Tournament

A tournament is a competition involving 4 or more teams, or a large number of competitors, all participating in a sport or game. More specifically, the term may be used in either of two overlapping senses:

1. One or more competitions held at a single venue and concentrated into a relatively short time interval.
2. A competition involving a number of matches, each involving a subset of the competitors, with the overall tournament winner determined based on the combined results of these individual matches. These are common in those sports and games where each match must involve a small number of competitors: often precisely two, as in most team sports, racket sports and combat sports, many card games and board games, and many forms of competitive debating. Such tournaments allow large numbers to compete against each other in spite of the restriction on numbers in a single match.

These two senses are distinct. Association football leagues like the Premier League are tournaments in the second sense, but not the first, having matches spread across many states in their past over a period of up to a season. Tournaments “are temporally demarcated events, participation in which confers levels of status and prestige amongst all participating members”.

A tournament-match (or tie or fixture or heat) may involve multiple game-matches (or rubbers or legs) between the competitors. In the later rounds of UEFA Champions League, each fixture is played over two legs. The scores of each leg are added, and the team with the higher aggregate score wins the fixture, with away goals used as a tiebreaker and a penalty shoot-out if away goals cannot determine a winner of the game.

Knockout tournaments

A knockout tournament or elimination tournament is divided into successive rounds; each competitor plays in at least one fixture per round. The top-ranked competitors in each fixture progress to the next round. As rounds progress, the number of competitors and fixtures decreases. The final round, usually known as the final or cup final, consists of just one fixture; the winner of which is the overall champion.

In a single-elimination tournament, only the top-ranked competitors in a fixture progress; in 2-competitor games, only the winner progresses. All other competitors are eliminated. This ensures a winner is decided with the minimum number of fixtures. However, most competitors will be eliminated after relatively few matches; a single bad or unlucky performance can nullify many preceding excellent ones.

A double-elimination tournament may be used in 2-competitor games to allow each competitor a single loss without being eliminated from the tournament. All losers from the main bracket enter a losers’ bracket, the winner of which plays off against the main bracket’s winner.

A triple elimination tournament allows a competitor to lose two games and creates a third bracket or fourth bracket which are usually followed by a playoff.

Some elimination tournaments are in a best-of-n series, requiring a competitor to lose a majority of n games (in a series against the same opponent) before being eliminated (e.g. in a best-of-7 games series, the winner must win 4 games).

Some formats use a repechage, allowing losers to play extra rounds before re-entering the main competition in a later round. The winners of these progress, but are at a disadvantage in later rounds owing to the extra effort expended during the repechage.

A family of tournament systems that grew from a system devised for the Victorian Football League, the historic predecessor to the Australian Football League (AFL), allows the teams with the best record before the playoffs to lose a game without being eliminated, whereas lesser qualifiers are not. Several of the most prominent leagues in Australia use such a system, such as the AFL and the National Rugby League in rugby league. The A-League of association football also used such a system, but then switched to a pure knockout playoff.

An extreme form of the knockout tournament is the stepladder format where the strongest team is assured of a berth at the final round while the next strongest teams are given byes according to their strength/seeds; for example, in a four team tournament, the fourth and third seed figure in the first round, then the winner goes to the semifinals against the second seed, while the survivor faces the first seed at the final.

Group tournaments

A group tournament, league, division or conference involves all competitors playing a number of fixtures (again, a fixture is one name for a tournament-match that determines who, out of two or three or more, will advance; a fixture may consist of one or more game-matches between competitors). Points are awarded for each fixture, with competitors ranked based either on total number of points or average points per fixture. Usually each competitor plays an equal number of fixtures, in which case rankings by total points and by average points are equivalent.

In a round-robin tournament, each competitor plays all the others an equal number of times, once in a single round-robin tournament and twice in a double round-robin tournament. This is often seen as producing the most reliable rankings. However, for large numbers of competitors it may require an unfeasibly large number of rounds.

A Swiss system tournament attempts to determine a winner reliably, based on a smaller number of fixtures. Fixtures are scheduled one round at a time; a competitor will play another who has a similar record in previous rounds of the tournament. This allows the top (and bottom) competitors to be determined with fewer rounds than a round-robin, though the middle rankings are unreliable.

There may be other considerations besides reliability of rankings. In some professional team sports, weaker teams are given an easier slate of fixtures as a form of handicapping. Sometimes schedules are weighted in favour of local derbies or other traditional rivalries.

In 2-competitor games where ties are rare or impossible, competitors are typically ranked by number of wins, with ties counting half; each competitors’ listings are usually ordered Wins–Losses(–Ties). Where ties are more common, this may be 2 points for a win and 1 for a tie, which is mathematically equivalent but avoids having too many half-points in the listings. These are usually ordered Wins–Ties–Losses. If there are more than two competitors per fixture, points may be ordinal (for example, 3 for first, 2 for second, 1 for third).

Multi-stage tournaments

Many tournaments are held in multiple stages, with the top teams in one stage progressing to the next. American professional team sports have a “regular season” (group tournament) acting as qualification for the “post season” or “playoffs” (single-elimination tournament).

A group stage (also known as pool play or the pool stage) is a round-robin stage in a multi-stage tournament. The competitors are divided into multiple groups, which play separate round-robins in parallel. Measured by a points-based ranking system, the top competitors in each group qualify for the next stage. In most editions of the FIFA World Cup finals tournament, the first round has been a group stage with groups of four teams, the top two qualifying for the “knockout stage” played as a single-elimination tournament. This format is common in many international team events, such as World Cups or Olympic tournaments.

Some tournaments have two group stages. As well as a fixed number of qualifiers from each group, some may be determined by comparing between different groups: at the 1986 FIFA World Cup and UEFA Euro 2016, the best four of six third-place sides qualified.

Sometimes, results from an earlier phase are carried over into a later phase. Formerly in the Swiss Football League, teams played a double round-robin, at which point they were split into a top “championship” group and a bottom “relegation” group; each played a separate double round-robin, with results of all 32 matches counting for ranking each group.

A similar system is also used by the Scottish Premiership and its historic predecessor, the Scottish Premier League. After 33 games, when every club has played every other club three times, the division is split into two halves. Clubs play a further 5 matches, against the teams in their half of the division. This can (and often does) result in the team placed 7th having a higher points total than the team placed 6th (because their final 5 games are considerably easier), nevertheless, a team in the bottom half never receives a higher final ranking than a team which qualified for the top half.

Promotion and relegation

Where the number of competitors is larger than a tournament format permits, there may be multiple tournaments held in parallel, with competitors assigned to a particular tournament based on their ranking. Many team sports involve teams in only one major tournament per year. In European sport, including football, this constitutes the sole ranking for the following season; the top teams from each division of the league are promoted to a higher division, while the bottom teams from a higher division are relegated to a lower one.

This promotion and relegation occurs mainly in league tournaments. The hierarchy of divisions may be linear, or tree-like, as with the English football league pyramid.