Danish Rating System

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Danish Rating System

This is a description of the Danish Rating System.

The system was developed at some time back in the 1980's.

Rank and rating

The 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 Games

Not 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.

  • If a players rating is below 5 kyu = -5,50 (not including), and he is playing WHITE, then games are only rated when he didn't give more than 5 stones in handicap. BLACK's games are always rated.
  • If a players rating is above 5 kyu = -5,50 (including), then games are only rated when there are not more than 4 stones in handicap. This is for both colors.
+----------+--------+-------+
| Rating   | BLACK  | WHITE |
+----------+--------+-------+
| < -5,50  | Always | Max 5 |
+----------+--------+-------+
| >= -5,50 | Max 4  | Max 4 |
+----------+--------+-------+

Winning percent

Prior 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:

  • Player 1 (-2,13) : N( -2,13 - -2,63 ; 0 ; 3,568 ) = 56 %
  • Player 2 (-2,63) : N( -2,63 - -2,13 ; 0 ; 3,568 ) = 44 %

Handicap stones

The 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 score

The 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:

  • A player has an accumulated winning percent of 2,37 from 6 games, and he won 3. So he had +0,63 better score than expected.

Bonus

If 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.

Coefficient

Before 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:

  • Rating: [ -18,50 ; -9,50 [ => 0,40
  • Rating: [ -9,50 ; -4,50 [ => 0,30
  • Rating: [ -4,50 ; -0,50 [ => 0,20
  • Rating: [ -0,50 ; +8,50 [ => 0,13

If the time is between [ 75 min ; inf [ the coefficient is:

  • Rating: [ -18,50 ; -9,50 [ => 0,60 = -9,88 ( =0.80
  • Rating: [ -9,50 ; -4,50 [ => 0,45
  • Rating: [ -4,50 ; -0,50 [ => 0,30
  • Rating: [ -0,50 ; +8,50 [ => 0,20

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 Distribution

Here 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.

  • [ 0,00 ; 0,05 [ => 0,50
  • [ 0,05 ; 0,14 [ => 0,51
  • [ 0,14 ; 0,23 [ => 0,52
  • [ 0,23 ; 0,32 [ => 0,53
  • [ 0,32 ; 0,41 [ => 0,54
  • [ 0,41 ; 0,50 [ => 0,55
  • [ 0,50 ; 0,59 [ => 0,56
  • [ 0,59 ; 0,68 [ => 0,57
  • [ 0,68 ; 0,77 [ => 0,58
  • [ 0,77 ; 0,86 [ => 0,59
  • [ 0,86 ; 0,96 [ => 0,60
  • [ 0,96 ; 1,05 [ => 0,61
  • [ 1,05 ; 1,14 [ => 0,62
  • [ 1,14 ; 1,24 [ => 0,63
  • [ 1,24 ; 1,33 [ => 0,64
  • [ 1,33 ; 1,43 [ => 0,65
  • [ 1,43 ; 1,53 [ => 0,66
  • [ 1,53 ; 1,62 [ => 0,67
  • [ 1,62 ; 1,72 [ => 0,68
  • [ 1,72 ; 1,82 [ => 0,69
  • [ 1,82 ; 1,93 [ => 0,70
  • [ 1,93 ; 2,03 [ => 0,71
  • [ 2,03 ; 2,14 [ => 0,72
  • [ 2,14 ; 2,25 [ => 0,73
  • [ 2,25 ; 2,36 [ => 0,74
  • [ 2,36 ; 2,47 [ => 0,75
  • [ 2,47 ; 2,58 [ => 0,76
  • [ 2,58 ; 2,70 [ => 0,77
  • [ 2,70 ; 2,82 [ => 0,78
  • [ 2,82 ; 2,94 [ => 0,79
  • [ 2,94 ; 3,07 [ => 0,80
  • [ 3,07 ; 3,20 [ => 0,81
  • [ 3,20 ; 3,34 [ => 0,82
  • [ 3,34 ; 3,48 [ => 0,83
  • [ 3,48 ; 3,63 [ => 0,84
  • [ 3,63 ; 3,78 [ => 0,85
  • [ 3,78 ; 3,94 [ => 0,86
  • [ 3,94 ; 4,11 [ => 0,87
  • [ 4,11 ; 4,29 [ => 0,88
  • [ 4,29 ; 4,48 [ => 0,89
  • [ 4,48 ; 4,68 [ => 0,90
  • [ 4,68 ; 4,90 [ => 0,91
  • [ 4,90 ; 5,14 [ => 0,92
  • [ 5,14 ; 5,41 [ => 0,93
  • [ 5,41 ; 5,71 [ => 0,94
  • [ 5,71 ; 6,05 [ => 0,95
  • [ 6,05 ; 6,47 [ => 0,96
  • [ 6,47 ; 7,00 [ => 0,97
  • [ 7,00 ; 7,75 [ => 0,98
  • [ 7,75 ; 9,20 [ => 0,99
  • [ 9,20 ; inf [ => 1,00

Ranking and rating interval

Here is a list of the rank and the intervals

  • 6 dan = [ 4,50 ; 5,50 [
  • 5 dan = [ 3,50 ; 4,50 [
  • 4 dan = [ 2,50 ; 3,50 [
  • 3 dan = [ 1,50 ; 2,50 [
  • 2 dan = [ 0,50 ; 1,50 [
  • 1 dan = [ -0,50 ; 0,50 [
  • 1 kyu = [ -1,50 ; -0,50 [
  • 2 kyu = [ -2,50 ; -1,50 [
  • 3 kyu = [ -3,50 ; -2,50 [
  • 4 kyu = [ -4,50 ; -3,50 [
  • 5 kyu = [ -5,50 ; -4,50 [
  • 6 kyu = [ -6,50 ; -5,50 [
  • 7 kyu = [ -7,50 ; -6,50 [
  • 8 kyu = [ -8,50 ; -7,50 [
  • 9 kyu = [ -9,50 ; -8,50 [
  • 10 kyu = [ -10,50 ; -9,50 [
  • 11 kyu = [ -11,50 ; -10,50 [
  • 12 kyu = [ -12,50 ; -11,50 [
  • 13 kyu = [ -13,50 ; -12,50 [
  • 14 kyu = [ -14,50 ; -13,50 [
  • 15 kyu = [ -15,50 ; -14,50 [
  • 16 kyu = [ -16,50 ; -15,50 [
  • 17 kyu = [ -17,50 ; -16,50 [
  • 18 kyu = [ -18,50 ; -17,50 [
  • 19 kyu = [ -19,50 ; -18,50 [
  • 20 kyu = [ -20,50 ; -19,50 [
  • 21 kyu = [ -21,50 ; -20,50 [
  • 22 kyu = [ -22,50 ; -21,50 [
  • 23 kyu = [ -23,50 ; -22,50 [
  • 24 kyu = [ -24,50 ; -23,50 [
  • 25 kyu = [ -25,50 ; -24,50 [

Danish Rating System last edited by 93.163.251.98 on April 6, 2012 - 19:57
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