How to Place Seeds and Byes in a Tournament Bracket: Calculating the Number of Matches and Rounds, and Making the Bracket
With exactly 8 or 16 entrants a tournament bracket is easy, but with awkward numbers like 6, 10 or 12 it is hard to know where the byes should go. This article covers how to calculate the number of matches and rounds in a knockout tournament, the bracket size and number of byes, seed positions that keep the strongest players apart until late, and when to add a third-place match or use a round robin instead.
A knockout tournament has “entrants − 1” matches
In a single-elimination tournament, exactly one player loses and drops out in every match. Everyone except the winner loses exactly once, so the number of matches is the number of entrants − 1. Byes don’t change this. A third-place match adds one more.
| Entrants | Bracket size | Byes | Rounds | Matches | Matches with a third-place match |
|---|---|---|---|---|---|
| 5 | 8 | 3 | 3 (including the final) | 4 | 5 |
| 6 | 8 | 2 | 3 | 5 | 6 |
| 8 | 8 | 0 | 3 | 7 | 8 |
| 10 | 16 | 6 | 4 | 9 | 10 |
| 12 | 16 | 4 | 4 | 11 | 12 |
| 16 | 16 | 0 | 4 | 15 | 16 |
| 20 | 32 | 12 | 5 | 19 | 20 |
| 24 | 32 | 8 | 5 | 23 | 24 |
The bracket size is the smallest power of 2 (2, 4, 8, 16, 32, 64…) that is at least the number of entrants. The shortfall is filled with byes, and players who get a bye skip the first round and start in the second. The number of rounds is the power of 2 that gives the bracket size: an 8-slot bracket has 3 rounds, 16 slots have 4 and 32 slots have 5, the last being the final.
Place seeds so that 1 and 2 can’t meet before the final
Seeding places players with the best previous results or the highest ability so that the strongest don’t knock each other out in the early rounds. In the standard layout, seed 1 goes at the top and seed 2 at the bottom, so that 1 and 2 can’t meet before the final, seeds 1–4 can’t meet before the semi-finals, and seeds 1–8 can’t meet before the quarter-finals. For 8- and 16-slot brackets, the seed numbers from top to bottom are as follows.
| Bracket | Seed numbers from top to bottom | First-round matches |
|---|---|---|
| 8 slots | 1, 8, 4, 5, 2, 7, 3, 6 | 1−8, 4−5, 2−7, 3−6 |
| 16 slots | 1, 16, 8, 9, 4, 13, 5, 12, 2, 15, 7, 10, 3, 14, 6, 11 | 1−16, 8−9, 4−13, 5−12, 2−15, 7−10, 3−14, 6−11 |
The key point is that in every first-round match, the two seed numbers add up to “bracket size + 1” (9 for 8 slots, 17 for 16 slots). High seeds meet low seeds, so if the favourites keep winning, the semi-finals are 1−4 and 2−3 and the final is 1−2. You can build this order by repeatedly splitting the bracket in half and pairing numbers as “1 and (size + 1 − 1)”, “2 and (size + 1 − 2)” and so on.
Give byes to the top seeds first
When there are fewer entrants than slots, the empty slots become byes. The byes go in the positions of the seed numbers in the table above that are larger than the number of entrants. In other words, the first-round opponents of the top seeds become empty slots, and byes are given from seed 1 downwards.
| Entrants | 8-slot order from top to bottom (— is a bye) | Who gets a bye |
|---|---|---|
| 5 | 1, —, 4, 5, 2, —, 3, — | Seeds 1, 2 and 3 |
| 6 | 1, —, 4, 5, 2, —, 3, 6 | Seeds 1 and 2 |
| 7 | 1, —, 4, 5, 2, 7, 3, 6 | Seed 1 |
- The byes are spread evenly between the top and bottom halves, so neither half ends up with more matches
- With 12 entrants (16 slots) there are 4 byes, and seeds 1 to 4 start in the second round
- With 10 entrants (16 slots) there are 6 byes, and only 4 first-round matches with 8 players are played
- If there seem to be too many byes, consider bringing the field closer to the bracket size (adding a repechage or a qualifying group stage)
If you don’t want players from the same team or school to meet in the early rounds, reorder the name list so that they end up in different halves. Since seed positions follow the order of the names, simply reordering them rebuilds the bracket.
Knockout or round robin?
A knockout has few matches and finds a winner quickly, but since one loss means you’re out, someone who travelled a long way may go home after a single match. A round robin gives everyone the same number of matches, but the number of matches grows with the square of the number of players. For 8 players they compare as follows.
| Knockout | Round robin | Group stage + knockout | |
|---|---|---|---|
| Matches for 8 players | 7 (8 with a third-place match) | 28 | 12 round-robin matches in 2 groups of 4 + 3 or 4 matches in a 4-player knockout for the top 2 of each group |
| Minimum matches per player | 1 | 7 | 3 |
| Rankings | Winner, runner-up, semi-finalists… | Everyone gets a ranking | Group positions and final placings |
| Best for | Competitions with limited time or many entrants | Practice sessions, small groups, or when everyone needs a ranking | Events that want both socialising and serious competition |
See how to work out round-robin matches and order for round-robin match counts and order, and how to rank a league for ranking in a group stage. If you just need to narrow a group down to one person, the rock-paper-scissors probability article shows how a knockout format also cuts down the number of rock-paper-scissors rounds.
Making a tournament bracket with the match schedule maker
- 1
Choose “Tournament bracket” and enter names from strongest to weakest
Names become seed 1, 2 and so on from the top of the list. It handles 2 to 128 entrants.
- 2
Decide how many seeds to fix and whether to draw the rest
The screen shows the bracket size and number of byes for your number of entrants. If you use a draw, “Reshuffle pairings” redraws it.
- 3
Decide whether to hold a third-place match
Turn it on and a match between the losing semi-finalists is added before the final, with match numbers in that order.
- 4
Tap the winner’s name to move them on
The winner’s line extends in colour, and the champion is shown at the end. Printing gives you a numbered match list and the bracket together.
If you decide the order by drawing lots before the first round, you can also use how to make an amidakuji (ghost leg) to assign numbers and list the names in that order.
FAQ
- How do I calculate the number of matches in a tournament?
- It is the number of entrants − 1. Each match eliminates one player, and everyone except the winner loses exactly once. 10 entrants means 9 matches, or 10 with a third-place match.
- With 6 entrants, where do the byes go?
- 6 entrants use an 8-slot bracket, which leaves 2 byes. In the standard layout, the first-round opponents of seeds 1 and 2 are the empty slots, so those two start in the second round. The first round has 2 matches: 4−5 and 3−6.
- How do I work out how many rounds a tournament has?
- It depends on which power of 2 the bracket size is, the bracket size being the smallest power of 2 that is at least the number of entrants. An 8-slot bracket has 3 rounds, 16 slots have 4 and 32 slots have 5, the last being the final. 12 or 10 entrants use 16 slots, so 4 rounds.
- Where should seeds be placed?
- The standard is seed 1 at the top and seed 2 at the bottom, so that 1 and 2 can’t meet before the final and seeds 1–4 can’t meet before the semi-finals. For 8 slots, the order from the top is 1, 8, 4, 5, 2, 7, 3, 6.
- When is the third-place match played?
- It is played between the two losing semi-finalists, usually before the final. Some competitions don’t decide a single third place and instead award third to both losing semi-finalists.
Tools in this article
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