Matchmaking and MMR

A while back, ranked matchmaking was added to Dota 2. With it came some confusion and frustration when it came to understanding MMR and its implications. In this article, I’ll aim to provide a better understanding of MMR and matchmaking. I also hope to clear up some common misconceptions.

What is MMR?

Your matchmaking ranking, or MMR, is number measuring how likely you are to win a game. Although it’s a seemingly simple metric, there are a lot of misconceptions when it comes to interpreting that number. Let’s go into the different components.

Relativity

First, your MMR is based off an Elo rating system. This means that your MMR is not an absolute measure; instead, it’s a relative measure.

Let’s take an example. Suppose you know that one of the teams in a match has an average MMR of 4500. You don’t actually know anything about who’s going to win the match! If the other team has an average MMR of 3500 then it’s pretty likely that the former team will win. If instead the second team had an average MMR of 5400, it’s more likely for the second team to win.

There’s actually a mathematical formula to determine how much likelier a team is to win given the MMR difference. (This is the basis behind and Elo system.) Although not public, it’s been reverse engineered here.

MMR Gain/Loss

With every win, you’ll gain MMR. With every loss, you’ll lose MMR. Assuming that you never abandon and that your game is counted, those are the only ways to gain or lose MMR.

The amount that you gain or lose is based on how favored you were to win the game. An even game, where both teams have about the same MMR, corresponds to a 25 point change for each player (winners gain 25, losers lose 25). You gain fewer points if you win a favored game and you gain more points if you win an unfavored game.

Suppose you won an even game and had a 6/4/7 KDA. It’s decent; you’d be happy with your 25 points. But what if you finished as 9/2/20? Shouldn’t you get more points?

The answer is no. The short answer is that Elo only cares about wins, losses, and how much a team was favored.

The long answer is that measuring your game stats and factoring that into your rating is too complex. First of all, there are a lot of potential factors: kills, deaths, assists, last hits, denies, wards bought, wards placed, TPs bought, etc. And those are only the measurable stats. There are a number of other factors that are much harder to measure: map awareness, itemization, ward placement, etc. Second, it’s unclear how these factors all contribute in any particular game. Third, these factors contribute in different ways for different games! (Consider itemization for split pushing vs team pushing as an example.) So, once again, it’s too complex to measure and factor in all of these things. It all boils down to the end goal: did you win or did you lose?

Change Over Time

It’s worth noting that your MMR is expected to stay about the same until you start playing consistently better or consistently worse. When this happens, your MMR will then increase or decrease until it settles at your true rating.

Let’s take an example. Suppose you currently have 3000 MMR, but your true rating is 3500 (in other words, you should be at 3500 MMR). Assuming that every other player’s MMR is accurate, your team’s average MMR will be 100 points less than what it actually should be. In other words, you’re around 15% more likely to win than the matchmaking system calculated (and therefore you’re getting favorable odds to win points). The eventual result is no surprise: your MMR increases to around 3500.

As you play, there will be lucky or unlucky streaks of games. However, they’ll cancel each other out in the long run.

Matchmaking

Now that we’ve taken a look at matchmaking rating, let’s take a look at matchmaking itself. The main focus here is understanding the fairness of the matchmaking system and understanding why you’re paired up with your particular teammates.

Win Rate

Valve aims to create games where both teams have an equal chance of winning. MMR measures exactly that—two teams with equal average MMRs should each have a 50% chance to win a game against one another.

There are likely a lot of factors that go into Valve’s matchmaking algorithm. I don’t know them. They include factors such as server preference, language options, etc. that may not correlate as strongly with win rate. However, I believe that Valve also aims to do things such as matching similarly sized parties and matching the MMR range of the two teams.

Of course, the ability to match players into even games relies on there being enough of a player pool looking for matches at any period of time. As a result, this means that it’s likelier that your matches will be more skewed in favor of one team if there are fewer players for Valve to match you with. This could be caused by a lack of players during a particular time in the day or a lack of players at a particular skill bracket (such as over 6k MMR). Although there will be unfair games, this is compensated for by the MMR gain/loss at the end of the game, as described above.

There’s a misconception that Valve will purposely put you into an unfavored game in order to force your win rate to get closer to 50%. This is a misunderstanding of probability. Entering a game where you have a 50% chance to win doesn’t tell you who will win or lose the game. It just means that if you play many of these 50% chance games, odds are you’ll win close to half and lose close to half.

Another misconception is that your win rate and MMR are correlated. Having a 56% win rate doesn’t mean you should have a better MMR than someone with a 52% win rate. Win rate tells you how often you win, but not who you won against. You could have won a bunch of games against a team that was worse than yours, bumping up your win rate. MMR tells you the odds of you winning against a team, but doesn’t tell you who to play against. Matchmaking is what brings the two together.

Mis-rated Players

Hopefully it will seem fair that your team has a (relatively) highly rated or poorly rated player if the opposing team also has one. However, some players get upset when another player, supposedly equally ranked, plays poorly. It seems that the two MMRs shouldn’t be equal if one player is so much worse at last hitting, map awareness, buying wards, whatever.

There are two simple factors that might cause this: that player’s having a bad game or they just aren’t playing at their MMR level. A more complex factor at play is that different players with equal MMRs can excel at different portions of the game.

Having a bad game is understandable. It happens to everyone. Lapse in judgment or awareness, other external factors affecting your play, whatever. It’s unfortunate, but it happens. Everyone’s done it.

Not playing at your MMR level happens as well. If you’ve played for a while, you probably know your good heroes and your bad heroes. You probably know which roles (support, carry, mid, etc.) you prefer to play. It shouldn’t be a huge surprise that a player who only plays carry won’t be nearly as good of a support as a player that only plays support, even if the two are exactly the same MMR. A 3.5k player who only plays support is probably not playing at the 3.5k level when they go mid. Moreover, they might be trying to learn a new hero, role, or style.

The last main factor is that two equally rated players are not good at the same things. In a way, this is similar to the previous point. A player might not be good at getting last hits, but maybe they know when and where they should go to get farm. A player might be terrible at avoiding ganks, but they might be great at positioning themselves during team fights. A player who excels at ganking might play poorly in a split push game. A player who loves snowball heroes might not understand how to play from behind. Each player has their own strengths and weaknesses; learn to adjust your play style to use your strengths to help compensate for their weaknesses.