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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.

Posted by: Aldo8150
as soon as i got to a highest skill of 39 it wouldn't let me get any higher even if i won


I assume your talking about Lone Wolves because that's all I see a 39 in. You've only played 9 games as a 39 and it's way to soon to conclude it won't let you get any higher. The system will always let you get higher but you do have to win more then you lose.

Your placements in those 9 games are as follows:

1st: 1
2nd: 1
3rd: 3
4th: 0
5th: 2
6th: 3

I see no reason there to move you up, but again it was only 9 games. You may move up again. The system hasn't stopped you. You'll just need to keep winning. It's generally safe to say if you win as much as you lose (like you did) you won't be going anywhere.

[Edited on 12.03.2007 11:03 PM PST]

  • 12.03.2007 11:01 PM PDT

Posted by: sesquipadelian
i am not demanding or expecting anything, but i am curious. my guess (and this is mere conjecture) is that streakiness is not a factor in the ranking system. you and the thread creator seem to understand the system completely and can grasp how different elements of the trueskill system affect ranks in different ways, so i am eager to know if either of you have any concrete reasons to suppose that streakiness is a factor.

Well, after doing way more reading and math than I ever wanted to, I have to agree that streaks may not be a factor. There is no variable in the formula to account for streaks differently then scattered wins and losses. I also came to the conclusion I do not understand the system completely :)

I was assuming that the amount of sigma increase a player gets between matches was related to a winning or losing streak. I don't think it would be hard to implement a system were if a player is winning/losing 2 or more games in a row unpredictably, their sigma is adjusted slightly higher than a person not on a streak. So many other factors go in to calculating sigma and mu that it is hard to find a real world example of someone on a streak getting more sigma.

Basically, this is how the system is known to work so correct me if I am wrong. Anything else is guessing. Sigma is lowered a variable amount for each game played depending on how you performed compared to how the system predicted you would perform. Perform predictably and your sigma lowers quickly. Perform unpredictably and your sigma stays higher. The system assumes a small skill change for each game played and compensates for this by adding a small amount of sigma between each game thus keeping it from reaching 0. The lower your sigma, the smaller the mu change. Once you reach the point of convergence (enough games completed in a predictable manner), it will take a large number of games to raise or lower your mu cause your sigma is low.

I am adding the following information because it is Microsoft's explanation to some issues people have mentioned in this thread. I know it has been explained to them but these are direct quotes from MS.

An explanation to one of the "flaws" of the team who only plays together and can't level up.
Obviously, it is difficult to update individual players' skills from team results only. To understand the difficulty and the solution consider the following analogy: Suppose you have four objects (players), each having an unknown weight (skill). Suppose further that you have a balance scale (game) to measure weight (skill) but are always only allowed to put two objects on each side of the balance. If you always combine the same pair of objects, the only information you can get is which pair of objects is heavier. But if you recombine the players into different pairs you can find out about their individual skills. As a consequence, the TrueSkill ranking system will be able to find out about individual players' skills from team outcomes given that players not only play in one and the same team all the time but in varying team combinations.

An explanation of how you can go down a level after a win.
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.

  • 12.04.2007 7:29 AM PDT

Halo/Bungie FTW!

I just wanted to know why i need to won 25 matches to gain ONE level



Is my sigma crap? I don't see reason for it to be so damn low because i'm a good player

  • 12.04.2007 8:30 AM PDT
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so ive done some in depth reading of this thread and other info about trueskill, and I cannot seem to find a good answer to my question. My friend and I just started playing Team Doubles. We are currently 24-1, and we both are skill level 18. At the current rate, we are destroying the competition. Should we intentionally lose a game to keep the system guessing, and then go on a winning streak again? Or should we just continue winning? What is the better way to skill up?

Does losing once in a while aid in our quest to get lvl 50's? or should we just win as much as we can?

  • 12.04.2007 11:09 AM PDT
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nice descritption but I kinda wish there were more ranks

  • 12.04.2007 11:32 AM PDT
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i think i should prob lose one intentionally to switch it up on the system. Thoughts?

  • 12.04.2007 11:35 AM PDT

Posted by: Stslimited84
so ive done some in depth reading of this thread and other info about trueskill, and I cannot seem to find a good answer to my question. My friend and I just started playing Team Doubles. We are currently 24-1, and we both are skill level 18. At the current rate, we are destroying the competition. Should we intentionally lose a game to keep the system guessing, and then go on a winning streak again? Or should we just continue winning? What is the better way to skill up?

Does losing once in a while aid in our quest to get lvl 50's? or should we just win as much as we can?


This is just my opinion so others may have a different opinions.

Level 18 after 25 games is not all that bad. There are a couple things to keep in mind. Playing with the same teammate and never playing with anyone else in that playlist may hamper your ability to level up. This is an issue with the skill system but it is too early to say whether it is going to hamper you or not. Continuing to win will keep your sigma higher longer allowing you to gain levels quicker but remember, the more you play the lower it gets and the more games you have to win to go up. If you lose a game that the system thought you should win, your skill will take a big hit. Just like if you win a game the system thought you should lose, your skill will get a nice boost.

If it comes down to it and you are stalled at a level for a large number of wins, I would suggest a few games with some randoms for both of you and then team back up. Simply losing once in a while "should" not help you level up quicker. A high sigma is good in the beginning because you can gain levels quickly. Once you get enough games in and your sigma is lower, it is going to take a large number of wins to go up. It can be bad in that sense but it can be good in the sense it also takes a lot of losses to go down.

  • 12.04.2007 11:37 AM PDT
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thanks for the reply. Any other thoughts from anybody? In essence, we should keep winning then, and not lose intentionally. I did not intend for it to seem like we were stuck at a skill level, i was just wondering what the best course of action is to ensure continually leveling up since we are winning so much. Thoughts?

i just dont want to get caught up in one of the querks of the system. You know? since we are working so hard at domination in doubles...

[Edited on 12.04.2007 11:45 AM PST]

  • 12.04.2007 11:41 AM PDT

etc etc/glaringly obvious/and so on, and such <=Not redundant!
Posted by: Cr4ne Style
Taxes do nothing to affect the share of wealth, since taxes are only applied to income.

So that's not even a part of the conversation at all, so it's pointless talking about it....

"for a "best" moral to exist, there must exist the "best" moral base. If the base of morality varies from location to location, culture to culture...then there can't be an absolute moral..

Posted by: Stslimited84
thanks for the reply. Any other thoughts from anybody? In essence, we should keep winning then, and not lose intentionally. I did not intend for it to seem like we were stuck at a skill level, i was just wondering what the best course of action is to ensure continually leveling up since we are winning so much. Thoughts?

i just dont want to get caught up in one of the querks of the system. You know? since we are working so hard at domination in doubles...


as long as we keep playing, this problem will be eliminated. as we all play more games against opponents who have played more games, we will get accurate ranks. getting accurate ranks simply takes time and data, and the game is still new and each and every one of us are playing with little history against opponents with little history.

  • 12.04.2007 11:53 AM PDT
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thanks for the reply, but im not sure how that applies to my situation?

  • 12.04.2007 11:57 AM PDT
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This helpes my anger problem a lot as far as getting MVP and top medals every game and still not leveling up.All in all nice info!

  • 12.04.2007 12:03 PM PDT

etc etc/glaringly obvious/and so on, and such <=Not redundant!
Posted by: Cr4ne Style
Taxes do nothing to affect the share of wealth, since taxes are only applied to income.

So that's not even a part of the conversation at all, so it's pointless talking about it....

"for a "best" moral to exist, there must exist the "best" moral base. If the base of morality varies from location to location, culture to culture...then there can't be an absolute moral..

Posted by: Stslimited84
thanks for the reply, but im not sure how that applies to my situation?


you mentioned wanting to rank up and not wanting to get caught in the kinks of the rank system. if you want to rank up and you win loads of games, then it will happen. the only problem that you may experience is that it may take you a little more time than you would like.

  • 12.04.2007 12:09 PM PDT
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ah. but shouldnt it be faster due to the constant winning? Winning indicates that you are better than the people playing, and thus need to move to a higher skill level to find possible competition.

  • 12.04.2007 12:11 PM PDT

The whole issue becomes how do you define faster. The idea is to get you to your skill quickly but things like only playing in the same team, not having good quality match-ups so your win doesn't mean much and the fact that once you get to a certain point it takes increasingly more wins to go up a level. Most of these things are out of your control so you can't do much about it. Like I said, the only thing is if you and your team mate only play DT with each other, you may get stalled and should play with a few randoms.

  • 12.04.2007 12:36 PM PDT
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cool, thanks for the advice.

  • 12.04.2007 12:37 PM PDT

Posted by: Stslimited84
so ive done some in depth reading of this thread and other info about trueskill, and I cannot seem to find a good answer to my question. My friend and I just started playing Team Doubles. We are currently 24-1, and we both are skill level 18. At the current rate, we are destroying the competition. Should we intentionally lose a game to keep the system guessing, and then go on a winning streak again? Or should we just continue winning? What is the better way to skill up?

Does losing once in a while aid in our quest to get lvl 50's? or should we just win as much as we can?
From my observation of way to many peoples stats then I care to admit winning to often is going to slow you down. There have been numerouse examples of people that go undefeated and win 100+ games but get stuck at 15 or 20. Bungie has recognized this problem. I believe to a lesser degree the same problem effects those that win 90% or more. The observed result is slow ranking. I've seen people win most of there games and if you average there levels per game I've seen anywhere between 3-7 which is in the range of somewhat slow to really slow.

I'd monitor your average level gains per game and if it starts to climb over 2 or 3 and you aren't getting any competition you might want to consider breaking up the team or losing some games. My observations seem to show that 80% win rate is roughly optimal, but as long as you feel you are climbing and not "stuck" I wouldn't worry about it.

Like I said this knowledge is from observation of the current system and not really backed by specific technical knowledge. At the moment 18 levels in 25 games is a good rate and doesn't warrent any change in behavior. At this point just keep winning and see what happens.

[Edited on 12.04.2007 1:33 PM PST]

  • 12.04.2007 1:32 PM PDT
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I'm no statistician, although I have taken my fair share of stats courses back in University...so hopefully I don't make any flawed assumptions here. Also, I know this thread is for explaining True Skill, rather than critcize it. I'm not going to criticize it here, but rather suggest a small tweak that may fix some problems. I could be totally wrong, but I'll give it a shot:

It seems one of the biggest gripes about the True Skill system comes down to Team Slayer. In the perfect world of Lone Wolves, you pretty much control your own destiny (with the exception of a poor matchup which happens from time to time and dropped connections). After the system collects enough info on everyone, sigmas will plummet. People's Lone Wolves rank should somewhat fall into place . It won't be perfect due to new players or players that retired before playing enough, but pretty damn close.

However, In Team Slayer over the long term, you eventually get teamed with your fair share of guys that may be good players, but cannot play well on a team. What's flawed here is that guys that know each other and play slayer are less likely to experience this vs. the average player that just lets the system pick his teammates. In the short term, you lose your fair share of game sbecause of these guys, and your sigma drops quick. Over the long run that average player quite simply will have a large number of losses due to "muppets" on their team, even if they personally are kicking arse. Obviously the higher you rank, the less muppets are likely to end up on your team....but in the very important beginning of your ranking process, People that get stalled out early due to sigma are less likely to keep playing ranked. So you end up having a situation where the guys that start of slow quit playing team slayer early, and skewing the overall ranking process.

So basically you have a situation where the system is trying to come up with your personal rank, but in reality it is severley watered down by the rest of the populations performance. In other words, you can't rank super high in Team Slayer unless you actually have an official team of guys. Maybe that is Bungie's point to Team Slayer? I don't know....but something tells me if you can be the best guy on the losing team, you should at minimum not be penalized. Been reading the forums a lot lately, and this seems to be the biggest ranking gripe against the system.

The thing that was good about Halo 2's system (correct me if I am wrong), was that the MVP got treated like they got 2 wins and the 4th place guy on the losing team got treated like he got 2 losses. I also believe the guys that got 4th (winning team) and 5th (losing team) had no effects on the ranking. Maybe if this small adjustment was added back into the system (True Skill would still be the system), it might fix a lot of the gripes.

  • 12.04.2007 3:43 PM PDT

Posted by: Baaaaaaaaaaaaah
The thing that was good about Halo 2's system (correct me if I am wrong), was that the MVP got treated like they got 2 wins and the 4th place guy on the losing team got treated like he got 2 losses. I also believe the guys that got 4th (winning team) and 5th (losing team) had no effects on the ranking. Maybe if this small adjustment was added back into the system (True Skill would still be the system), it might fix a lot of the gripes.
No, in Halo 2 all the members of the winning and losing teams were treated equally. So it didn't matter if you came in 4th on the winning team or 1st and similiarly it didn't matter if you were 5th or 8th. The "problem" you speak of was existent in Halo 2 as well and there were certainly people who complained.


Posted by: Baaaaaaaaaaaaah
However, In Team Slayer over the long term, you eventually get teamed with your fair share of guys that may be good players, but cannot play well on a team. What's flawed here is that guys that know each other and play slayer are less likely to experience this vs. the average player that just lets the system pick his teammates. In the short term, you lose your fair share of game sbecause of these guys, and your sigma drops quick. Over the long run that average player quite simply will have a large number of losses due to "muppets" on their team, even if they personally are kicking arse. Obviously the higher you rank, the less muppets are likely to end up on your team....but in the very important beginning of your ranking process, People that get stalled out early due to sigma are less likely to keep playing ranked. So you end up having a situation where the guys that start of slow quit playing team slayer early, and skewing the overall ranking process.
For the sake of dicussion lets say we have a mature playlist. In other words most people are at there skill level and the system is pretty certain it's correct. Now lets look at two people who are both equally skilled. They are new to the playlist and we'll say they are destined to be 45's. They go into matchmaking seperatly. It's true do to the randomness of events one player may lose more then the other, but this has no overall effect. The system is designed to judge you based on many games played. Randomness will average out and there is no way a few more losses for one will stall them to the point they would notice any difference. For every player you get matched up with that does poorly you are going to get matched with someone who does well. The same holds true for the teams you play against. They are equally likely to draw the short straw. In the end the only variable is the individuals skill. Those that get stuck get stuck because there skill isn't good enough to go higher.

Those that gripe about the issue you speak of don't understand things average out. They tend to be overly concerned with that one game they went positive but lost and went down a rank. Of course you're unlikely to see that person saying they should be penalized when they go negative, but win. Seems people want it both ways. I understand the perception here but those people need to understand that there is no overall consequence to that loss.

For anyone who says individual performance should be considered I pose the follwing question. What makes a player good? Remember we have multiple different gametypes so the definintion of good may very from gametype to gametype. I guarantee the resulting answer will be debatable. If Bungie tried to judge people based on individual performance I guarantee the solution would be inacurate, frustrating, and very messy.

People who do play together all the time pose a problem. They can't be judged indepentently. This is a true shortcoming of the system. However, the problem only manifests itself if the team decides to play seperatly. I find this to be an acceptable problem. Halo 2's system did no better in this regard.



[Edited on 12.04.2007 6:07 PM PST]

  • 12.04.2007 6:00 PM PDT
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Thanks for the clarification on Halo 2 ranking. I didn't play it too much and my theory on the ranking was only from my own observations.

I do disagree with you on one point. You say that over time in Team Slayer that everyone will will receive their fair share of "muppets" (I'm one half the time) and that things will average out. However, you can rank up very quickly in your first 50-100 games and then start to avoid that part of the population...or at least encounter them less often. You may argue that 50-100 is a big enough sample size to give people an equal opportunity to get bad teams...but if you are someone that plays with a close group of guys (yet switch it up a bit), you have likely reducing the muppet variable substantially. Basically your probability of getting bad teams is slightly dependant on your first sample set. You are assuming each person has a relatively equal chance of playing with anyone else at the same level, when that is not necessarily true. I would hypothesize the amount of people that play with structured teams are not an insignificant portion of the population. Regardless, your performance over your first 100 or so games will determine whether you will need to play 200 or 2,000 games to achieve your true rank. In a perfect world where people play 10,000 games that may not matter, but I suspect many players get disheartened much quicker because they have to grind rank from the bottom of the barrel due to low sigma.

I dunno, just my two cents.

  • 12.04.2007 6:52 PM PDT

Posted by: Baaaaaaaaaaaaah
Thanks for the clarification on Halo 2 ranking. I didn't play it too much and my theory on the ranking was only from my own observations.

I do disagree with you on one point. You say that over time in Team Slayer that everyone will will receive their fair share of "muppets" (I'm one half the time) and that things will average out. However, you can rank up very quickly in your first 50-100 games and then start to avoid that part of the population...or at least encounter them less often. You may argue that 50-100 is a big enough sample size to give people an equal opportunity to get bad teams...but if you are someone that plays with a close group of guys (yet switch it up a bit), you have likely reducing the muppet variable substantially. Basically your probability of getting bad teams is slightly dependant on your first sample set. You are assuming each person has a relatively equal chance of playing with anyone else at the same level, when that is not necessarily true. I would hypothesize the amount of people that play with structured teams are not an insignificant portion of the population. Regardless, your performance over your first 100 or so games will determine whether you will need to play 200 or 2,000 games to achieve your true rank. In a perfect world where people play 10,000 games that may not matter, but I suspect many players get disheartened much quicker because they have to grind rank from the bottom of the barrel due to low sigma.

I dunno, just my two cents.
Well I don't know that I understand your defintion of "muppet" but let me put it this way. A person who is trully a 10 is there for a reason. They in theory are equal in skill to other 10's. A 30 is also equal in skill to other 30's. When you get paired with a 10 your partners will on average break even because they are competing against other 10's. The same holds true for 30's. It doesn't matter wheather you get paired with 10's or 30's, your random partners are going to do exactly the same. They're at there level and thus the odds of them going positive or negative should be about equal. The only difference between 10's and 30's is your ability. Someone destined to be a 40 will be so much better then 10's that there teams are almost guaranteed to win. However, as they rise in ranks there personal influence on the team becomes less drastic. That's why people generally fly by the lower ranks and then slow down as they approach there true skill level. Slowing down has FAR more to do with and individuals ability to control the game (there skill) then it does Sigma.

Yes I concede a team of 4 who may all be 40's won't get paired with random people and thus should be able to win just about every game at the lower levels. This is in contrast to a 40 who goes in alone and does very well but ultimatly will lose a few games (most likely no fault of his). However, you are under the impression the early losses will drastically change how fast you can level. This isn't really the case. A great player will be so good there teams in the lower ranks are unlikely to lose. They won't lose much at all and they will level very fast. Perhaps a few more losses then the team of 4 but not enough to be noticable. I think that's where you and I disagree here. You won't slow down terribly until you get near your level. At that point you're so close to your level that it doesn't matter if it takes an extra 20-40-60 games to get that final rank. A few more early losses are insignificant. It's just not going to make such a drastic change in speed that you seem to believe it will.

I'm a 44 in Team Objective. When I finally hopped into the Team Slayer playlist it was fairly mature. I went from a 1 to a 38 in only 50 games. Games were pretty easy for me too. Currently I'm a 45. Those next 7 ranks took me about 49 more games. However, this had so much more to do with my skill then the few extra losses I might have gotten earlier on. Truth be told as a 38 my performances were more normal. Competition was better and despite eventually pushing up to a 45 the skill difference between me and the competition was much closer. Games were far more fun and competative. If I was better I wouldn't have slowed down as early. A better player would probably fly up to the 44's before starting to show any signs of slowing.

Could a team of 45's make it there sooner. Maybe. But is 100 games so unreasonable for an individual, especially when I was playing competativly for half of them. I dont' think so. This is where I'm coming from. I don't think the difference is as drastic as you think. Those early losses just don't do as much damage as you are hypothesizing.

I've seen a lot of people complain about not getting passed a rank and blaming the "muppets". In EVERY single case I've looked at there last 50 games and seen the exact same outcome. The person in question only won about half there games and there k/d spread was effectvily ZERO. I have seen absolutly no evidence to show the system is capable of making it frustratingly slow to level do to random partners performance. Can a team do it faster? Yes, it's absolutly possible. But so much so that it makes a difference. No.

That's just my opinion based on a lot of data that I've seen, the little knowledge I have of the system and my own experiences. Maybe I'm wrong but I've yet to see evidence of a problem. Then again I concede I don't care about my skill level for any other reason other then matching me up in fun competative games. Could 40 extra games to get to a 45 piss people off who actually care about the 45...ya maybe, but odds are those people aren't quitting because of it and I bet they'll deal with it.

[Edited on 12.04.2007 8:08 PM PST]

  • 12.04.2007 8:02 PM PDT
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Fair enough...everything you said makes sense. I guess any detrimental effects of losing early on apply to all the playlists anyways, not just TS.

  • 12.04.2007 8:28 PM PDT
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now i think you keep refering to playing in team slayer, but does lone wolves go the same way?

  • 12.04.2007 11:50 PM PDT
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Thanks for the help, I'm still not entirely sure why I have so much trouble ranking up, but since ive got a good team of friends now, i think i should start going up very soon. More consistent winning streaks.

As well this will win me a slurpee bet with one of my friends, its nice to hold all of the cards.

-D

  • 12.05.2007 12:57 AM PDT
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Okay, I just thought I would throw in my two cents after reading the original explanation and tons of these posts.

First off, I would like to say that I dislike this ranking system in practice. Second, I would like to double-check the master formula you provided, because I don't believe it makes any sense mathematically. Also, you fail to clearly define K.

Mu - (K*sigma) = rank. This is the master formula you provided. In statistics, mu = mean, and sigma = standard deviation, or in some cases volatility.

You say, "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." I will assume that the "Mu difference between the winner and loser" becomes a factor for determining K, the unknown constant.

For your rank to increase slowly, you would have to have a HIGH sigma, according to the formula, because you are subtracting a greater amount from Mu (which just increased because you won). If you had a LOW sigma, you would be subtracting a lesser amount from your Mu (which just increased because you won), which would result in a greater net increase in your rank. You claim that by winning, all you are doing is increasing your Mu value. If that is the case, then this would make much more sense:

Rank = Mu
Rank after a win = Mu + (K*sigma)
Rank after a loss = Mu - (K*sigma)

I believe this is a correct formula that you meant to provide. Your formula doesn't make any sense, and this one does. Also, you mentioned that Mu = rank in one part of your explanation, but then you are also using it in your formula to calculate rank. Wtf?

Please, somebody respond to this post and verify that this revised formula is actually correct. I don't see why you are subtracting anything from Mu unless you are losing (unless K can be negative), and I think it should be clarified that Mu is actually your rank, not some arbitrary number.



[Edited on 12.05.2007 2:38 AM PST]

  • 12.05.2007 2:37 AM PDT

Posted by: KeYzErSoZe03
Okay, I just thought I would throw in my two cents after reading the original explanation and tons of these posts.

First off, I would like to say that I dislike this ranking system in practice. Second, I would like to double-check the master formula you provided, because I don't believe it makes any sense mathematically. Also, you fail to clearly define K.

Mu - (K*sigma) = rank. This is the master formula you provided. In statistics, mu = mean, and sigma = standard deviation, or in some cases volatility.

You say, "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." I will assume that the "Mu difference between the winner and loser" becomes a factor for determining K, the unknown constant.

For your rank to increase slowly, you would have to have a HIGH sigma, according to the formula, because you are subtracting a greater amount from Mu (which just increased because you won). If you had a LOW sigma, you would be subtracting a lesser amount from your Mu (which just increased because you won), which would result in a greater net increase in your rank. You claim that by winning, all you are doing is increasing your Mu value. If that is the case, then this would make much more sense:

Rank = Mu
Rank after a win = Mu + (K*sigma)
Rank after a loss = Mu - (K*sigma)

I believe this is a correct formula that you meant to provide. Your formula doesn't make any sense, and this one does. Also, you mentioned that Mu = rank in one part of your explanation, but then you are also using it in your formula to calculate rank. Wtf?

Please, somebody respond to this post and verify that this revised formula is actually correct. I don't see why you are subtracting anything from Mu unless you are losing (unless K can be negative), and I think it should be clarified that Mu is actually your rank, not some arbitrary number.

The formula the OP provided is correct. The formula you are questioning is used to determine the visible skill level (the one that actually appears next to gamertag).

For every player Mu and Sigma are tracked. These values are stored behind the scenes. The skill level you actually see is a conservative estimate and is calulated by: Skill Level = Mu - K*Sigma

K in that formula is a constant that is chosen by the developer and the OP did mention that. Microsoft's paper on the subject states that K is typically 3, but we don't actually know what Bungie is using.

Sigma is the deviation and Mu can be thought of as a players skill level (but not the one we see)

If you want to know exactly how Mu and Sigma are changed after each win/loss you can check out the this link which the OP provided.

I hope that cleared things up.

Just out of curiosity what about the system in practice don't you like?





[Edited on 12.05.2007 3:23 AM PST]

  • 12.05.2007 3:22 AM PDT