Elo Ratings

The EMZ player ranks are based on the ELO system developed by Dr. Arpad Elo. This system is used by FIDE, the international chess federation, to rate chess players. It is ideally suited for rating the results of 1v1 games, such as Doom 3 Tourney mode.

Ratings tend to converge on a player's true strength relative to their opponents after about 30 matches.

Calulating the Rating

Each player is given an initial rating of 1500. As each match is played the rating for the players are updated based on the following formulas:

R_n = R_o + K × (W - W_e)

R_n is the new rating, R_o is the old (pre-match) rating.

K is the weight constant for the player:

• 25 for players with fewer than 30 games;
• 15 for players with a rating less than 1800;
• 10 for all other players;

W is the result of the game (1 for a win and 0 for a loss).

W_e is the expected result (win expectancy) from the following formula:

W_e = 1 / (10^(-dr/400) + 1)

dr equals the difference in ratings between the two players.

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