.


First, I'll take this in general as 7 is a rather low number to be complaining about, (according to the OP you should be looking at 50 or so) but that feature of your ranking experiences does not belie its validity.

This is the sort of thing to which would-be helpers would inevitably respond: "you have to win against higher ranks!" (Along with certainty calculations, etc.). And they will start flaming and indicting you on various charges of being ignorant of the trueskill dynamics, of not being good, and the like -- almost as if it's your fault that you are not getting to play against the type of enemy (taking into account their certainty and ranks) against whom you will benefit from beating. It is rather silly that 10 or 20 wins against opponents of slightly lower ranks will get you nowhere, but one slip-up and you go down. This is nowhere near the 50%-50% win ratio that should be attained. It would be more in the interest of the "stuck" player if he were to play consistent games against higher ranks and once in a while lose. I, for example, have gone on long winning streaks against players slightly lower -- but the thing is I probably would just as well go on such streaks, with an occasional loss, against higher players if I could. (That is, I wish my wins would be significant but I'm winning against lower levels, which I have no control over and which are expected).

So there is a legitimate question there, a latent concern that many people mean but are not asking, and that is: why am I not allowed the opportunity to rank up? I know I have to win consistently, but what do you expect me to do except hope and pray that the enemy has higher levels? I'm already winning consistently against lower levels, but you can't blame me for getting matched with them!

In Halo 2, you did not have to have a fear that you would not rank up, regardless of games played. In a game where a disparity existed among player ranks, everyone could prove themselves and rank up but now only half can (the lower). And we've been accused of wanting to "grind the system" -- but that's somewhat misrepresentive of the situation. Our very concern is that we don't want to grind it, we don't want to have to win x games, with an auspicious fraction of that x counting towards rank. I just think I'd like to throw that out there and I hope it clears up some of the unrecognized ambiguity and unwarranted acrimony that usually accompanies the question (why am I not ranking up?).

(The only definite solution I can see is to play in a party where your teammates are higher -- but this can be difficult, especially as you get closer to 50).

And while there are certain other troublesome peculiarities that the OP doesn't really address, I think it's overall a very good write-up on trueskill that will certainly prove instructive to the masses.

[Edited on 11.12.2007 7:42 PM PST]

  • 11.12.2007 6:22 PM PDT
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Nice

  • 11.12.2007 6:26 PM PDT
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This is really helpful thank you, nice job on it!

  • 11.12.2007 7:03 PM PDT
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Great Explanation, and Very Well done.

  • 11.12.2007 7:05 PM PDT
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nice

  • 11.12.2007 7:29 PM PDT
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Very well written. All I need to do now is get up to level 25 and it's smooth sailing.

SHA NAH NAH!!!!!!!

  • 11.12.2007 7:46 PM PDT
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A virtue is a mean between two extremes.

Excellent explanation! I've been wondering how the system worked for a long time now.

  • 11.12.2007 8:01 PM PDT
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Wow That was amazing. thank you for writing this

  • 11.12.2007 8:32 PM PDT
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GT: AccidentsProne

"A wise man once told me don't argue with fools, cause people from a distance can't tell who is who"

*Saves thread*

I will now post this everytime someone makes a new thread whining "WAHH I JUST WON THREE GAMES AND DIDNT RANK UP, THE SYSTEM IS BROKE"

  • 11.12.2007 8:34 PM PDT

Thanks mate, thread's like these are few and far between.

It clears up quite a few things, I would assume I have a mid to low sigma now, my Team Slayer and Doubles bob around abit but they average around level 30.

But in more Layman's terms, Mu = Experience (A La Halo 2 ranking system) Sigma = Amount that can be earned. so you win you get Mu, but if your sigma is low because you played alot of games you will get meager amounts of Mu.

In a little table, this is how I interpret it.

1st game in a playlist
All Players level 1
Mu = 100 points
Sigma at 100%
win a game you level up

Thanks to some more clarity from the op, I can update these figure's.
given same end game place finishs.

50th game
Your level = 15 Player levels 13 (75 Mu/win 125Mu/loss) 14 (85 Mu/win 115Mu/loss) 15 (100 Mu/win/loss) 17 (125 Mu/win 75Mu/loss)
Sigma at 50%
you place 2nd
L13 was 1st
L15 was 3rd
L14 was 4th
L17 was 5th
in this you would get:
L13 You would lose 62 Mu -(50% of 125 Mu)
L14 You would gain 42 Mu +(50% of 85 Mu)
L15 You would gain 50 Mu +(50% of 100 Mu)
L17 You would gain 62 Mu +(50% of 125 Mu)


So, after this game you would gain 154 Mu but lose 62 and thus a net change of 92 Mu gained. After more and more games, your Sigma will fall so you gain and lose even less (so if you have a sketchy history at level 20 but roughly even amounts of wins/losses your rank will eventually stop around 19-21)

So, 100th game
Sigma = 5%
Your skill 20
Player skills L15, L19, L25, L22
You place 3rd
L25 1st (5% of 150 Mu) -7 Mu
L22 2nd (5% of 115 Mu) -6Mu
You placed 3rd
L19 4th (5% of 95 Mu) +4 Mu
L15 5th (5% of 50 Mu) +2 Mu

Please take these as rough guesses and I would have no Idea how much Mu is need to gain or lose levels. also, forgive any sketchy math, I didnt like my math teacher. but these show roughly what happen as per my interpretation and information gleaned from the Op.

*Edit*

Also, I do not know any of the rates the sigma rises or falls either. this is just a bit of an easier interpretation (I hope its somewhat correct)

*Edit #2*

With recent post's made by the op, I would like to change the second game example to make it more accurate.

[Edited on 11.14.2007 7:17 AM PST]

  • 11.12.2007 8:35 PM PDT

HHDDVVDDBVD 692 others

OK, yes, it is very true that I'm a dumb ass. I'm not denying that. However, isn't the whole point of a beta to increase the amount of users until you get someone dumb enough to try something you haven't anticipated.
Johnrap - Unofficial Dumbass of Halo 3 Beta

μ and Σ or σ

You could edit those into the first post. Either way good job.

  • 11.12.2007 9:02 PM PDT
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Finally sumthing 2 stop the whiners. :D

You can has Recon!

[Edited on 11.12.2007 9:14 PM PST]

  • 11.12.2007 9:14 PM PDT