Tournament Swiss

Swiss tournament

Introduction

In a Swiss-system tournament, teams are paired round by round according to their accumulated performance. Unlike elimination-based formats, no team is removed from the tournament after a loss. All teams continue playing until the configured number of rounds is completed.

The system uses match points to group teams for the next round:

• Win: 3 points
• Draw: 1 point
• Loss: 0 points

When the number of teams is odd, one team receives a bye for that round. The bye is assigned, when possible, to the lowest-ranked team that has not yet received one, and it is scored as a win for pairing and ranking purposes.

By default, the number of rounds is calculated automatically from the number of teams (using the smallest number of rounds that can cover all participants), but this can be overridden from the tournament options.

Options

The Swiss format includes three configurable options:

1. Number of rounds You can explicitly define the number of rounds to be played. If left empty, the application calculates it automatically based on the number of teams.
2. Tie-break rule When two or more teams end with the same match points, ranking order can be resolved using one of the supported Swiss tie-break systems: Buchholz, Median Buchholz, Sonneborn-Berger, Direct Encounter, or Point Differential.

The available systems are interpreted as follows:

• Buchholz: Sum of the match points achieved by all opponents faced by a team. A higher value indicates a stronger strength of schedule.
• Median Buchholz: Same as Buchholz, but removing the lowest and highest opponent scores when possible. This reduces the impact of extreme results.
• Sonneborn-Berger: Sum of defeated opponents' points, plus half of drawn opponents' points. It rewards wins against high-performing opponents.
• Direct Encounter: Compares only the results among tied teams that faced each other. It prioritizes head-to-head performance inside the tie group.
• Point Differential: Difference between points scored and points conceded across played fights. It rewards teams with stronger overall scoring margins.

Swiss tie-break resolution order

The application does not stop at the selected tie-break rule. It applies a fixed fallback chain until the tie is resolved, and only then falls back to the next scoring criteria.

Principal rule	If still tied...	If tied again...	Then...	Finally...
Buchholz	Median Buchholz	Sonneborn-Berger	Direct Encounter	Point Differential
Median Buchholz	Buchholz	Sonneborn-Berger	Direct Encounter	Point Differential
Sonneborn-Berger	Buchholz	Median Buchholz	Direct Encounter	Point Differential
Direct Encounter	Buchholz	Median Buchholz	Sonneborn-Berger	Point Differential
Point Differential	Buchholz	Median Buchholz	Sonneborn-Berger	Direct Encounter

In other words, the last two tie-break options reuse the remaining Swiss criteria in this order: Buchholz -> Median Buchholz -> Sonneborn-Berger -> the other one of the last two rules.

If a critical position is still tied after applying the full chain, the tie is resolved with an daihyōsen combat.

3. Avoid repeated pairings When enabled (default), the pairing algorithm prevents teams from facing each other more than once whenever possible. If no valid pairing can be produced under that constraint, the system relaxes it to allow round generation.

Match examples

The following examples use teams composed of one competitor each.

Team	Competitor
Team 1	Bernard, Paul
Team 2	Colombo, Sempronio
Team 3	Dupont, Pierre
Team 4	Durand, Jacques
Team 5	Evans, Harry
Team 6	Fabbro, Caio
Team 7	Férnandez, Fulano
Team 8	Lopes Marques, Pedro

Example 1: 3-round Swiss points progression (8 teams)

Swiss points used in this example:

• Win: 3 points
• Draw: 1 point
• Loss: 0 points

Round results:

Round	Group	Pairing	Result	Points granted
1	A	Team 1 vs Team 2	Team 1 wins	Team 1 +3
1	A	Team 3 vs Team 4	Team 4 wins	Team 4 +3
1	A	Team 5 vs Team 6	Team 5 wins	Team 5 +3
1	A	Team 7 vs Team 8	Team 8 wins	Team 8 +3
2	A	Team 4 vs Team 1	Team 4 wins	Team 4 +3
2	A	Team 5 vs Team 8	Draw	Team 5 +1, Team 8 +1
2	B	Team 2 vs Team 3	Team 2 wins	Team 2 +3
2	B	Team 7 vs Team 6	Team 7 wins	Team 7 +3
3	A	Team 4 vs Team 8	Draw	Team 4 +1, Team 8 +1
3	B	Team 5 vs Team 1	Team 5 wins	Team 5 +3
3	B	Team 2 vs Team 7	Team 2 wins	Team 2 +3
3	C	Team 3 vs Team 6	Team 3 wins	Team 3 +3

Final Swiss points after round 3:

Team	Competitor	Swiss points
Team 4	Durand, Jacques	7
Team 5	Evans, Harry	7
Team 2	Colombo, Sempronio	6
Team 8	Lopes Marques, Pedro	5
Team 1	Bernard, Paul	3
Team 3	Dupont, Pierre	3
Team 7	Férnandez, Fulano	3
Team 6	Fabbro, Caio	0

Example 2: 11-team Swiss with byes

This example illustrates how byes are resolved when the tournament has an odd number of teams. In this case, there are 11 single-person teams.

Team	Competitor
Team 1	Bernard, Paul
Team 2	Colombo, Sempronio
Team 3	Dupont, Pierre
Team 4	Durand, Jacques
Team 5	Evans, Harry
Team 6	Fabbro, Caio
Team 7	Férnandez, Fulano
Team 8	Lopes Marques, Pedro
Team 9	Martin, Tizio
Team 10	Navarro, Mengano
Team 11	Ortega, Zutano

In this Swiss tournament setup:

• A bye is assigned each round when the number of teams is odd.
• The system assigns the bye to the lowest-ranked team that has not received a bye yet.
• If all eligible low-ranked teams already received one, the lowest-ranked team receives it again.
• A bye is scored as a win: +3 Swiss points.
• For ranking purposes, the bye is also counted as one won fight and one fight done.

Bye distribution example across three rounds:

Round	Bye team	Reason (as implemented)	Bye score effect
1	Team 11	Lowest-ranked team at round start, no previous bye	+3 points
2	Team 10	Lowest-ranked team in current ordering without previous bye	+3 points
3	Team 9	Lowest-ranked team in current ordering without previous bye	+3 points

A practical consequence is that byes are spread across different teams whenever possible, instead of repeatedly benefiting the same participant.

Complete 3-round flow example (including byes, 11 teams):

Round	Group	Pairing	Result	Points granted
1	A	Team 1 vs Team 2	Team 1 wins	Team 1 +3
1	A	Team 3 vs Team 4	Team 4 wins	Team 4 +3
1	A	Team 5 vs Team 6	Team 5 wins	Team 5 +3
1	A	Team 7 vs Team 8	Team 8 wins	Team 8 +3
1	A	Team 9 vs Team 10	Team 10 wins	Team 10 +3
1	A	Team 11	Bye	Team 11 +3
2	A	Team 11 vs Team 8	Draw	Team 11 +1, Team 8 +1
2	A	Team 5 vs Team 4	Team 4 wins	Team 4 +3
2	A	Team 10	Bye	Team 10 +3
2	B	Team 1 vs Team 2	Team 2 wins	Team 2 +3
2	B	Team 3 vs Team 6	Team 3 wins	Team 3 +3
2	B	Team 7 vs Team 9	Team 7 wins	Team 7 +3
3	A	Team 10 vs Team 4	Draw	Team 10 +1, Team 4 +1
3	A	Team 11 vs Team 8	Team 11 wins	Team 11 +3
3	B	Team 2 vs Team 3	Draw	Team 2 +1, Team 3 +1
3	B	Team 1 vs Team 7	Team 7 wins	Team 7 +3
3	C	Team 5 vs Team 6	Team 5 wins	Team 5 +3
3	C	Team 9	Bye	Team 9 +3

Swiss points after round 3:

Team	Competitor	Swiss points
Team 4	Durand, Jacques	7
Team 10	Navarro, Mengano	7
Team 11	Ortega, Zutano	7
Team 5	Evans, Harry	6
Team 7	Férnandez, Fulano	6
Team 2	Colombo, Sempronio	4
Team 3	Dupont, Pierre	4
Team 8	Lopes Marques, Pedro	4
Team 1	Bernard, Paul	3
Team 9	Martin, Tizio	3
Team 6	Fabbro, Caio	0

This sequence shows how byes are integrated in both pairing and scoring logic while maintaining Swiss progression across rounds.

Example 3: tie-break impact on teams with equal Swiss points

In this scenario, Team 4 and Team 5 are tied with 7 Swiss points. Depending on the selected tie-break system, their final order may change.

Team	Competitor	Swiss points	Buchholz	Median Buchholz	Sonneborn-Berger	Direct Encounter	Point Differential
Team 4	Durand, Jacques	7	11	8	8.5	0	+4
Team 5	Evans, Harry	7	8	7	7.0	0	+6

Resulting order in this example:

• With Buchholz, Median Buchholz, or Sonneborn-Berger: Team 4 ranks above Team 5.
• With Direct Encounter: no change in this case, because there is no decisive head-to-head result.
• With Point Differential: Team 5 ranks above Team 4.

Example 4: different outcomes between Buchholz, Median Buchholz, and Sonneborn-Berger

The following case shows three teams tied on Swiss points, where each tie-break system produces a different order.

Team	Competitor	Swiss points	Buchholz	Median Buchholz	Sonneborn-Berger
Team 1	Bernard, Paul	6	18	11	8.0
Team 2	Colombo, Sempronio	6	17	12	9.5
Team 8	Lopes Marques, Pedro	6	16	10	10.0

Resulting order for this scenario:

• With Buchholz: Team 1, Team 2, Team 8.
• With Median Buchholz: Team 2, Team 1, Team 8.
• With Sonneborn-Berger: Team 8, Team 2, Team 1.

Interpretation:

• Buchholz rewards the strongest overall opponent set.
• Median Buchholz reduces the effect of extreme opponent scores.
• Sonneborn-Berger gives more weight to wins against stronger opponents and can therefore invert the order.

This is why selecting the tie-break rule should be considered part of the tournament definition and communicated to participants before the first round starts.