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Draws, byes and the maths of a Saturday

How to seed a tournament bracket

Why brackets come in powers of two, where the byes go and why, the three ways to seed a draw, and an honest estimate of how long your format will take before somebody has to leave for dinner.

Why brackets are powers of two

A single-elimination bracket halves the field every round: sixteen become eight, eight become four, four become two, two become one. That only works cleanly if you start at a number you can keep halving — 2, 4, 8, 16, 32, 64. Anything else leaves a player standing around with nobody to play.

So the bracket doesn't shrink to fit your ten entrants; it grows to sixteen and leaves six slots empty. Those empty slots are the byes.

The number of rounds is just how many times you halve: a bracket of 8 is three rounds, 16 is four, 32 is five, 64 is six. That's worth knowing early, because rounds — not games — are what set the minimum length of your day.

How byes work

A bye is a free pass through round one. It isn't a game, it isn't a walkover, and it doesn't get recorded as a win against anybody. The player simply appears in round two.

The arithmetic is short:

Two things matter about where they land. First, byes go to the top seeds: seed 1 gets the first bye, seed 2 the second, and so on. That's not favouritism for its own sake — it's the point of seeding. A ranked draw is a promise that the best players don't knock each other out early, and a bye is the strongest version of that promise. Second, byes must be spread across the draw, never stacked in one half, or one side of the bracket walks to the semi-final while the other fights through a full round.

If you're running a random draw instead of a ranked one, hand the byes out at random too — and say so out loud before you draw, because otherwise the person who drew one gets accused of arranging it.

Standard seed pairing

Once you've got seeds, the pairing isn't a matter of taste. The rule is that every first-round pair adds up to bracket size + 1, and the halves are arranged so 1 and 2 can only meet in the final, 1 and 4 only in the semi, and so on. For a bracket of 16, top to bottom:

1 v 16   8 v 9   5 v 12   4 v 13
3 v 14   6 v 11   7 v 10   2 v 15

Every pair sums to 17. For a bracket of 8 it's 1v8, 4v5, 3v6, 2v7 — each summing to 9. For a bracket of 4, 1v4 and 2v3. With twelve entrants in a sixteen bracket, seeds 13 to 16 don't exist, so seeds 1 to 4 have no round-one opponent: that's your four byes, already correctly spread.

Three ways to seed

Random draw

Everyone goes in a hat. Fastest, needs no rankings, and nobody can complain about the committee, because there wasn't one. The cost is that the two best players might meet in round one and the final might be a mismatch. For an office ping-pong ladder or a backyard comp among friends, that cost is usually worth paying — random is socially cheap, and the story of the round-one blockbuster is half the fun.

Ranked seeding

Order the field best to worst and use the pairing above. Use it when you have something real to rank on: last term's ladder, a club rating, head-to-head history. Ranked draws protect the final and reward form. They also mean the bottom seed opens against the champion, which is either a great yarn or a miserable four minutes depending on the person.

No rankings? Two honest shortcuts. Ask everyone to self-rate out of five and sort on that — people are surprisingly accurate about their own ability when nothing's at stake. Or seed only the top few you're confident about, put those at the far corners of the draw, and randomise the rest.

Snake (serpentine) seeding

This one's for pools, not brackets. To split sixteen players into four even pools, deal seeds down and back like a snake draft:

Pool A   1   8   9   16
Pool B   2   7   10   15
Pool C   3   6   11   14
Pool D   4   5   12   13

Every pool adds up to 34, which is the point: no pool of death, no pool of doom. The same snake is how you split a field into balanced teams.

One more seeding convention worth borrowing: separate the obvious pairs. Housemates, doubles partners, the two people from the same team — put them in opposite halves so they meet late or not at all. It costs nothing and it kills the "why do I have to play my own brother first up" complaint before it starts.

Which format for your group

The format decides two things: how many games get played, and how many people go home after twenty minutes. Pick with both in mind.

How many games, and how long

Single elimination is always entrants − 1 games, because every game eliminates exactly one player and you need to eliminate all but one. Round robin is n × (n−1) ÷ 2. Double elimination is about 2n − 2, plus one more if you play a reset final when the winners'-bracket leader loses once.

EntrantsBracketByesRoundsSingle elimDouble elimRound robin
4402366
58334810
682351015
880371428
10166491845
121644112266
1616041530120
2432852346276
3232053162496

Now the wall clock. Take your realistic game length including changeover — for office ping pong, best of three to 11 is about ten minutes by the time people stop chatting; a FIFA match is fifteen; backyard cricket, however long it takes to find the ball.

And the reason round robin quietly eats weekends: twelve entrants is 66 games. On one table at ten minutes each, that's eleven hours. Pools of four plus a knockout gets you a comparable result in an afternoon.

Don't draw it by hand. The bracket maker takes 2 to 64 names, pads to the right power of two, spreads the byes properly, and gives you one link the whole group can watch fill in. Run one free, no signup.

Six things that go wrong

FAQ

Why do brackets have to be a power of two?

Because single elimination halves the field each round. Only 2, 4, 8, 16, 32 and 64 can be halved all the way down to one winner. Any other entrant count gets padded up to the next power of two, and the empty slots become byes.

How do byes work in a tournament bracket?

A bye is a free pass into round two, given to a player when the bracket has more slots than entrants. The number of byes is bracket size minus entrants — ten players in a bracket of sixteen means six byes. A bye isn't a win and isn't a walkover; the player simply starts in round two.

Who should get the byes?

In a seeded draw, the top seeds: seed 1 gets the first bye, seed 2 the second, and so on. That's the whole purpose of seeding — keeping the strongest entrants apart until late. In a random draw, allocate them randomly and say so before you draw. Either way, spread them across the bracket rather than stacking them in one half.

How many games are in a single elimination tournament?

Entrants minus one, always. Every game eliminates exactly one player, and you need to eliminate everyone but the winner. Twelve players is eleven games regardless of how many byes there are.

Single or double elimination?

Single if time is short or the field is big — it's the only format that reliably fits a lunch hour. Double if the result matters and you have eight to sixteen entrants, since it takes roughly twice as many games but stops one bad start ending someone's day.

How long will a tournament actually take?

Multiply games by your realistic game length including changeover. On one table, twelve players in single elimination at ten minutes a game is about two hours. With extra tables you can only parallelise within a round, so the absolute floor is rounds times game length — four rounds at ten minutes is forty minutes, no matter how many tables you have.

Then build it

All of the above works just as well on butcher's paper, and there's no shame in that. If you'd rather the maths handled itself, the tournament bracket maker takes your list of names, pads to the right bracket size, spreads the byes using the pairing above, and lets you choose a random draw or your typed order as the seeding. You tap winners as games finish and everyone else watches the same link update. Free, no signup, no accounts to chase.