How does the ELO ranking system work

Archive: Elo ranking system

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The Elo ranking system was used for ranked matches in League of Legends prior to the introduction of the league system.

The Elo rating system is a method around that relative ability of a player compared to other players. It is named after its inventor Arpad Elo, an American physicist and chess player of Hungarian origin, who originally designed it for games with two players, such as chess.[1] Nowadays this system is also used in various modified variations for other team games.

In League of Legends, this method was used to find equally strong players and opponents for ranked games. The Elo ranking system was never used for custom or co-op vs. AI games. Each player had different ones Elo ratings for the different ranking queues: 3v3 arranged, 5v5 solo and 5v5 arranged teams. The rating was only visible after 5 games in a queue. Similar to today's class rewards, players received medals in the Summoner profile for their achievements at the end of Season 1 and Season 2.

  • Bronze (old): Between 1250 and 1399 (3v3: 1249-1409, pre-made 5v5: 1249-1409) (Top 25%)
  • Silver (old): Between 1400 and 1519 (3v3: 1410-1519, pre-made 5v5: 1410-1499) (Top 10%)
  • Gold (old): Between 1520 and 1899 (3v3: 1520-1699, pre-made 5v5: 1500-1749) (Top 3%)
  • Platinum (old): 1900 and above (3v3: 1700+, pre-made 5v5: 1750+) (Top 0.2%)

About a month ago before the end of Season 2, a new ranking system was introduced:[2]

  • Bronze: Between 0 and 1149 (Team: 0-1249) (Top 100%)
  • Silver: Between 1150 and 1499 (Team: 1250-1449) (Top 68% -13%) majority of active players
  • Gold: Between 1500 and 1849 (Team: 1450-1649) (Top 13% -1.5%)
  • Platinum: Between 1850 and 2199 (Team: 1650-1849) (Top 1.5% -0.1%)
  • Diamond: 2200 and above (Team: 1850+) (Top 0.1%)

It was also introduced that ranks were broken down into smaller parts, such as: B. Bronze V or Gold 2. These follow each 70 elo one after the other. (1150 - 1220 is silver 5, 1220 - 1290 is silver IV, etc.)

Those were the ranks for the North American server, they differ a little depending on the server.

Elo calculation

The specific formulas which were used for Elo calculations in League of Legends are unknown. However, most Elo implementations share the same basics as that originally designed for chess. A brief summary is given below. For a more detailed discussion, see Wikipedia.

It is assumed that a person's performance varies from game to game in approximately a normal distribution and a person's Elo rating was the mean of that distribution. A person with a higher Elo may perform better on average than a player with a lower Elo, although usually it was mainly to do with the teamwork around that player. This score was determined entirely by win / loss statistics in relation to other players. For players A and B with respective Elo ratings of Ra other Rb the expected victorious outcome Ea of the game for player A was given by the following formula:

For every difference of 400 points, the team / player with the higher score is ten times as likely to win as the other team / player. This standard is for Chess and may have been different in League of Legends. After a game the actual outcome was compared to the expected outcome and each team / players rating is adjusted to bring them closer to where they should actually be. As a result, if a team was expected to win and does their score changes less than if they were expected to lose and instead won. Successive games would have eventually brought each player / team to a point where they were expected to win 50% of the time against opponents of equal score.

A player's change in rating was linear to the difference between the expected outcome and the actual outcome. It was given by the following formula where Sat is the result of the game and is presumably 1 for a win and 0 for a loss.

The magnitude of the score change was determined by the player's K value and other things, like a server crash (When the score you get is 50%). In chess initially this K value is big (25 for their first 30 games) resulting in large changes in Elo. This is so a player can rapidly find her or his correct place in the ranking system. As their number of wins and losses became more even this K value was reduced to prevent dramatic changes in Elo against evenly matched opponents (K = 15 to 7). This also prevented inflation in ratings at high Elo play. It appears that League of Legends used a similar system of changing K values: K appeared to be starting around 100, eventually leveling out to about 25.[3]

All players started ranked play with an Elo of 1200 for their first 10 games at level 30. From there they were assigned a score and changes are made as normal.[4]

Loss of rating

Prior to the Season 2 rating system remake, Elo decayed over time when you were above 1400 Elo:[5]

  • Elo decayed at a rate of 50 Elo for Diamonds, 35 Elo for Platinums, 25 Elo for Golds, 10 Elo for Silver, and 0 Elo for Bronze for every 4 consecutive weeks of inactivity and every 7 days thereafter.
  • For normal rating, inactivity was defined as no activity in any queue.
  • For ranked rating, inactivity was defined as no activity in the specific queue (arranged 5x5, arranged 3x3, and solo / duo 5x5 are all tracked separately). Ranked decay only applied to people who were ranked above 1400 rating.
  • The decay timer was reset after a game was played in that specific queue.

More facts

  • Elo changes were larger for the first ~ 50 games, ranging from 50-13.
  • Playing ranked matches with a partner never had any additional effect on Elo loss / gain.
  • The preliminary Elo rating was displayed after 5 games, but to complete your Elo placements you needed 10 games, like today.

See also