Arimaa Rating System

The Arimaa rating system is simple and straight forward (well compared to some of the other rating systems at least).

Each player has a rating and a rating uncertainty. When a player wins a game the rating goes up and when they lose the rating goes down. If the player was expected to win based on the current ratings, then the rating does not go up as much. The more of an upset a game is, the more it changes. The players rating uncertainty also effects how much the rating changes. The more uncertain a players rating is the more it can change. The rating uncertainty goes down as a player gets more experience with the game.

After a rated game is over the new ratings of both players are computed as follows:

  (WRnew, WKnew) = newRating(WRold, BRold, WW, WKold)
  (BRnew, BKnew) = newRating(BRold, WRold, BW, BKold)

  WR - White (or Gold) players rating 
  BR - Black (or Silver) players rating 
  WK - White rating uncertainty
  BK - Black rating uncertainty
  WW - 1 if White won, 0 if Black won, 0.5 if draw
  BW - 0 if White won, 1 if Black won, 0.5 if draw

  function newRating(MyR, OpR, Iwon, MyK)

            OpR - MyR
    Rdiff = ---------

    winProb =   -------
               1.0 + 10**Rdiff

    MyRnew = int(MyR + MyK*(Iwon - winProb) +0.5)

    MyKnew = int(0.98*MyK + 0.6)

    return(MyRnew, MyKnew)

  New players start with a rating of 1400 and a
  rating uncertainty of 120.

  The rating uncertainty of all players increases by one point
  per week if the rating uncertainty is between 30 and 120.

Some properties of this rating system:

The rating uncertainty will never get below 30. It decreases from its initial value of 120 down to 30 in about 70 games.

If two new players (with an inital rating of 1400 and rating uncertainty of 120) only play each other and one player always wins and the other always loses; the rating of the winning player will stabalize at 1755, 30 and the losing player at 1046, 30. The difference between their ratings is 709. Even if the rating uncertainty did not decrease and was kept constant at 120, the ratings would stablize to 1873 and 928; a difference of 943.

If a player always plays new players (with an inital rating and uncertainty of 1400 and 120) and always wins; the players rating will stabalize at 2109, 30. This is 709 points more than 1400. If the player had always lost against new players than the rating would stabalize at 691, 30; which is 709 points less than 1400.

Performing as expected against a player with a rating difference of about 800 points or more will not change your rating much.

The ratings have an intrinsic error of about +-30 and it takes about 90 games for the rating error to converge to this level.

Basics of Ratings Systems:

Other Rating Systems