Sonneborn-Berger: Chess tie-break method

Sonneborn-Berger

Definition

The Sonneborn-Berger score (often abbreviated “SB,” and historically known as the “Neustadtl score”) is a tie-break method used primarily in round-robin chess tournaments. It rewards players for scoring points against opponents who performed well in the event.

Computation (individual events): Add the final scores of every opponent you defeated, plus half the final scores of every opponent you drew. Losses contribute nothing.

• Win vs Opponent X: add Opponent X’s final score.
• Draw vs Opponent Y: add half of Opponent Y’s final score.
• Loss vs Opponent Z: add 0.

How it is used in chess

The Sonneborn-Berger score is one of the most common tie-breaks in all-play-all (round-robin) events—from club championships to elite invitationals. It is designed to distinguish between players who scored the same number of points by valuing results achieved against stronger-performing opponents.

In Swiss-system events, SB is used less frequently (Buchholz and its variants are more common), though some tournaments include SB in their tie-break order. Team competitions (like the Chess Olympiad) often use a team-specific “Olympiad Sonneborn-Berger” variant.

Exact tie-break order varies by event regulations. SB may appear after head-to-head results or number of wins, or as a primary/secondary criterion in round-robins.

Why it matters (strategic and historical significance)

Strategically, SB can influence late-tournament decisions: a draw against a high-scoring opponent may be as good for tie-breaks as a win against a tail-ender. Players and coaches often track live SB standings to understand which results (their own and others’) will improve their tie-break prospects.

Historically, the method dates to the late 19th century. While the modern name credits William Sonneborn and Johann Berger, the idea was originally proposed by Hermann Neustadtl; hence the alternate name “Neustadtl score.” Berger helped popularize the approach through his influential chess writings.

Calculation details

Let S(O) be an opponent’s final score. For each of your results against that opponent:

• Win: add 1 × S(O)
• Draw: add 0.5 × S(O)
• Loss: add 0

Equivalently: sum over all opponents of [your result against them] × [their final score]. The method rewards results earned against opponents who ultimately finish with high totals.

Important note: SB values are only final once the tournament finishes, because they depend on opponents’ final scores.

Worked example (5-player round-robin)

Players: Anna (A), Ben (B), Cara (C), Diego (D), Emil (E). Final totals: A = 3.0, B = 3.0, C = 2.0, D = 1.5, E = 0.5.

Anna’s individual results: A–B draw, A–C win, A–D win, A–E draw.

1. Wins over C (2.0) and D (1.5): add 2.0 + 1.5 = 3.5
2. Draws with B (3.0) and E (0.5): add 0.5 × 3.0 + 0.5 × 0.5 = 1.5 + 0.25 = 1.75
3. Anna’s SB = 3.5 + 1.75 = 5.25

Ben’s individual results: B–A draw, B–C win, B–D draw, B–E win.

1. Wins over C (2.0) and E (0.5): add 2.0 + 0.5 = 2.5
2. Draws with A (3.0) and D (1.5): add 0.5 × 3.0 + 0.5 × 1.5 = 1.5 + 0.75 = 2.25
3. Ben’s SB = 2.5 + 2.25 = 4.75

Both A and B score 3.0/4, but Anna places ahead on tie-break because her SB (5.25) exceeds Ben’s (4.75). Her points came largely against higher-performing opponents.

Practical implications and tips

• Late-round pairing awareness: A draw versus a top-performer often helps SB more than beating a low scorer.
• Scoreboard watching: Your SB rises when your past opponents gain points; sometimes your best tie-break boost comes from results in other boards.
• Stability: SB isn’t stable until all games conclude. Interim tables can be misleading.
• Event rules matter: Always check the published tie-break order. SB might be primary, secondary, or not used at all.

Variants and related tie-breaks

• Neustadtl score: Historical name for the same system.
• Olympiad Sonneborn-Berger (team events): A team adaptation that weights each opponent’s final match points by the board points your team scored against them (exact formula per event regulations). Used in the Chess Olympiad and other team competitions.
• Buchholz: Popular in Swiss events; sums opponents’ final scores regardless of your result. SB can be viewed as a “result-weighted” counterpart.
• Direct encounter and number of wins: Common alternative tie-breaks that tournaments may use before or after SB.

Interesting facts

• Attribution quirk: Although widely called “Sonneborn-Berger,” the method was earlier described by Hermann Neustadtl; Johann Berger’s influential work helped cement its adoption.
• Philosophy: SB embodies the idea that “who you beat” matters. Beating someone who later surges in the standings is extra valuable.
• Edge cases: Events sometimes specify how unplayed or forfeit games affect tie-breaks; these can alter SB computations and are worth checking in advance.

Quick reference

• Formula: sum(defeated opponents’ final scores) + 0.5 × sum(drawn opponents’ final scores).
• Best for: Round-robin tie-breaks.
• Key property: Rewards points scored against high finishers.