Reference

Tournament formats and what each one costs

Every format is a trade between match count, fairness, schedulability and how far someone travels to play one game. Here is the arithmetic behind each trade.

A format is not a matter of taste. It is a set of numbers you commit to before you book the venue, and those numbers determine how many matches you must run, how long the day is, how much one bad game costs a good competitor, and whether you can promise anyone that the final starts at seven.

Four things are always in tension:

  • Match count — venue hours, station-hours, staff, and the cost of everything.
  • Fairness — how likely the strongest entrant is to actually win, and how much a single bad result costs.
  • Schedulability — whether you can publish a timetable in advance and hold to it.
  • Entrant experience — how many matches someone gets for the cost of getting there.

No format wins all four. The bracket calculator will run these numbers for any field size.

Single elimination

Lose once, go home.

Matches: N − 1. Always, for any field size and any bracket shape. Every match eliminates exactly one entrant, and to crown a champion you must eliminate N − 1 of them. No arrangement of a single-elimination bracket changes this.

Rounds: ceil(log2 N). Byes: (next power of two) − N.

A bracket must be a power of two to work, so a 12-entrant field runs in a 16-slot bracket with 4 byes. A bye is a free win, so it must go to a top seed. Award byes at random and you have added a lottery to the part of your event that is supposed to be the fairest.

The strengths are real: cheapest per entrant, shortest, easiest to explain, and continuous jeopardy — which is why almost every televised playoff in any sport ends this way.

The weaknesses are equally real. Half the field plays exactly one match. If those people flew in, that is a poor product. Variance is at maximum: a single bad map, a technical failure or an unlucky draw removes the strongest entrant with no recourse. Seeding matters more here than anywhere else, because seeding is the only tool you have for controlling when the top entrants meet.

Double elimination

Lose twice, go home.

Matches: 2N − 2, or 2N − 1 if the grand final is reset. Same counting argument, run on losses: the event ends when everyone except the champion has two losses. That is 2(N − 1) losses, and each match produces exactly one. If the lower-bracket side wins the grand final and a reset is played, one extra loss is required, so one extra match.

Rounds: ceil(log2 N) in the upper bracket, 2·ceil(log2 N) − 2 in the lower, plus the grand final. An entrant knocked out of the first upper-bracket round who runs the lower bracket to the end plays 2·ceil(log2 N) matches — eight, in a sixteen-entrant field, against the four a clean upper-bracket run requires.

That asymmetry is the format's central problem and its central honesty. The upper-bracket finalist has earned an advantage; the question is what form it takes. Give them nothing and their run bought a rest and little else. Require the lower-bracket side to win two series — the bracket reset — and the advantage is meaningful, but you can no longer tell the venue or the audience when the event finishes. Both choices are defensible. There is no third option that is fair and schedulable simultaneously.

Round robin

Everyone plays everyone.

Matches: N(N − 1)/2. Rounds: N − 1 if N is even, N if N is odd — with an odd field, someone sits out each round.

This is the fairest structure available and it is quadratic, which is why you almost never see it above six entrants. Sixteen is 120 matches and 15 rounds: a season, not a weekend. Four is 6 matches, and that scale is why round robin survives as a group format and as a league structure over months.

Schedulability is excellent — every round is exactly floor(N/2) matches — and the broadcast weakness is specific: dead rubbers. Once qualification is mathematically settled, the remaining matches have nothing at stake, and in a four-team group the final round frequently contains one. Add tiebreaks (head-to-head, then round difference, then a playoff) and you also get standings that need a paragraph to explain on air.

Swiss

Pair entrants against others on the same record; nobody is eliminated until the rounds run out.

Matches: R × floor(N/2) for R rounds. Everyone plays every round. With an odd field, one entrant receives a bye each round.

The system comes from chess, where it dates to the late nineteenth century, and it answers a specific question: how do you rank a large field without playing a round robin? After round one you have winners and losers; pair like with like, and after R rounds the records separate the field surprisingly well. You need at least ceil(log2 N) rounds for a single undefeated entrant to be possible — the same figure as single elimination, for the same reason.

The costs: more matches than a bracket (a 64-entrant field is 63 matches single-elimination but 192 across six Swiss rounds), pairings cannot be published in advance because they depend on the previous round, and there is no bracket to show an audience. The story lives in a table, which broadcast handles badly.

The benefits are why large open events use it anyway. Everyone plays every round, so nobody travels to play once; the hall is never idle; the matches per round are fixed regardless of whether N is a convenient shape; and one bad game does not eliminate you.

GSL groups

A four-entrant double-elimination group. Two opening matches; the winners meet and that winner advances; the losers meet and that loser is out; the remaining two play a decider for the second slot.

Five matches per group. Two advance. Each entrant plays two or three.

The format is named for the Global StarCraft II League, which popularised it, and it has two properties that beat a four-team round robin for broadcast:

  • No dead rubbers. Every match after the openers either eliminates or qualifies somebody. A four-entrant round robin costs one more match, six, and routinely produces a meaningless one.
  • No tiebreak ambiguity. The bracket resolves the order itself. Nobody has to explain a three-way tie at the end of the night.

The cost is that seeding within the group matters a great deal — the opening pairings decide who has to beat whom — and that an entrant can be eliminated having played only two matches.

The numbers side by side

Sixteen entrants, in each structure:

Format Matches Rounds Matches per entrant
Single elimination 15 4 1–4
Single elimination + third-place match 16 4 1–4
Double elimination 30 (31 with a reset) 4 upper + 6 lower + final 2–8
Four GSL groups, then a top-8 bracket 27 3 + 3 2–6
Swiss, 4 rounds 32 4 4
Round robin 120 15 15

The hybrid line is the one to notice. Groups feeding a bracket costs slightly less than double elimination, guarantees everyone at least two matches, and produces a clean single-elimination playoff for the stage. That is why nearly every real event of any size is a hybrid rather than a pure format — and why circuit stops, which had to seat a large open field and still finish with a watchable final, converged on it.

The axis that is not the format

One thing the table hides: a "match" above is one series, and whether that series is a single game or a best-of-three changes the outcome distribution far more than the bracket does.

A single game between two closely matched entrants is close to a coin flip. A best-of-three is meaningfully more likely to be won by the stronger side; a best-of-five more so again. If your event feels too random, extending the series length in the late rounds is usually a cheaper fix than switching to double elimination — it adds games, not rounds, and rounds are what eat your schedule.