Single elimination math
For any single elimination bracket with N teams:
- Total matches = N - 1. Every team except the champion loses exactly once, so there are N - 1 losses, so N - 1 matches.
- Total rounds = ceil(log2(N)). Each round halves the field; you need enough rounds to halve N down to 1.
- Byes needed = next_power_of_2(N) - N. A 10-team bracket needs 6 byes to fill a 16-slot bracket. Byes are assigned to the highest seeds first.
The "top seeds get the byes" rule is the universal convention used by the NCAA (March Madness regional brackets), the ATP (tennis Grand Slam main draws), the WBSC (international baseball), and most international youth tournament federations. The opposite convention - giving byes to the worst seeds - exists nowhere in modern competitive play.
Double elimination math
For any double elimination bracket with N teams:
- Total matches without reset = 2(N - 1). Every team except the champion has to lose twice, so 2(N - 1) losses, plus the winners bracket champion finishes the Grand Final in one match - this nets out to 2(N - 1) matches if the winners champion wins the first Grand Final game.
- Total matches with reset = 2(N - 1) + 1. If the losers bracket champion wins Game 1 of the Grand Final, both teams now have one loss each. A Game 2 (the reset) is played. This is the standard bracket-reset rule used in EVO fighting game tournaments, most esports majors, and the Little League World Series.
- Guaranteed games per team = 2. Every team plays at least one winners bracket match plus at least one losers bracket match before being eliminated.
Round-robin math
For any round-robin tournament with N teams:
- Total matches = N(N - 1) / 2. Every pair of teams meets once; the number of pairs is the binomial coefficient C(N, 2). A 6-team round robin has 15 matches. An 8-team round robin has 28 matches.
- Total rounds (even N) = N - 1. The standard circle method produces a schedule where every team plays every round.
- Total rounds (odd N) = N. One team sits out per round.
- Standings tiebreak defaults to total points; we surface head-to-head, goal difference, and total goals scored as common tiebreak hierarchies (used by the Premier League, FIFA group stages, and most domestic leagues).
Our round-robin scheduler implements the circle method, which is the rotation algorithm used by chess tournament software for decades and matches the schedule used by the FIFA World Cup group stage. The circle method produces balanced schedules without back-to-back games for any one team where possible.
Swiss math
For any Swiss tournament with N players:
- Number of rounds = ceil(log2(N)). The same formula as single-elimination rounds. After ceil(log2(N)) rounds, there is statistically only one undefeated player. Typical formats: 8 players need 3 rounds, 16 players need 4 rounds, 32 players need 5 rounds, 64 players need 6 rounds. Chess clubs and CCG/LCG tournaments often play more rounds than the minimum to spread out the standings (a 16-player chess Swiss commonly runs 5 rounds, not 4).
- Pairing rule: pair players with the same win record. If groups are odd-sized, float one player up or down. No two players who have already played meet again.
- Bye assignment when N is odd: the lowest-scoring player who has not yet received a bye gets the bye (worth 1 point) for that round.
Our Swiss implementation pairs by record and avoids rematches but does not implement the full FIDE Swiss system specified in FIDE Handbook C.04 (Dutch System) or C.04.4 (Burstein System). It does not track or balance the colour assignment that matters in rated chess, and it does not implement accelerated pairings for the first two rounds. For a serious FIDE-rated chess event use a FIDE-compliant pairing engine. For everything else - casual chess, MTG and Pokemon TCG locals, esports community tournaments - simplified Swiss is fine.
Tiebreak references: chess Swiss commonly uses Buchholz (sum of opponents' final scores), Sonneborn-Berger (sum of beaten opponents' scores plus half of drawn opponents'), Direct Encounter (head-to-head among tied players), and the number of wins. See FIDE Handbook section C.02.13 Tie-break Regulations for the formal definitions.
Seeding conventions
The standard single-elimination bracket places seeds in the order 1, 8, 4, 5, 3, 6, 2, 7 for an 8-team bracket. The general rule: the top seed plays the lowest-ranked team in round 1, and the bracket is arranged so the top seeds meet only at the latest possible round.
For 16-team brackets the order extends to 1, 16, 8, 9, 5, 12, 4, 13, 6, 11, 3, 14, 7, 10, 2, 15. This is the layout used by the NCAA for each regional bracket, by the ATP for Grand Slam main draws, and by FIFA for the Round of 16 knockout stage.
For non-power-of-2 counts the byes go to the top seeds first. In a 12-team bracket with the top 4 seeded teams getting byes (the College Football Playoff format from the 2024 season onwards), Round 1 is Seeds 5 to 12 playing Seeds 12, 11, 10, 9 respectively; Round 2 (the quarterfinals) brings in the top 4 seeded teams against the Round 1 winners.
Sources
The math and conventions used on this site are grounded in:
- FIDE Handbook, section C.04 Swiss Systems and section C.02.13 Tie-break Regulations - the source of record for chess Swiss pairing and tiebreak rules. handbook.fide.com
- NCAA Men's Basketball Bracket Principles - publicly described by the Selection Committee each year. The S-curve seeding methodology and the geographic/conference protections that influence bracket placement.
- FIFA Tournament Regulations - World Cup group stage and knockout stage structure (32 teams 2022, 48 teams from 2026).
- UEFA Champions League Regulations - the 2024-25 single-table league phase replacing the old group stage, and the post-league knockout playoff and Round of 16 to Final structure.
- NFL Tournament Rules - the current 14-team playoff format with the No. 1 seed in each conference receiving a first-round bye.
- NHL Stanley Cup Playoff Format - 16-team conference-based bracket with the top 3 in each division plus 2 wild cards per conference.
- College Football Playoff Format - the 12-team bracket adopted starting with the 2024 season.
What we do not implement
- Full FIDE Swiss with colour balance, accelerated pairings, and float rules.
- Losers bracket rendering for double elimination (the math is correct; the visual rendering is on the build list).
- Live multi-device editing (the shareable URL is a snapshot).
- Sport-specific overtime rules (we record final scores only; how you reached the final score is up to your sport).
- Re-seeding between rounds (the bracket is locked at the start; this is the standard NCAA approach, not the NBA approach where the highest remaining seed always plays the lowest remaining seed each round).
Update cadence
This site is updated when:
- The math or seeding logic of a tournament we cover changes (e.g. the CFP expanding to 12 teams in 2024, the UEFA Champions League switching to league-phase format in 2024-25).
- A bug in the bracket math, seeding output, or shareable-URL encoding is reported and fixed.
- A new format or N-team page is added.
We do not refresh the date stamp without a real change.
Updated 11 May 2026.