# Single Knockout Tournament Format

Keywords: Theory, Tournament

Single Knockout Tournament Format, also known as Single Elimination, is a format for pairing players to play games in tournaments.

In the first round, players are paired to play. Those players that lose are eliminated, knocked out of, the tournament. Those players that win, are promoted to the second round. This procedure is repeated till only a single player remains, that player is the tournament winner.

The number of rounds required is the ceiling of the log base 2 of the number of players in the tournament. (Example: 30 players necessitates 5 rounds of play because 2^5 = 32.) As a result, unless the number of players is equal to a power of 2, some players will play one more round than the others. Often the strongest players are not paired in the first round.

According to BGA,

• The probability that the best player wins is surprisingly small.
• There is no satisfactory way to produce an ordering for players other than the overall winner.

Mark Glickman, creator of the Glicko Rating system widely used by chess federations and servers, has a paper entitled: Bayesian Optimal Design of Knockout Tournaments. The paper presents two approaches:

1. maximize the probability that the best player will advance to the next round (goal focused on a single player)
2. maximize the expected log-probability of game outcomes over all possible sets of pairings (goal focused on all players)

Note: that these two approaches may produce conflicting pairings. This is not surprising.

The Cup System offered by OpenGotha is a variation of Single Knockout. Losing players do not stop competing altogether, but are paired down into the so called Loser Bracket. Unlike in the Double Elimination format, they can never return to the Winner Bracket.

Single Knockout Tournament Format last edited by hnishy on September 14, 2022 - 05:23