Sonneborn-Berger

    Keywords: Rules, Tournament

Sonneborn-Berger is a method to determine a tournament result if two players have an equal number of wins. It takes the opponents' strength into account.

Example: Each player has played two games against each other player. 1 indicates a win, 0 a loss.

      +---------+---------+------------------+--------------+
      | 1st     | 2nd     | won games        | Sonneborn-   |
      | round   | round   |                  | Berger       |
      |---------+---------|                  |              |
      | A B C D | A B C D | score | opponent | score        |
  +---+---------+---------+-------+----------+--------------|
  | A | - 1 1 1 | - 0 1 0 |   4   | B C C D  | 4+3+3+1 = 11 |
  | B | 0 - 1 1 | 1 - 0 1 |   4   | A C D D  | 4+3+1+1 =  9 |
  | C | 0 0 - 1 | 0 1 - 1 |   3   | B D D    | 4+1+1   =  6 |
  | D | 0 0 0 - | 1 0 0 - |   1   | A        | 4       =  4 |
  +---+---------+---------+-------+----------+--------------+

Player A and B both have 4 wins, thus the Sonneborn-Berger method is used to determine the tournament winner: For each won game the opponent's final primary score is added to the winner's Sonneborn-Berger score. For example, A won against B, C, C and D, his Sonneborn-Berger score is 4+3+3+1 = 11. B has a Sonneborn-Berger score of 9, thus A is the tournament winner.

Related links


Discussion

Dieter: Is this what we call SOS (Sum of Opponent's Scores?) in MacMahon - The Program ?

SAS: No, it's what is sometimes called SODOS (Sum Of Defeated Opponents' Scores), at least in the absence of draws. SOS makes more sense than Sonneborn-Berger for McMahon Pairing tournaments. Sonneborn-Berger is mainly used for all-play-all tournaments, where SOS doesn't work at all.


Tim Brent: There is also a modified version at Little Golem where the score is double the opponent's points (i.e. if second has 2 points and first won, the Sonneborn score is 4).


This is a copy of the living page "Sonneborn-Berger" at Sensei's Library.
(OC) 2005 the Authors, published under the OpenContent License V1.0.
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