Posted by Zileas 09-16-2009:

 

NOTE: This explanation is current as of the patch going out late in the week of Sept 15th (wed, thurs or fri)

Summary:
The system guesses how good you are based on who you beat and who you lose to. It tries to make matches where it thinks you have a 50/50 chance of winning.

It knows pre-made teams are an advantage, so it gives you tougher opponents when you are in a pre-made team. We did fancy math to make the pre-made teams vs solo players matching fair. I even ran it by two math Ph.Ds and they said it made sense!

Details:

A lot of people have asked how our matchmaking system works, and we’ve seen a lot of posts that advance misconceptions about how it choose matches.

The basic concept is that the system over time understands how strong of a player you are, and attempts to place you in games with people of the same strength. As much as possible, the game tries to create matches that are a coin flip between players who are about the same skill.

The basic priorities of the system are in order:
1) Protecting newbies from experienced players.
2) Fairness & creating competitive matches
3) Finding a match at all. The longer you wait, the less important priorities #1 and #2 are.

How are matches made?

First, the system places you in the appropriate pool –which is basically game type (normal games in general, ranked solo/duo, ranked 5-man team, other game modes, etc).

Once in the pool, the system starts trying to find you matches, the goal being to get a match where the teams are equal and both have a 50% chance of winning.

Step 1: Determine your strength:

We use a modified version of the Elo system. The basic gist of the Elo system is that it uses math to compare two player ratings to guess the game result – like, “Bob will win vs Jim 75% of the time”.

From there, the game is played. If you win, you gain points, if you lose, you lose points. If your win was “surprising” (i.e. the system thought you would lose), the points you gain are larger. Additionally, if you are a newer player, you gain and lose points more rapidly so that you get to your skill level faster. Over time, this means that good players end up high rated because they do better than the system expects, until the system is guessing correctly how often they will win.

We modified this for team use, and basically, the concept is that you get a team elo based on whoever is on the team, and if you win, it’s assumed that everyone on the team was “better” than the guess, and gains points. There are some problems with this, but it generally works out, especially if people use pre-mades a little bit.

We also do a few little things to nudge your elo rating in the right direction when you start out so that people get where they need to get faster.

• We use various proprietary methods to identify players that are significantly more skilled than a typical newb, and boot their rating up a bunch behind the scenes when we notice this.
• Gaining levels boosts your elo rating a lot. This further helps separate level 30 summoners from low level summoners.

For more details on how the Elo system works on a theoretical level, you can read about it at:
https://en.wikipedia.org/wiki/Elo_rating_system

So wait, how did you determine how to deal with pre-made teams vs solos?
Some matchmaking pools avoid this completely by only allowing 5 man pre-mades vs 5 man pre-mades (ranked games, etc).

Others mix pre-mades and solos freely, and to be fair in these cases, we performed analysis on several hundreds of thousands of games to identify how much of a skill advantage this gives people. We found that a variety of factors influence how much of an advantage being a pre-made is, ranging from the size of the pre-made (i.e. 2,3,4,5 people), to the skills of the players involved, to combinations of pros and newbs, to other more subtle factors that must be used as well.

Having found these advantages, we know how much we need to boost your rating by in a team to make a fair match, and apply the appropriate, mathematically justified adjustment. These results in some cases are very surprising (while still appearing correct in the statistics)

While we will not give precise values because those are trade secrets, we can say that:
5-man pre-mades are only moderately stronger than solo queuers.
Partial pre-mades are only a little bit of an advantage.
Newbs don’t benefit much from being in a pre-made, while experts benefit a lot.

Okay, fine, but why do you even match pre-mades vs non-premades at all?
There are a few reasons for this:

• It helps the system find your skill rating much faster, so that you get fair matches faster. This works because if you pre-make, it reduces the amount that “bad” or “good” luck related to your teammates causes you to win or lose games. If you pre-make, you join up with people of about your skill, and you now get less random teammates boosting you/screwing you, so your rating gets to an accurate value more quickly because more of each game result is due to you and your friend, who are close in skill.
• We want people to easily play with their friends because they will have more fun if they do, and you can’t have a 5v5 matchmaking pool of all 2 man teams, or all 3 man teams – you need a mixture for it to work. We chose to include 5-man because it’s a lot of fun – if we have large enough pools later, we might separate 5-man premades from the partial pre-mades – but the data we have shows that this won’t improve the fairness of matches much at all, it will be about the same.

Other Common Questions:

Q: Why don’t you include other little details like how many kills I had, etc, to determine my rating?

A: Because this is gamable, and because it’s hard to figure out how much of that was you playing a gank champion (like Twitch or Master Yi), and how much of that was you just being good. It also incents players who wish to boost their rating playing long games where they farm a lot of enemies, rather than winning. By putting as many measurements and incentives as possible on winning, we avoid side behaviors that aren’t as fun, and which confuse the rating process.

Q: So, because I won a few games in a row, I’m going to get an impossible match now, right?

A: Not exactly. Your rating will rise, so you’ll get harder and harder opponents – but we don’t really care if you go 50/50 win/loss, just that you rating seems to be an accurate prediction of game results. Eventually, you will hit your limit, and you WILL see roughly 50/50 win loss though. Players who are above average will tend to do slightly better than 50/50 because there are more players below them than above them, so matches, when made, will tend to be slightly “downwards”. For expert players near the top of our rankings, they will often run 90% win rates.

Q: How will you do persistent teams, like in WoW arenas?

A: This is an EXCELLENT approach and will allow us even better matchmaking. We will do these eventually, and use new methods we develop on our own for a similar purpose. We will need to do elaborate things to figure out how good you are in general (e.g. personal ratings), while allowing you to freely create/destroy teams. This is a big project, but we are really excited about it.

Q: I'm a jerkface leaver. I can game this system by being a jerkface leaver right?

A: No. You incur elo adjustment based upon team result. We don't care if you left or not -- if your team won, you will gain points, if your team lost, you will lose points. You do however incur other penalties for being a leaver. This is because various measures to account for people leaving end up being gamable or cause weird effects on the system. For example, if we reduced the rating loss of your teammates if you left, then you might leave to help them preserve their rating. If we gave you a penalty even if they won, we would be "deflating" the entire system of ratings down over time, causing newbs to run into pros eventaully. Above all else, the system must be "capped" zero sum (so that, there is some inflation, but there is a limit). Otherwise, weird things happen.