Sonneborn–Berger score

The Sonneborn–Berger score (or the Neustadtl score) is a scoring system often used to break ties in chess tournaments. It is computed by summing the conventional score of each defeated opponent, and half the conventional score of each drawn opponent.

See also: Tie-breaking in Swiss-system tournaments

Neustadtl score is named after Hermann Neustadtl, who proposed it in a letter published in Chess Monthly in 1882. It is often called the Sonneborn–Berger score, though this is something of a misnomer, since William Sonneborn and Johann Berger were actually strong critics of the system; they proposed their own tie-breaking system that added in the raw score of each player but that did not help with tiebreaking and was therefore never popular and is not in use today.

More common tiebreaking methods in chess tournaments include the Neustadtl Sonneborn–Berger score, head-to-head score, Koya score, or favouring the player with the most wins (or black games). In Swiss system events, comparison of the Buchholz scores and the sum of progressive scores are common.

Neustadtl Sonneborn–Berger score

A player's Neustadtl Sonneborn–Berger score is calculated by adding the sum of the conventional scores of the players he/she has defeated to half the sum of the conventional scores of those he/she has drawn against.

The main point is to give more value for a win/draw against a player ranked high, than for a win/draw against a player ranked low in the tournament.[1][2]

Since players may share the same Neustadtl score, further means of breaking ties may be required; common methods include considering the score in games played between the tied players or favouring the player with the most wins. Some tournaments do not use Neustadtl to break ties at all (Linares, for example, gives preference to the player with the most wins), and others use no tie-breaking method at all, sharing the prize money on offer between players. In national championships or events which act as qualifying tournaments for others, there may be a blitz playoff between the tied players. Neustadtl remains the most common tie-breaking method in round-robin tournaments, though in Swiss system events, comparison of the Buchholz scores and the sum of progressive scores is more common.

Example

As an example of the system in action, here is the crosstable of the 1975–80 World Correspondence Chess Championship Final (here cs indicates conventional score, ns Neustadtl score):

                  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  cs   ns
1.  Sloth         X ½ ½ 1 ½ ½ 1 1 ½  1  ½  1  1  1  1  11   69.5
2.  Zagorovsky    ½ X 0 ½ 1 ½ 1 1 1  ½  1  1  1  1  1  11   66.75
3.  Kosenkov      ½ 1 X ½ ½ ½ ½ ½ 1  1  ½  1  1  1  1  10½  67.5
4.  Khasin        0 ½ ½ X ½ 1 ½ 0 1  1  ½  1  ½  1  ½  8½   54.75
5.  Kletsel       ½ 0 ½ ½ X ½ ½ ½ ½  0  1  1  ½  1  1  8    47.75
6.  De Carbonnel  ½ ½ ½ 0 ½ X ½ ½ 0  1  ½  ½  0  1  1  7    45.25
7.  Arnlind       0 0 ½ ½ ½ ½ X ½ 1  0  ½  ½  1  1  ½  7    42.5
8.  Dunhaupt      0 0 ½ 1 ½ ½ ½ X 0  ½  1  0  1  ½  1  7    41.5
9.  Maedler       ½ 0 0 0 ½ 1 0 1 X  1  ½  ½  ½  ½  1  7    41.5
10. Estrin        0 ½ 0 0 1 0 1 ½ 0  X  1  1  1  0  1  7    40.5
11. Walther       ½ 0 ½ ½ 0 ½ ½ 0 ½  0  X  0  1  ½  1  5½   33.25
12. Boey          0 0 0 0 0 ½ ½ 1 ½  0  1  X  ½  ½  1  5½   28.5
13. Abramov       0 0 0 ½ ½ 1 0 0 ½  0  0  ½  X  ½  1  4½   24.75
14. Siklos        0 0 0 0 0 0 0 ½ ½  1  ½  ½  ½  X  1  4½   22.75
15. Nun           0 0 0 ½ 0 0 ½ 0 0  0  0  0  0  0  X  1    7.75

As can be seen, both Jørn Sloth and Vladimir Zagorovsky finished with 11 points from 14 games, but Sloth was declared Correspondence Chess World Champion because of his superior Neustadtl score of 69.5 vs Zagovorsky's 66.75.

As an example, Sloth's score is calculated as:

0.5*11 + 0.5*10.5 + 1.0*8.5 + 0.5*8.0 + 0.5*7.0 + 1.0*7.0 + 1.0*7.0 + 0.5*7.0 + 1.0*7.0 + 0.5*5.5 + 1.0*5.5 + 1.0*4.5 + 1.0*4.5 + 1.0*1.0 = 69.5

Non-Neustadtl Sonneborn-Berger score

The Non-Neustadtl Sonneborn–Berger score is the scoring system proposed by William Sonneborn and Johann Berger as an improvement to the Neustadtl score. Sonneborn was a strong critic of the Neustadtl score, and suggested adding in the player's raw score. Berger supported this. In truth, adding in the raw score does no good when ranking tied players, so the suggestion died out and is seldom used today. However, the Neustadtl score is now commonly known as the Sonneborn–Berger score.[3]

See also

References
  1. Ahrens, W. (1901), "Zur relativen Bewertung von Turnierpartien", Wiener Schachzeitung, 4 (Nr. 10/11 October-Novemb.): 181–192
  2. Chess.com: Tie-break methods
  3. The Oxford Companion to Chess, Hooper and Whyld, 1992, p. 270
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