Tournament Of Elements

A tournament is a competition involving at least three competitors, all participating in a sport or game. More specifically, the term may be used in either of two overlapping senses:
# One or more competitions held at a single venue and concentrated into a relatively short time interval.
# 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. All golf tournaments meet the first definition, but while match play tournaments meet the second, stroke play tournaments do not, since there are no distinct matches within the tournament. In contrast, association football leagues like the Premier League are tournaments in the second sense, but not the first, having matches spread across many venues over a period of up to a season. Many tournaments meet both definitions; for example, the Wimbledon tennis championship. 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 one or more game-matches (or ''rubbers'' or ''legs'') and if necessary one or more tiebreak-matches between the competitors. For example, in the Davis Cup tennis tournament, a tie between two nations involves five rubbers between the nations' players. The team that wins the most rubbers wins the tie. 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 extra time, and if necessary, a penalty shoot-out used if the scores are level after both matches conclude. In this case, the first tiebreak-match is extra time (modified game-match with reduced duration) and the second tiebreak-match is a penalty shoot-out.

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. It is commonly used in curling tournaments.

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. Rowing regattas often have repechage rounds for the "fastest loser" from the heats. 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), allow 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 through its 2011–12 season, but now uses a pure knockout playoff. Similar systems are used in cricket's Indian Premier League and most curling tournaments, and were also used by the Super League of European rugby league before being scrapped after the 2014 season.

In athletics meetings, fastest losers may progress in a running event held over several rounds; e.g. the qualifiers for a later round might be the first 4 from each of 6 heats, plus the 8 fastest losers from among the remaining runners.

An extreme form of the knockout tournament is the stepladder format where the strongest team (or individual, depending on the sport) 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. Four American sports organizations either currently use this format, or have in the past:
* Since the mid-1960s, most ten-pin bowling events use a stepladder final, usually involving five bowlers.
* Two U.S. college conferences operate a tournament format in basketball that combines two stepladder tournaments into one—that is, both halves of the bracket are organized as stepladder tournaments. When eight teams are involved in the tournament, the bottom four teams play in the first round; the survivors will face the #3 and #4 seeds, and the winners of those matches take on the top two seeds in the semifinals. This format was used by the West Coast Conference (WCC) for its men's and women's tournaments from 2003 through 2013, and has been used by the Ohio Valley Conference (OVC) for men since 2011 and women from 2011 through 2014. From 2019 forward, the WCC tournaments will return to the aforementioned format, but add an extra round so that all 10 current conference members will participate (the OVC tournament does not involve all of the league's members, currently 12).
* In the Philippines, the UAAP Basketball Championship and the NCAA Basketball Championship both use the stepladder format if a team wins all elimination round (group stage) games. This format has been adopted to other sports in both leagues, and to other leagues. If no team wins all elimination round games, the playoffs remain in the usual two-round playoff format.
* The now-defunct Women's Professional Soccer used this format in all of its three seasons of existence. For an example of its playoff system, see 2009 Women's Professional Soccer Playoffs.

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. The English County Championship in cricket did not require an equal number of matches prior to 1963.

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. Unlike regular Groups format, fixtures are scheduled one round at a time and depending on the results of the previous one; 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.

For clarification, this means in hypothesis UEFA adopts a Swiss System for UEFA Champions League, the second matchday in the first stage (today's Groups Stage) would depend on the results of the first matchday of the same stage, the third matchday would depend on the results of both the first and the second matchday, and so on, in contrast to the predetermination of all Groups Stage fixtures upon the initial draw.

Another tournament system that attempts to reduce the number of fixtures per competitor is the Pot System. Under that system, competitors are divided to different "pots" based on predetermined ranking and are drawn to play one rival from each pot, including their own pot. For example, in a 36-team World Cup, teams would be divided into 3 pots, with each team playing 3 matches - one against a Pot A team, one against Pot B team, and one against a team from Pot C. All teams are then placed in one general standing the defines qualification to the following stage.

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. For example, NFL teams play two games against each of the other three teams in their division, one game against six of the other twelve teams in their conference, and one game against five of the sixteen teams in the other conference.

American sports are also unusual in providing fixtures between competitors who are, for ranking purposes, in different groups. Another, systematic, example of this was the 2006 Women's Rugby World Cup: each of the teams in Group A played each of the teams in Group B, with the groups ranked separately based on the results. (Groups C and D intertwined similarly.) An elaboration of this system is the Mitchell movement in duplicate bridge, discussed below, where north–south pairs play east–west pairs.

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, or 3 points for a win and 1 for a tie, which de-emphasizes ties in favor of playing to a decisive result. 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).

General requirements for tournaments

The primary objective of a tournament is to determine the winner of a competition. Ideally, the tournament should be designed in such a way that all participants have an equal chance to compete and progress, regardless of factors like seeding or scheduling. The influence of luck or chance on the results should be minimised. The tournament should also be an exciting and engaging event for participants and spectators. Hence the following requirements for an ideal tournament:

* The tournament should determine the actually best competitor as the competition winner with the greatest possible probability. The final rankings should also reflect the true strength of the competitors as accurately as possible. (For example, the round-robin tournament is significantly better than the single-elimination tournament in these respects).

* The tournament should ensure the decisive importance of each match for the final ranking. Meaningless matches for one or both participants, tactical results, collusion at the expense of third parties should be excluded by the rules of the tournament. (This is always fulfilled in the single-elimination tournament, but usually not in the last rounds of the round-robin tournament).

* Other general framework conditions should also be as equal as possible for all competitors. For example, all competitors should have approximately the same regeneration time between matches. As a consequence, both participants playing a match should, as a rule, have played the same number of matches in the tournament so far. (Not fulfilled in the double-elimination tournament)

* Tiebreak criteria should be transparent and based on sporting merit only. (Problematic in the round-robin tournament and in the Swiss system tournament)

* For the spectators, exciting matches between the best pretenders to the championship are desirable. Therefore, the proportion of such games should be as high as possible.

* The winner of the competition is to be determined at the end of the tournament in a final of the two best competitors.

* The tournament should correspond to the sport-specific, organisational and temporal framework conditions of the specific competition, e.g. competition duration, minimum and maximum number of matches in total and individually for each competitor, etc.

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, for example the 1982 FIFA World Cup or the 1999–2000 UEFA Champions League. 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; at the 1999 Rugby World Cup the best one of five third-place sides did so.

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, since 2000. After 33 games, when every club has played every other club three times, the division is split into two halves. Clubs play a further five matches, against the teams in their half of the division. This can (and often does) result in the team placed seventh having a higher points total than the team placed sixth (because their final five 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.

A multi-stage pool system was implemented by Curling Canada for the Canadian championship curling tournaments (the Scotties Tournament of Hearts for women and the Montana's Brier for men) starting in 2018. The change was intended to allow the expansion of the main stage of the tournament from twelve to sixteen teams while keeping the round robin at eleven games. The teams are seeded using a ranking system in which points are calculated based on the teams' results in all competitive bonspiels using a complicated formula. Seeds 1, 4, 5, 8, 9, 12, 13 and 16 and placed in Pool A while seeds 2, 3, 6, 7, 10, 11, 14 and 15 are placed in Pool B. After each team has played seven games, the top four teams from each pool advance to the "Championship Pool". Carrying over their entire round robin records with them, Championship Pool teams play one game against each of the four teams in the opposite pool, with the top four teams qualifying for the page playoffs. In contrast, teams that fail to qualify for the Championship Pool play only one additional "Placement Round" game against the team that finished in the same position in the opposite pool for the purposes of determining final tournament ranking. For these teams, there is little else to play for since there is no form of relegation (and, with the expansion of the field to sixteen teams, no "pre-qualifying tournament") and seeding is based solely on the performances of the participating teams and not the past results of the provinces and territories they represent.

The top Slovenian basketball league has a unique system. In its first phase, 12 of the league's 13 clubs compete in a full home-and-away season, with the country's representative in the Euroleague (an elite pan-European club competition) exempt. The league then splits. The top seven teams are joined by the Euroleague representative for a second home-and-away season, with no results carrying over from the first phase. These eight teams compete for four spots in a final playoff. The bottom five teams play their own home-and-away league, but their previous results ''do'' carry over. These teams are competing to avoid relegation, with the bottom team automatically relegated and the second-from-bottom team forced to play a mini-league with the second- and third-place teams from the second level for a place in the top league.

Super 6s / Super 8s

Sometimes, results from an earlier phase are carried over into a later phase. At the Cricket World Cup, the second stage after group stage, known as Super 6s, features three teams from two preliminary groups, total six teams into one same group. At this stage the qualified teams do not replay the others they have already played, but instead reuse the original results in the new league table, to determine the teams qualified for the knockouts. However, in the T20 World Cup