Arpad Elo, a Hungarian-American physics professor is known for developing a rating system based on the skill-level of players in zero-sum games. Elo’s system was initially inculcated in the sport of chess in the 1960s.
The Elo rating system soon found its usage in other games and sports, one of them being tennis. In tennis, two players are given a skill rating. Based on this skill rating, a result is expected. The expected result and the actual result determines the amount of player ratings that will increase or decrease after each match. There are two formulas used to calculate Elo ratings. One is a conventional formula and the other is an update formula.
On a probability scale, results between two players are as follows: 1 for a win, 0 for a loss and 1/2 for a draw. A win for the higher rated player takes only a few points from the losing player. However, if the lower-rated player scores an upset win, then more points are deducted from the player with the higher rating. In case of a draw, it is the played with the higher rating whose points are deducted.
The conventional formula for calculating a player’s Elo rating is as follows:
Probability of win (for player A) = 1/1 + 10 ^ (Result of player B – Result of Player A)/400
As a general rule, if the difference in ratings of the two players is of 100 points, then the stronger player has a 64% win-rate. In case of a 200-point difference, this probability increases to 75%. A 300-point difference means that the higher rated player has an 85% chance of winning. The 400 used in the formula has been used conventionally since the time the Elo ratings were adapted in chess.
The update formula takes 32 as a constant in its formula for reasons unknown. The new rating of a player is calculated as follows:
New rating = Current rating + 32(Result – Expected result)
As mentioned above, an expected result can be anywhere on a probability scale of 0 to 1.
The Elo system changes from match-to-match and represents a player’s true skill and consistency. In some local tournaments, Elo ratings are used to pool players of same ratings to ensure a fair play.
Jeff Sackman of TennisAbstract.com is credited for maintaining the Elo ratings of most professional players on tour. The website also maintains an Elo system for players based on the type of surface (hard/grass/clay) the matches were played on.