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Danish Rating System
Keywords: Rules, Tournament
Danish Rating SystemThis is a description of the Danish Rating System. The system was developed at some time back in the 1980's. Rank and ratingThe rating is calculated with 2 decimals. In general: A negitive number is a kyu player and a positive number is a dan player, but Shodan's (1 dan) has negative numbers from -0,50 and positive number up to +0,49. (Scroll down to the end of this page to see all rank and corresponding rating interval.) Rated GamesNot all games are to be rated, or more precise, not all games are to be rated for both players. When the Rank difference between 2 players is very large, then only some of the games are rated.
+----------+--------+-------+ | Rating | BLACK | WHITE | +----------+--------+-------+ | < -5,50 | Always | Max 5 | +----------+--------+-------+ | >= -5,50 | Max 4 | Max 4 | +----------+--------+-------+ Winning percentPrior to a games in a tournament the winning percentage for both players is calculated using an accumulated normal distribution. The distribution uses the parameters x_=0 ; and s=3,568. (Scroll down and see the table for the accumulated normal distrution at the end of this page.) From 2 players with ranking -2,13 and -2,63 the winning percent is calculated to be:
Handicap stonesThe system also works using handicap stones. When a handicap is given in a game the rating difference is reduced by the number of stones given. A player with rating -2,13 and a player with rating -5,87 has a difference of -2,13 - -5,87 = 3,74. In the accumulated normal distribution this gives a winning percent of 85 % for the player with rating -2,13, and 15 % for the other. If they played a handicap game with 3 stones this would be -2,13 - -5,87 - 3 = 0,74, and a winning percent of 58 % for the stronger player and 42 % for the weaker. Compare with actual scoreThe winning percent is calculated for all games in the turnament. All winning percent are accumulated and compared with the actual score in the turnament. Example:
BonusIf the difference between expected score and actual score is larger than 1, then a bonus is given by doubling the part over 1. Example: If the expected score is 1.88 and actual score is 3, the difference is 3 - 1,88 = 1,12. Bonus 1 + 0,12 x 2 = 1,24. CoefficientBefore the new rating for a player is found, the score difference is multiplied by a coefficient to reduce fluxtuation. The coefficient is selected using 2 parameters; Main thinking time and the strength of the player. If the time is between [ 45 min ; 75 min [ the coefficient is:
If the time is between [ 75 min ; inf [ the coefficient is:
So with a score differencece of +0,63 and a thinking time of 45 min, the player with rating -2,13 would become -2,13 + 0,63 x 0,20 = -2,00 A player with rating +1,06, a score difference of -0,17 and a thinking time of 75 min would become: +1,06 + -0,17 x 0,20 = +1,03. A player with rating -10,00, a score difference of +1,34 and a thinking time of 90 min would become: -10,00 + ( 1,00 + 0,34 x 2 ) x 0,60 = -8,99. Accumulated Normal DistributionHere is a list of the an accumulated normal distribution with x_=0 and s=3,568. When the rating diffence is negative, then 1 - accumulated value must be used.
Ranking and rating intervalHere is a list of the rank and the intervals
This is a copy of the living page "Danish Rating System" at Sensei's Library. ![]() |