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Elo Rating
    Keywords: Tournament

In the early 1960's, Arpad Elo developed the Elo rating system.

It was the first rating system that had probabilistic underpinnings. Originally, Elo developed it for the game of chess, and chess federations around the world adopted it quickly. It became popular and common for many other games too, including Go, Scrabble, table tennis, etc.


Elo Ratings

Game federations do not use identical (parameters for) rating systems. They attach different titles to a rating, and they have different rule sets to determine an initial rating for new participants.

Usually, an average amateur player's rating ranges between 1300 and 1700 Elo points.

[ext] U.S. Chess Federation's classes are:

  Elo rating    class    members
  -----------   -------  -------
  2200 - 2800   Master      4 %
  2000 - 2200   Expert      8 %
  1800 - 2000   Class A    12 %
  1600 - 1800   Class B    18 %
  1400 - 1600   Class C    18 %
  1200 - 1400   Class D    20 %
     0 - 1200   Class E    20 %

[ext] International Chess Federation's top ratings are:

  Elo rating    title
  -----------   --------------------------
  2650 - 2800   world champions
  2500 - 2650   international grandmasters

Winning Probabilities

The rating indirectly represents the probability of winning against other rated players. This probability depends only on the difference between the two players' ratings as follows:

   rating     probability
  difference  of winning
  ----------  -----------
     400       .919
     300       .853
     200       .758
     100       .637
      50       .569
       0       .500
     -50       .431
    -100       .363
    -200       .242
    -300       .147
    -400       .081

This represents the area under the standard bell-shaped curve where 200 * sqrt(2) points are taken as one standard deviation. The table shows some sample points on this curve, adequate for good approximations of rating calculations by interpolation.


Determing an appropriate initial rating

One method is: A new participant plays three initial games against opponents with already established ratings. These games, for example, account as:

  • won game: new member's rating = opponent's rating + 200 points
  • draw game: new member's rating = opponent's rating
  • lost game: new member's rating = opponent's rating - 200 points

These initial game results are averaged and used for the new member's initial rating.

Example: A new member loses a game against a 1700-opponent, draws against a 1400-opponent and wins against a 1300-opponent. The result is an initial rating of 1467 = ( (1700-200) + 1400 + (1300+200) ) / 3.


Converting Elo Ratings into Go Ranks

The Elo system can be modified to implement Go ranks at a Go server.

Internally, DGS uses:

  Points   Go rank
  ------   -------
   2300      3 dan
   2200      2 dan
   2100      1 dan
   2000      1 kyu
   1900      2 kyu
   1800      3 kyu
   1500      6 kyu
   1000     11 kyu
    500     16 kyu
      0     21 kyu
   -100     22 kyu
   -200     23 kyu
   -300     24 kyu

Related Links


Elo Rating Discussion

Tim Brent: Originally 2000 in the Chess rating was a base point, based upon a 50% score at the US Open. The original idea was using Chess to find out if mental activity decreases with aging.

Frs: What does the Elo rating system have to do with an age-dependent decrease of mental activity?

Tim Brent: He had a theory that you could use success in chess as a basis for showing the effects of aging on mental activity, i.e. a player who could play at a 2400 level in his forties is now playing in his fifties at a 2260 level. Could it be proof that his cognitive ability went down 6 percent over that period? (Of course this theory doesn't consider that the aforementioned player might simply have started losing against a group of stronger players.)



This is a copy of the living page "Elo Rating" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.