Tables and tournaments

A tournament table is a square table that records the outcomes of matches between $n$ players or teams, where each player plays every other player exactly once. The table helps analyze results, such as total wins, losses, and possible scores.

Important properties

• The table is usually square, with the same number of rows and columns as players.

• The diagonal (where a player would play themselves) is often left blank or marked specially.

• Each off-diagonal entry shows the result of a match between two different players.

• The sum of wins for all players equals the total number of matches.

• In a round-robin tournament with $n$ players, there are $\frac{n(n-1)}{2}$ matches.