Monday, October 14, 2013

LP, MMR, Elo, Matchmaking, and Leagues Explained

Hi, everyone. I see a lot of confusion regarding LP, MMR, and Leagues, especially as the season starts to come to an end. I'm going to try to hit the confusing points that have been repeatedly questioned in a short, meaningful way. Disclaimer: Riot's system is a proprietary variation on the Elo rating system, meaning they don't release all the details of their system to the public. I'm making reasonable assumptions based on my research, experiments, and knowledge.
About me, and why you should trust me:
  • I've been playing League of Legends for a year and a half plus.
  • I'm a professional researcher that does some of my research in MMR-type systems.
  • I've cited my work using [this format] as much as I can.
  • Elo: Elo rating, a 3- or 4-digit number that expresses a player's skill at a game.
  • MMR : Matchmaking Rating, a number used to place players into matches based on an algorithm.
  • LP : League Points. The point system used by League of Legends to determine when a player can enter a series to move to a higher division
In order to understand the whole system, we should first start with MMR/Elo. This is the hardest part to understand, especially for new players who didn't have experience with the direct Elo system in League, but it's necessary in order to understand the LP/League system. The Elo system was originally invented for use in professional chess. It was created by Arpad Elo, a fellow who literally wrote the book on it (in 1968). This means it's Elo, not elo or ELO. Here's how it works:
1) Everyone starts out with the same Elo [Elo, 1968].
2) When you win, your Elo rating goes up. When you lose your Elo rating goes down [Elo, 1968].
3) If you get an unexpected result (win against a tough opponent, loss against an easy opponent), your Elo rating changes more than if you get an expected result (win against an easy opponent, loss against a tough opponent) [Elo, 1968].
4) At the beginning, your rating is allowed to change by larger chunks than later on, thanks to something called a "K factor" [Elo, 1968].
5) In single player games, over a large number of matches this rating is proven to converge, and will represent a player's skill [Elo, 1968].
6) After the system has held a large number of matches, a new player can be sorted to the correct Elo in ~30 matches [Elo, 1968].
7) When a player learns a new skill, has a new insight into the game, etc, this will be incorporated into his Elo in ~30 matches (This is seen commonly in professional chess; players on a climb will climb by a series of plateaus rather than a smooth climb [Elo, 1968]).
Now, let's talk about how this worked for League of Legends:
1) Same. 1200 is the starting point.
2) Same.
3) Same, but change "opponent" into "opposing team".
4) Same.
5) This is not "proven", but it has been shown to work.
6) This number has not been calculated (as (5) hasn't been proven), but some experiments show it in the ~30-50 range. (Edit: courtesy of /u/aikimillerLyte states that with Riot's system, most players converge in 150 games, but in corner cases it could take up to 1000.. 30-50 claims are based on an automated simulation with not nearly as many variables as humans playing League. Take all "50 game" claims further on in the post with a grain of salt.)
7) Same, with the same caveats as (6).
8) Because it's a team game and your Elo only changes for wins/losses, Elo represents not only personal skill, but how you use that skill within a team context. (ex: Maybe you aren't a great player, but your Alistar head butting and pulverizing allows your mediocre teammate Vayne to play like a good Vayne; maybe your warding as jungler keeps your top Darius from feeding the enemy jungler 3 kills. On the other side, maybe you're an amazing laner but terrible team fighter.)
Now, the cool thing about the Elo rating is that it can be used to calculate the chances of one team beating another team [Elo, 1968], which is great for matchmaking. Ideally those matches that have an expected 50/50 outcome should be real nail-biters, and therefore really fun to play! This is why the Elo rating is also used as a matchmaking rating (MMR). To my understanding, Riot uses Elo rating identically as an MMR.
League of Legends banks on the fact that the game can create compelling matches on a regular basis for its players, and it does this by using Elo ratings as an MMR to put people together that it thinks will match up for a compelling game. From my experience, looking at a totally unscientific and not-random sampling of my own games, featured games, and other games that I have access to, it appears that the matchmaking system tries to make games that each team has a nearly-equal chance of winning. The largest Elo-calculated chance-disparity that I have seen is a 54%/46% chance of outcome.
What does this mean? This means if you win 55% of your games, you'll gain Elo, because you'll be outperforming expectations in the long run [Math].
Whether the system intentionally tries to match slightly-weighted games or not is a matter that I have no real insight upon. One might argue that getting as close to 50/50 as possible is good. One might argue that slightly weighted games, like 48/52 offer the less-skilled players a chance to see slightly more-skilled players, and lead to improved system-wide player skills. After all of this, though, there are other issues, like only being able to match people that are in queue, and wanting to keep queue times down.
League of Legends does keep separate track of your normal and ranked Elo/MMR, and does not let the two affect each other.
League of Legends also slightly artificially inflates the MMR it uses to match you into a game based on how many people you are queueing with (theory being that 4 people who queue together will be better-coordinated than 4 singles placed on the same team).
Elo Resets
At the end of each season, Riot performs a partial reset of Elo ratings (MMR ratings) to bring the high and low ends of the Elo ratings closer to the center, and allows them to correct for problems such as Elo deflation or inflation due to Elo decay, players leaving the system, and the introduction of new players.
This works as follows:
  • Players below the desired mean have their Elo ratings raised.
  • Players above the desired mean have their Elo ratings lowered.
  • The further you are from the chosen desired mean, the more your rating will change. A 2100 Elo player may have their rating reset to 1650, while a 1500 player might have their rating reset to 1350 (Numbers chosen were to match roughly what happened with S2->S3 soft reset).
  • The exact details of the process are relatively arbitrary, and don't matter terribly much, thanks to Elo/MMR point (6). After 30-50 games in the new system, you'll be back to your deserved Elo.
Leagues & LP
Leagues are a wrapper around the Elo system, to make things more personal. The theory here is that it feels like more of an accomplishment to hit Gold V than to hit 1500 Elo (which doesn't feel that different from hitting 1400 or hitting 1600). That being said, it appears that the underlying machinery is still a function of the Elo rating system, which is good: It means all you have to do is keep winning games, and you'll move up in league.
  • When you win a game, you gain LP and Elo. When you lose a game, you lose LP and Elo/MMR.
  • When you dodge a game you lose only LP [source!].
  • When you go inactive for 28 days, you decay only LP [source!].
LP (League points) might look a lot like Elo at the first glance, but the side-effects that some people see that might seem strange at first are caused by the disconnect.
  • LP/League is not used for matchmaking. Your MMR (Elo rating) is. This is why you can find yourself consistently matched against players in a higher/lower league than you are. (See the player in Bronze playing in diamond-league games, because he/she always dodges promotion games).
  • The change in league after a promotional series appears to be a function of hidden MMR. This is why you can be promoted from Silver IV to Silver II in a single promotion series (if your MMR is significantly higher than expected for your division).
  • The change in LP as your near the top of the first division in your league also appears to slow to make sure that your MMR is high enough for a league promotion, as these promotions are permanent. The consensus seems to be that moving from the bottom of the first division to being promoted is about as much work/time/effort as moving from the bottom of division IV to the top of division II [taken from multiple player posts/comments since S3 start].
Placement Matches 
As per point (4) in Elo/MMR, your Elo rating will change very rapidly at first. This is why placement matches exist (so that people don't flip out over losing 100 Elo in their first game, or feel too pressured to win that first game to go up 100 Elo). A frequently asked question is "what record do I need to hit division X". The answer is always "it depends". The consistent point is that if you win the game you are playing right now, you'll be placed higher than you would be if you lose. The average placement division seems to be Silver V, from what I have seen, but going 5/5 does not guarantee this. If you win games early in your placement, you'll be matchmade in tougher teams, which gives you more opportunity to move upward. Going WWWWWLLLLL could lead to a potentially very different placement than going WLWLWLWLWL or LLLLLWWWWW.
Thanks to point (6) in Elo/MMR, however, you don't have to stress about your placement matches. The math is very nice in that it erases whatever happened more than 50 games ago. If you have a streak of d/cs, trolls, bad teammates, or whatever other complaint you might have, after 50 games the effect that the streak had will be erased from your Elo.
Get better, win games, move up.

By: Sixtox

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