Knock-out tournaments

A tournament is a competition among teams to a fixed schedule that decides a winner. The choice of type depends on season, time, play fields, equipment, the activity, officials and budget.

Single knock-out: a team losing once is out. Matches = N - 1. Byes = next power of two minus N, given in order: bottom of lower half, top of upper half, top of lower half, bottom of upper half. With odd N the upper half has (N + 1) / 2 teams. Rounds: 5-8 teams 3, 9-16 teams 4, 17-32 teams 5.

Seeding places strong teams apart so they meet late; special seeding sends top teams straight to a later round (subtract them first, then find the byes). Merits: quick and cheap, keen contests. Demerits: a team may go out by chance; winners wait for other matches.

Consolation type I: teams losing their first match play again among themselves. Type II: every loser of the regular round plays again; matches = 2N - 3.

Double elimination: a team must lose twice to go out (2N - 2 or 2N - 1 matches); it finds the true winner. Bagnall-Wild decides the first three places fairly.