Neustadtl score
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The Neustadtl score is a scoring system often used to break ties in chess tournaments. It 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 which was never popular and is not used today.
A player's Neustadtl score is calculated by adding the sum of the conventional scores of the players they have defeated to half the sum of the conventional scores of those they have drawn against.
As an example of the system in action, here is the cross-table of the 8th Correspondence Chess World Championship Final:
1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
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 53.5
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
The penultimate column shows the players' main scores, with their Neustadtl scores shown in the last. As can be seen, both Jørn Sloth and Vladimir Zagorovsky finished with 11/14, but Sloth was declared Correspondence Chess World Champion because of his superior Neustadtl score.
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.
