Elo rating system

19.05.2019 03:05

The Elo system was originally invented as an improved chess rating system over the previously used Harkness system, but is also used as a rating system for multiplayer competition in a number of video games, association football, American football, basketball, Major League Baseball, table tennis, board games such as Scrabble and Diplomacy, and other games.

The difference in the ratings between two players serves as a predictor of the outcome of a match. Two players with equal ratings who play against each other are expected to score an equal number of wins. A player whose rating is 100 points greater than their opponent's is expected to score 64%; if the difference is 200 points, then the expected score for the stronger player is 76%.

A player's Elo rating is represented by a number which may change depending on the outcome of rated games played. After every game, the winning player takes points from the losing one. The difference between the ratings of the winner and loser determines the total number of points gained or lost after a game. If the high-rated player wins, then only a few rating points will be taken from the low-rated player. However, if the lower-rated player scores an upset win, many rating points will be transferred. The lower-rated player will also gain a few points from the higher rated player in the event of a draw. This means that this rating system is self-correcting. Players whose ratings are too low or too high should, in the long run, do better or worse correspondingly than the rating system predicts and thus gain or lose rating points until the ratings reflect their true playing strength.

An Elo rating is a comparative rating only, and is valid only within the rating pool where it was established.

Our tournaments rating is calculated using ELO system using the following formula (for two players А and В):

Rа, new = Rа, previous + К * (Са - Еа)

Rа, new – new rating of player A in the tournament;
Rа, previous – current rating of player A in the tournament;
К – index 30 if rating value is less than 2000, index 20 – when rating is from 2000 to 2400, index 10 if rating value is higher than 2400;
Са – number of points scored de facto by Player A (1 point for win, 0,5 for a draw game and 0 for loss );
Еа – expected score for Player A, calculated on the basis of Player's rating.

Еа = 1 / (1 + 10 ^ ( (RB, previous – Rа, previous) / 400 ))

When a tournament ends, the Player's rating earned in that tournament is added to the Player's global rating.