ELO: How does it work?

General Information on ELO ranking systems
Several turnbased 2player games use a system called ELO to measure an individual player’s strength compared to other players of the game.
The purpose of this system is to continuously measure and rank a player’s skill level by comparing his expected winning ratio with actual game results, allowing the system to match players with comparable rankings into a game.
The ELO system works by comparing the rank of two opponents: A higher ranking means the player scored better in the games he played previously.
Example:
If two players with more or less equal ELO rankings play against each other, you’d expect both to win 50% of all the matches they play against each other.
After a game the expected result is compared to the actual result of the game: If a player with a high ELO ranking wins against a player with a low ranking, his score will only increase slightly as the score difference already pointed to him as a likely winner. However if a lowranking player wins a game against a highranking player, that players ranking will increase significantly. Meanwhile the loosing player’s ranking will drop more significantly if he had a higher score than winner at the start of the game.
ELO Lists for the Catan Universe in detail:
Catan player are ranked in a permanent ELO List that extends across all mobile versions. Unlike in a normal ranking or high score list (e.g. total number of games won), the playing skills of the participating players are included in the ELO calculation. Winning against a player whose ELO ranking is lower than yours earns you fewer points than winning against a player whose ELO ranking is higher than yours. To some degree, the ELO ranking therefore represents a player's playing skills. ELO was first developed for chess and is typically used in 2player games. For Catan Universe, the ELO system has been modified to make it work also for games with more than 2 players, such as the Catan Board Game.
After a game has concluded, the rankings are calculated based on sidebyside comparisons between the players. This means that in a 4player game (player A, player B, player C, and player D) the calculation is performed as if the players had competed against each other in pairs. For this purpose, the ELO formula is used to calculate the result for the combinations AB, AC, AD, BC, BD, and CD (always taking into account the perspective of both players). The sum of a player’s individual rankings is added to, or subtracted from, his or her previous ELO rating.
This is how the formula looks like:
• Victory = 1 (if player a wins)
• Victory = 0 (if player a loses)
• Victory = 0.5 (in case of a tie)Example:
Place/Player/ELO
1 /A/1000
2/ B /800
3/C/1200Player A vs. B (+2) and C (+6). A receives +8 points for his ELO ranking. Player B vs. A (2) and C (+7). B receives +5 points because he has won against the strong player C, even though he has lost against A. C fares comparatively badly; he loses 13 points off his ELO ranking.