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Dynamic Queue MMR effects

Goumindong·3/29/2016, 9:06:40 PM·3 votes·1,485 views

Introduction

Without an MMR adjustment for the number of players on a team dynamic queue is fundamentally broken in a mathematical sense. This happens by both increasing the variance in MMR for games of all queue sizes and also introducing team size bias. To explain this i will be going over how MMR systems work in general, how team size effects the MMR of players, and how this changes the variance in MMR for games.

How MMR Works

MMR is pretty simple once you get down to the core concept. By adding and subtracting rating from players after a win or lose the system forces MMR differences between players to conform to win rates between players for a given population. So if two players are the same MMR they will have a both 50% win rate against players of the same MMR. Because they both have 50% win rate against the same MMR we can be reasonably confident that they would win 50% against each other.

Now in league there is more than one player on a team. And so sometimes your play doesn't matter. This, in the end, has no effect on MMR. Suppose for a second that 80% of the time your individual play didn't matter(and so your win rate was 50% during those "coin flip" games), and only 20% of the time it did. If this is the case then your overall win rate against people of your proper MMR would be will be 40% + .2 * your win rate. If your win rate was higher than 50% then you would go up. If your win rate was lower than 50% your win rate would go down. It would do so until your win rate against your listed MMR was 50%.

It would take longer to get to the point where your MMR was correct. But it would not be inaccurate. Indeed this is the case regardless of the number of games which are "coin flip" compared to the number of games which depend on your skill. 99% coin flip, 1% skill? It still converges.

The only time the system does not converge is if the percentage of games played that depend on your skill approaches zero as the total number of games goes to infinity and you had not played enough games already to achieve significant convergence.

MMR in Groups

It should be fairly clear from the previous section how this effects MMR in groups. When you play in a group you have communication and coordination advantages not generally afforded to soloqueue players. Additionally as you continue to play with a group this coordination and communication advantage increases. If we do not assume this advantage then Dynamic Queue works. But not assuming this advantage would be foolish. Professional teams stomp soloqueue teams regardless of the MMR of the soloqueue team. Teams that play together transcend their soloqueue MMR.

To this end, all 5's groups will eventually be playing in two different groups. Games against 5's groups and games against less than 5's groups. The games against 5's groups will naturally have a 50% win rate for their proper MMR. But the games against groups of less than 5? They will also be forced to a 50% win rate by increasing or decreasing the MMR of the group. Just like in the prior situation where only 20% of your games played mattered.

Such, the inherent advantage of being in a larger group means that groups comprised of people with the same individual MMR will attain a higher actual MMR depending on how often they play in a larger group. This raises the MMR of all players who primarily play in groups above those who play solo. And it does so regardless of the number of games any individual group plays.

This last part seems counter intuitive but is pretty easy to follow logically. Suppose for a second we look at a the possible situation of two games played by the same 5's team on one side. Generally this can be two games against 5's, or a game against less than 5 and then a game against 5's, or a game against 5 and then a game against less than 5, or two games against less than 5. We can omit the second two because, eventually, that 5's team will play another 5's team and so give us a two game set of "game against less than 5, game against 5" to compare.

In the first situation. Where our hypothetical 5's team plays a 5's team twice in a row there is no net MMR gain or loss in the population of 5's teams. What one team loses another team gains. But in the second, where our hypothetical 5's team plays a team of less than 5, and then a team of 5 there is. If our hypothetical team wins the first match the population of 5's will have higher MMR than they did afterwards regardless of who wins the second match. If our hypothetical team loses the first match the population of 5's will have a lower MMR than they did afterwards regardless of who won the second match. This will continue until the hypothetical team should win 50% against smaller queues, pushing the MMR of all 5's groups up until it reflects the real advantage accrued by playing in a larger group.

So the difference in win percentage between 5's and 4's and 3's and so on and so forth will eventually propagate throughout the system regardless of the percentage of games played against lesser opponents, just so long as that percentage is not zero. And because this propagates through all of the queues where each advantage accrues for people playing double or triple queues it works regardless of whether or not a team of 5's actually ends up playing a team of 1's. And because its a queue wide effect, the total number of games your 5's group has played outside of the 5's group isn't a factor in convergence.

Such, so long as you're around the general MMR of your group*, playing in groups gives you an advantage and will increase your MMR, playing in a consistent group will do so more as the advantage is more pronounced the more you play with the same players.

*as there is another inter group effect which pulls the MMR of everyone who plays in a consistent group towards the same MMR. If you are significantly higher than the rest of your group the overall effect could be negative.

MMR Variance

MMR variance can generally be referred to as the amount of confidence we have in a players MMR. Low MMR variance is good, because it means that if we match a 50% game we will probably get a 50% outcome. High MMR variance is bad, because it means if we match a 50% game then we are still moving one of the participants MMR. Note that this actually increases the variance of game outcome since game outcome variance is peak at 50% win.

But players who play in groups, especially consistent groups, now have, effectively two sets of skill level. They have a skill level for when they play in a group and a skill level for when they don't and their MMR is neither of these unless they only queue in one manner primarily. Players who play in groups will have a higher MMR than their real skill level when playing outside; since their dynmaic MMR will be inflated due to the advantage playing in groups. Players who generally play outside of groups will have a lower MMR than their real skill level when playing in groups; since their Dynamic MMR will be deflated due to not playing with team advantages.

This inflation/deflation makes games more one sided if the system doesn't have a way to determine which teams have which types of players are which, or doesn't include a balancing term to weight the quality of players.

Effects of a Balancing Term

OK, so what if they add a balancing term? Prior to this season there was a term added to duo queue players to match them against better players in general, compared to their soloqueue MMR. Duo queues would look like they were say 20 to 30 MMR[i don't know the actual number] higher than they actually were, to the match maker and to MMR adjustments.

Generally that isn't a bad way to fix things. It reduces the MMR variance and fixes many of the issues of the advantages of larger queues. Its not perfect, but it is better than nothing, so long as the difference between the actual average effect and the term is less than the difference between the actual average effect and zero. That is because that number is both the number which creates the larger team MMR bias as well as the MMR variance in games.

But it can't fix all of the problems. Teams which do not have a coordination effect as large as the balancing term will tend to not play as a group. And teams which do will tend to play as individuals.

TL/DR

The takeaway here for players is twofold. For a personal player interested in increasing their MMR as high as possible, i suggest you find a good group and play primarily with them. For a player who plays casually and doesn't care about their MMR but wants the most competitive games, i suggest not playing in a group at all. This will mean that you do not have to play against your own inflated MMR.

For Riot its an either or: Give players a true solo queue or put some balancing terms in so that groups do not receive an inherent advantage.

13 Comments

Very Hard Engage3/29/2016, 9:25:33 PM1 votes

its flat out wrong because it averages the difference, and someone whos plat 5 and recently played poorly and has his MMR at the gold ~2 ish level. and the gold 2 and silver 2 player average together because they're besties, gold 4 MMR.

riot logic - "yup, they're close enough, stick em in the room together."

lets bet on who the silver 2 gets to lane against.....

oh wow, the plat 5 player is snowballing, who knew?!?

games donzo. the duo queue failed, miserably. and when the 2 decide to duo again... and again... and again! and their win rate together is 20~40% together and they just keep doing it.....

Gergor3/30/2016, 1:08:49 AM1 votes

I made it halfway through, but there are so many assumptions and things making me go "Huh? Based on what?" that I didn't continue. It's just a series of assertions building on each other, and without being able to see clear reason to believe the foundations of the argument, continuing toward the end is pointless. For example:

  • Why are the 80% of games out of your control a 50% win rate? Lack of control doesn't guarantee even odds, and as far as I know the notion that you only control X% of your games is a nice idea but didn't necessarily come from evidence. I get that the first section is just trying to say "MMR means you'll have a 50% win rate," but don't follow your logic for why.

When you play in a group you have communication and coordination advantages not generally afforded to soloqueue players. Additionally as you continue to play with a group this coordination and communication advantage increases. If we do not assume this advantage then Dynamic Queue works. But not assuming this advantage would be foolish.

Assuming the advantage is always there is equally foolish. I am usually in a group because I like the people, and know they won't be a jerk. We're often not in voice chat and without that we have zero advantages over solo queue - just chat and pings.

Professional teams stomp soloqueue teams regardless of the MMR of the soloqueue team.

OK

Teams that play together transcend their soloqueue MMR.

Says who? The preceding sentence certainly doesn't prove it.

Such, the inherent advantage of being in a larger group means that groups comprised of people with the same individual MMR will attain a higher actual MMR depending on how often they play in a larger group.

You are assuming that a group of 5 is better than a group of less than 5 with the same MMR, as you're assuming that communication and coordination (c&c) advantage always exists. Beyond that being an assumption (they may not be in voice chat), it ignores that a group of less than 5 could be a 2-man and a 3-man. They may not all five be working together, but if their two smaller teams each have c&c, then they could be plenty competitive.

I just don't see how what you've said proves that a 5 group is going to definitively win more than lose against equal MMR less-than-5 groups, and everything else hinges on that declaration.