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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 RatingsGame 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.
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 %
Elo rating title ----------- -------------------------- 2650 - 2800 world champions 2500 - 2650 international grandmasters Winning ProbabilitiesThe 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 ratingOne method is: A new participant plays three initial games against opponents with already established ratings. These games, for example, account as:
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 RanksThe 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 LinksElo Rating DiscussionTim 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. ![]() |