Clever counting » Competitions

Full competition and a half competition

In a full competition every team plays each other twice. Also known as a double all-play-all tournament or a double round-robin tournament.
In a half-competition every team plays each other once. Also known as a all-play-all tournament or a round-robin tournament.

How do you calculate the number of matches?
Take n for the number of teams.
Full competition = n × (n – 1)
Half-competition = n × (n – 1) : 2

Knockout system

Also known as a single-elimination tournament or a sudden death tournament.
In a knockout system every participant is paired up with another participant.
The winner goes to the next round and for the loser, the tournament is over.

How do you calculate the number of matches?
The number of participants is always a power of 2. Using n for the number of participants and m for the number of matches, the formula will be m = n – 1.

Examples
16 participants: 8 + 4 + 2 + 1 = 15
32 participants: 16 + 8 + 4 + 2 + 1 = 31

When there is also a consolation game/third place playoff you have the same number of matches as you have participants.