Sonneborn–Berger tie-break

Sonneborn–Berger

Definition

The Sonneborn–Berger (SB) score is a tie‑break method used to rank players who finish with the same number of points in a tournament, most commonly in round-robin events and sometimes in Swiss events. It is also known historically as the “Neustadtl score.”

The idea: reward wins (and, to a lesser extent, draws) against opponents who themselves scored highly. Formally, a player’s SB score is the sum of the final scores of the opponents that player defeated, plus half the final scores of the opponents with whom the player drew.

How it’s used

Organizers specify SB in the tie‑break order to separate players tied on total points. It is especially common in all‑play‑all round‑robins (invitational groups, leagues, club championships), and adapted versions are used in some team competitions.

• Individual tournaments (standard SB): add the final scores of all opponents you beat, plus half of the final scores of the opponents you drew against.
• Team events (team SB variants): similar philosophy, but computed using match points or board points of the opposing teams, weighted by the result against those teams. Exact formulas vary by event regulations.
• Swiss events: SB is less common than Buchholz, but may appear in the tie‑break order. Because pairings are uneven in Swiss systems, some organizers prefer Buchholz or Median-Buchholz; SB is still used as an additional or fallback criterion.

Why it matters

SB aims to recognize the “quality” of a player’s results. Beating or drawing players who perform well is worth more than scoring the same result against players who perform poorly. This helps differentiate between tied players who took different paths to the same total score.

Formula

Let Opp(wins) be the set of opponents you defeated, and Opp(draws) the set of opponents you drew against. Let S(opp) be each opponent’s final tournament score.

• SB = Σ S(opp) for opp in Opp(wins) + 0.5 × Σ S(opp) for opp in Opp(draws).
• Losses contribute 0.
• Final scores are taken after the event finishes, so SB can change as other games conclude.

Worked example (4‑player round‑robin)

Players: Alice (A), Boris (B), Carla (C), Diego (D). Each plays everyone once.

• Alice: beats Boris, draws Carla, loses to Diego → total points = 1.5.
• Boris: beats Diego, draws Carla, loses to Alice → total points = 1.5.
• Carla: draws Alice, draws Boris, loses to Diego → total points = 1.0.
• Diego: beats Alice, beats Carla, loses to Boris → total points = 2.0.

Final scores: A=1.5, B=1.5, C=1.0, D=2.0. Tie to break between Alice and Boris.

• Alice’s SB: win vs Boris → +1.5; draw vs Carla → +0.5×1.0 = 0.5; loss vs Diego → +0. Total SB = 2.0.
• Boris’s SB: win vs Diego → +2.0; draw vs Carla → +0.5×1.0 = 0.5; loss vs Alice → +0. Total SB = 2.5.

Result: Boris ranks ahead of Alice on SB because his win was against the event’s top scorer.

Relationship to other tie‑breaks

• Buchholz: sums all opponents’ final scores, regardless of result. SB instead weights only the opponents you scored against (full weight for wins, half for draws).
• Direct encounter (head‑to‑head): compares results among the tied players only; often used before or alongside SB.
• Number of wins: rewards decisiveness; sometimes precedes SB, sometimes follows it.

Strategic implications

• Beating leaders helps twice: you gain a point and you add a large chunk to your SB if they finish high.
• Rooting interest: after you’ve beaten someone, you benefit if they continue to score well, as their final total boosts your SB.
• Draw selection: a draw with a high‑scoring opponent is worth more SB than a draw with a tail‑ender, which can matter in final‑round strategy if tie‑breaks decide prizes.

Practical notes and edge cases

• Timing: SB depends on opponents’ final scores, so standings may reshuffle as other games end.
• Unplayed games/forfeits: event regulations specify how these are treated for tie‑breaks; some exclude unplayed games from the opponent’s “final score” in SB calculations or assign specific values. Always check the tournament’s rule sheet.
• Team variants: “Team Sonneborn–Berger” typically multiplies the opponent team’s total match (or board) points by the match (or board) points your team scored against them, then sums over all matches. Details vary by organizer.
• Volatility in Swiss events: because opponent sets differ, SB can swing significantly based on pairings and late results; many Swiss events therefore place SB after Buchholz-type criteria.

Historical and contextual notes

The method has been in use since the late 19th and early 20th centuries and is widely recognized under the eponym “Sonneborn–Berger,” while “Neustadtl” is a common historical label. Modern regulations from many federations list SB among standard tie‑breaks, especially for round‑robin groups.

Additional examples

• Suppose you score 2.5/3 by beating two players who each finish on 3.5/5 and drawing a player who finishes on 5.0/5 in a larger round‑robin. Your SB contribution is 3.5 + 3.5 + 0.5×5.0 = 10.0, which can outstrip a rival who scored 2.5/3 against lower‑finishing opponents.
• Conversely, if your early victims collapse in the last rounds, your SB can drop behind a rival who beat mid‑table opponents that rallied late.

Tips for players

• Know the tie‑break order before the event. If SB is high in the order, prioritize beating direct rivals and leaders.
• If you are tied late in the event and can’t change your result, keep an eye on the boards involving your past opponents—those results can swing SB.
• When risk‑managing final rounds, remember that a draw versus a top performer may be tie‑break‑valuable compared to a speculative win attempt against a tail‑ender; context matters.

Summary

Sonneborn–Berger is a principled tie‑break that rewards performance against successful opposition. It is straightforward to compute, widely used in round‑robins, adapted for team competitions, and offers players practical incentives to score well specifically against the event’s in‑form competitors.