The formula
league = n × (n − 1) ÷ 2 · knockout = n − 1 · rounds of fixtures = n − 1 if n is even
Where it comes from
In a league every pair meets once, and the possible pairs are the combinations of two from n. In a knockout the count is simpler still: every match eliminates exactly one entrant, and everyone but the champion has to be eliminated, so n − 1 matches are played whatever happens.
How to work it out by hand
- For a league, multiply the teams by one fewer and divide by two
- Double it if they play home and away
- For a knockout, subtract one from the number of teams
- The rounds are the base-two logarithm, rounded up
What is worth knowing
With an odd number of teams every round of league fixtures leaves one sitting out, so it takes as many rounds as there are teams rather than one fewer. In a knockout, if the number of entrants is not a power of two some get byes in the first round and go straight through. The difference in scale between formats is striking: twenty teams is 380 league matches and only 19 in a knockout.