Building a tournament schedule starts with two questions: how many rounds does each division need, and how many first-round byes are there. Both come straight out of the entry count, and both are one formula — which matters when you are re-doing the brackets at seven in the morning because six people registered at the door.
Twelve entrants need 4 rounds. The bracket is 16 slots, so 4 competitors get a first-round bye, and 11 matches get fought.
The example
Three divisions from the same event, each sized straight from its entry list.
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | Division | Entrants | Rounds | Bracket size | Byes | Matches |
| 2 | Youth 8-10 | 12 | 4 | 16 | 4 | 11 |
| 3 | Teen sparring | 19 | 5 | 32 | 13 | 18 |
| 4 | Adult forms | 24 | 5 | 32 | 8 | 23 |
The formula
Four short columns, each depending on the one before it:
How it works
The logic behind each column:
LOG(B2,2)asks how many times you can halve the field before one competitor is left. Twelve entrants gives 3.58, so the field cannot be resolved in three rounds.ROUNDUP(...,0)takes that to 4. Rounds are whole things; there is no partial round in single elimination.POWER(2,C2)is the bracket size — the next power of two at or above the entry count. Sixteen slots for twelve people.D2-B2is the byes, the empty slots, andB2-1is the match count: every match eliminates exactly one competitor, and all but the winner get eliminated.
Multiply matches by average match length plus changeover to get mat time. That is the number that tells you whether the event finishes at four o'clock or at seven.
Try it: interactive demo
Enter the number of entrants in a division.
Variations
Double elimination match count
A double-elimination bracket runs roughly twice the matches, less one: everyone but the winner has to lose twice.
Mat time for the division
Matches times match length plus changeover. Round up to the nearest quarter hour so the schedule has somewhere to absorb the overruns.
Pitfalls & errors
On an exact power of two, floating-point can push LOG(32,2) to 5.0000000000000009, and ROUNDUP turns that into 6 — a phantom extra round. Guard it with =ROUNDUP(LOG(B2,2)-0.0000001,0) if your divisions ever land exactly on 8, 16, 32 or 64.
A division with 1 entrant breaks the log: LOG(1,2) is 0 rounds, which is correct but usually means the division should be merged rather than run. Flag anything under 3 entrants before the brackets print.
Byes should go to the top seeds, not to whoever is listed first. The formula tells you how many byes exist; the seeding decides who gets them, and that decision belongs to a person.
Practice workbook
Frequently asked questions
Why is the match count always entrants minus one?
Do byes change the number of matches?
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