Tiebreak Systems

As the USCF Handbook notes, no tiebreak system is perfect — each has trade-offs. SwissSys supports up to six tiebreaks per tournament, applied in order until a tie is broken.

Individual Tiebreaks

Modified Median

The most commonly used median tiebreak. Sums the final scores of all opponents, then removes the highest or lowest based on the tied player’s score:

• Even score (equal wins and losses): Remove both high and low.
• Plus score (more wins than losses): Remove only the low.
• Minus score (more losses than wins): Remove only the high.

In tournaments of nine or more rounds, two scores are removed from each end using the same criteria. Unplayed games count as opponents scoring 0.

Median (Med)

Also known as the Harkness Median. Works like Modified Median, but the highest and lowest opponent scores are always removed regardless of the tied player’s score. Modified Median is now generally preferred.

Solkoff

Sum of all opponents’ final scores with no scores removed. Popular in short tournaments.

Buchholz, Median Buchholz, Buchholz Cut

FIDE equivalents of the median tiebreaks. The base calculation is the sum of opponents’ final scores, but unplayed games are handled differently than in the median systems.

For a player with an unplayed game, the virtual opponent is assigned the player’s own final score. This follows the April 2024 FIDE rule update.

Cumulative Score

Sum of running (cumulative) scores across all rounds. For a player who scores 1, 1, 0, 1, the cumulative scores are 1, 2, 2, 3 — tiebreak = 8.

The theory: players who win early face tougher opponents throughout, so early wins deserve credit.

Cumulative Scores of Opposition

The same calculation as cumulative, applied to each of the tied player’s opponents rather than to the player themselves.

Progressive Scores (PS)

Listed in the SwissSys UI as Progressive scores (PS). Also known as FIDE Cumulative.

Like cumulative, but discards the first X rounds — you set X (the number of rounds to discard) in a spin box when you add the tiebreak. SwissSys does not raise X automatically; to break stubborn ties you add this tiebreak multiple times, each with a different discard count (e.g. discard 1, then discard 2). Unlike other tiebreaks, it can be selected more than once.

Kashdan

Rewards aggressive play: Win = 4, Draw = 2, Loss = 1, Unplayed = 0. Players with equal scores but fewer draws score higher.

Performance of Opposition

Averages the performance rating of opponents, computed with the +400/-400 method:

• Win — opponent’s rating + 400
• Draw — opponent’s rating
• Loss — opponent’s rating - 400

When a player beats an opponent rated more than 350 points lower, the player’s own rating + 50 is used instead, to prevent inflated values.

Listed in the tiebreak selection dialog as Performance of opposition (Op. perf.) — distinct from Avg. performance rating of opp. (APRO), which averages opponents’ tournament performance ratings rather than the +400/-400 figure used here.

Average Opposition

Averages the ratings of all opponents faced.

Drop-Low Average Opposition (Avg Op-C1)

Same as Average Opposition but drops the lowest opponent rating before averaging. Listed in the SwissSys UI as Avg. opposition cut 1 (Avg Op-C1).

Head-to-Head (1-on-1)

The direct result between tied players. All players in the same score group must have played each other for this tiebreak to apply — if any pair has not met, the value is 0 for the entire group.

When all tied players have met, each player’s tiebreak value is the sum of their actual game results against the other tied players in the group.

Known weaknesses:

1. Cannot resolve three-way ties where A beats B, B beats C, C beats A.
2. A draw between two tied players does nothing to resolve the tie.
3. Returns 0 if any pair of tied players has not played each other.

Total Blacks

Number of games played with the Black pieces. Advantages players who faced harder color assignments.

Extra for Black (BAP System)

Points by result and color: Win as Black = 3, Win as White = 2, Draw as Black = 1, all others = 0.

Number of wins (WIN)

Total number of wins, including full-point byes and forfeit wins — every full-point result counts, whether or not a game was actually played. Contrast Number of games won (WON) below, which counts only wins in games actually played. Rewards aggressive play, similar to Kashdan.

Round Robin Tiebreaks

Sonneborn-Berger (Round Robin)

For each player in the tie: add the final scores of all opponents defeated, plus half the final scores of all opponents drawn. Most common round-robin tiebreak.

Koya (KS)

Sums results against opponents who scored at or above a configurable percentage threshold (default 50%). A popular FIDE tiebreak for round robins.

Team Tiebreaks

These break ties between teams in any event that produces team standings. Game Points and U.S. Amateur apply to both Individual/Team and Fixed-Roster formats. Weighted depends on fixed board order, so it is a Fixed-Roster option only.

Game Points

Total individual board points scored by the team across all rounds. See Game Wins - Fixed Roster Tournaments.

Weighted (Illinois High School Association)

Uses a formula that weights game points scored against opponents by those opponents’ final standings. More complex than straight game points.

U.S. Amateur

For each round, multiplies the opposing team’s final score by the number of points scored against them. Recommended over plain game points because it compensates for lopsided wins against weak teams.

Additional Tiebreaks

SwissSys supports a number of additional tiebreak systems beyond those described above. These are available in the tiebreak selection dialog:

Choosing Tiebreaks

Related Topics

• Game Wins - Fixed Roster Tournaments - Game points tiebreak for team events
• Team Tournaments Overview - Team format scoring overview
• Rules for Pairing - Where to configure tiebreaks