This is part one of a four-part series on Elo and Elo Hell in League of Legends. View the Elo Hell category for future entries.



Basic Elo Theory

The Elo system is based on the assumption that your performance at whatever you’re being rated on can be expressed as a random variable within a bell curve, centered on your rating. Your rating vs. your opponent’s rating can then be used to estimate the expected outcome of a game. Then, the outcome of the actual game is compared to the expected outcome, and rankings are adjusted accordingly.

Let’s say (with completely made-up numbers for example), a 1400 Elo player will beat a 1200 Elo player 60% of the time. That means the expected value for the 1400 Elo player is .6 (a win is 1, a loss is 0). When you win (1 point), that’s 0.4 higher than expected! You move up .4 times the scaling variable, which is a number that just defines how fast the ratings change (this is higher for players with few games and lower for players with more, in order to quickly shuffle newcomers to somewhere more useful). However, if you lose, it’s 0.6 lower than expected, and you cough up 50% more Elo than you would have won (and vice versa for the 1200 Elo player).

Matchmaking and Solo 5×5 Ratings

League of Legends uses a modified Elo system. The specifics of the modifications are kept quiet, but we more or less know that matchmaking tries to match up five players so that their average Elo is around the same as the opposing team’s. Duo queue players’ Elo ratings get a bit of a bump for averaging purposes, since duo queueing is an obvious advantage. Blue/bottom left team also gets a bit of a bump, because stats have shown that the blue team has a bit of an advantage over the purple team (so they make up for it by making purple team a bit better).

At the end of the match, your personal Elo is stacked against the enemy team’s average for the final rating change calculation.

Other Notes