Single-elimination tournament

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A single-elimination, knockout, or sudden-death tournament, is a type of elimination tournament where the loser of each match-up is immediately eliminated from the tournament. Each winner will play another in the next round, until the final match-up, whose winner becomes the tournament champion. Each match-up may be a single match or several, for example two-legged ties in European sports or best-of series in North American pro sports. Defeated competitors may play no further part after losing, or may participate in "consolation" or "classification" matches against other losers to determine the lower final rankings; for example, a third place playoff between losing semi-finalists. In a shootout poker tournament, there are more than two players competing at each table, and sometimes more than one progresses to the next round. Some competitions are held with a pure single-elimination tournament system. Others have many phases, with the last being a single-elimination final stage, often called playoffs. [1]

Contents

Nomenclature

In English, the round in which only eight competitors remain is generally called (with or without hyphenation) the quarter-final round; this is followed by the semi-final round, in which only four are left, the two winners of which then meet in the final or championship round.

The round before the quarterfinals has multiple designations. Often it is called the round of sixteen, last sixteen, or (in South Asia) pre-quarterfinals. In many other languages the term for these eight matches translates to eighth-final (e.g., in these European languages: "huitième de finale" in French, octavos de final in Spanish, Achtelfinale in German, åttondelsfinal in Swedish, ottavi di finale in Italian, oitavos-de-final in Portuguese, optimi de finală in Romanian osmifinále in Czech, osemfinále in Slovak, and osmina finala in Serbo-Croatian), though this term is rare in English itself, with noticeable use in American debate tournaments.

The round before the round of sixteen is sometimes called round of thirty-two in English. Terms for this in other languages generally translate as "sixteenth final".

Earlier rounds are typically numbered counting forwards from the first round, or by the number of remaining competitors. If some competitors get a bye, the round at which they enter may be named the first round, with the earlier matches called a preliminary round, qualifying round, opening round, or the play-in games.

Examples of the diverse names given to concurrent rounds in various select disciplines:

By competitorsFraction of final Grand Slam tennis [t 1] FA Cup football Coupe de France [2] NCAA Men's Basketball North American Debating Ch'ship Snooker
Round of 2 Final Final Final FinalNational ChampionshipFinalFinal
Round of 4SemifinalsSemifinalsSemi-finalsSemifinals Final Four
(National semifinals) [t 2]
SemifinalsSemi-finals
Round of 8QuarterfinalsQuarterfinalsquarter-finals [t 3] Quarterfinals Elite Eight
(Regional finals) [t 4]
QuarterfinalsQuarter-finals
Round of 16Eighth-finalsRound of 16 (US Open [4] ),
4th round [5] [ citation needed ]
5th round [t 5] 8th-finalsSweet Sixteen
(Regional semifinals) [t 6]
Round 7Last 16, 4th Round[ citation needed ]
Round of 3216th-finals3rd round4th round [t 5] 16th-finals3rd/2nd round [t 7] [t 8] Round 6Last 32,
3rd Round
Round of 6432nd-finals2nd round3rd round [t 5] 32nd-finals2nd/1st round [t 7] [t 8] Round 5Last 64,
2nd Round
Round of 12864th-finals1st round2nd round [t 9] [t 5] 8th qualifying round [t 10] First Four [t 7] Round 4 [t 11] Last 128,
1st Round

Notes:

  1. In singles only (the other disciplines have fewer rounds)
  2. The NCAA also uses the "final four" terminology in the Division I women's tournament, as well as the Division III tournaments for both men and women. In Division II for both sexes, this round is called the "semifinals"; both championship events in that division consist of eight teams instead of four.
  3. The quarter-finals were called the "sixth round" until 2016–17, the first in which replays were discontinued for this round. [3]
  4. In the Division II men's and women's tournaments, the Elite Eight is the championship event, with all qualifying teams participating at a single site. The NCAA does not use "Elite Eight" in Division III, simply calling this round the "regional finals".
  5. 1 2 3 4 The first to fifth rounds are often called the "first/second/etc. round proper", to distinguish them from the "first/second/etc. qualifying round".
  6. The NCAA only uses the term "Sweet Sixteen" in the Division I tournaments.
  7. 1 2 3 Starting in 2011, 68 teams played in the Championship, with four play-in games, nicknamed the First Four, before the top 60 teams enter at the round of 64. (From 2001 to 2010, there was a single "opening round" game before the round of 64.) The NCAA originally called the First Four the first round, making the rounds of 64 and 32 the second and third rounds respectively; in 2014 it announced that from 2016 it would revert to calling the rounds of 64 and 32 the first and second rounds. [6]
  8. 1 2 Since the NCAA Division I women's tournament expanded beyond 32 teams in 1986, the round of 32 has always been called the "second round", and the preceding round the "first round". The women's tournament involved 64 teams from 1994-2021 before expanding to 68 in 2022.
  9. The FA Cup 2nd round involves 40 teams, of which 20 qualify for the 3rd round, to which the top 44 teams will have received byes.
  10. The 8th qualifying round involves 88 teams, of which 44 qualify for the 32nd-finals, to which the top 20 teams will have received byes.
  11. The number of eligible teams is typically less than 128, but more than 64, so not all teams play this round.

Example

The knockout round of the 2002 FIFA World Cup tournament:

 
Round of 16 Quarter-finals Semi-finals Final
 
              
 
15 June – Seogwipo
 
 
Flag of Germany.svg  Germany 1
 
21 June – Ulsan
 
Flag of Paraguay (1990-2013).svg  Paraguay 0
 
Flag of Germany.svg  Germany 1
 
17 June – Jeonju
 
Flag of the United States.svg  United States 0
 
Flag of Mexico.svg  Mexico 0
 
25 June – Seoul
 
Flag of the United States.svg  United States 2
 
Flag of Germany.svg  Germany 1
 
16 June – Suwon
 
Flag of South Korea (1997-2011).svg  South Korea 0
 
Flag of Spain.svg  Spain (p)1 (3)
 
22 June – Gwangju
 
Flag of Ireland.svg  Republic of Ireland 1 (2)
 
Flag of Spain.svg  Spain 0 (3)
 
18 June – Daejeon
 
Flag of South Korea (1997-2011).svg  South Korea (p)0 (5)
 
Flag of South Korea (1997-2011).svg  South Korea (a.s.d.e.t.)2
 
30 June – Yokohama
 
Flag of Italy.svg  Italy 1
 
Flag of Germany.svg  Germany 0
 
15 June – Niigata
 
Flag of Brazil.svg  Brazil 2
 
Flag of Denmark.svg  Denmark 0
 
21 June – Shizuoka
 
Flag of England.svg  England 3
 
Flag of England.svg  England 1
 
17 June – Kobe
 
Flag of Brazil.svg  Brazil 2
 
Flag of Brazil.svg  Brazil 2
 
26 June – Saitama
 
Flag of Belgium (civil).svg  Belgium 0
 
Flag of Brazil.svg  Brazil 1
 
16 June – Ōita
 
Flag of Turkey.svg  Turkey 0 Third place play-off
 
Flag of Sweden.svg  Sweden 1
 
22 June – Osaka 29 June – Daegu
 
Flag of Senegal.svg  Senegal (a.s.d.e.t.)2
 
Flag of Senegal.svg  Senegal 0Flag of South Korea (1997-2011).svg  South Korea 2
 
18 June – Miyagi
 
Flag of Turkey.svg  Turkey (a.s.d.e.t.)1Flag of Turkey.svg  Turkey 3
 
Flag of Japan.svg  Japan 0
 
 
Flag of Turkey.svg  Turkey 1
 

Classification

Without any additional matches, the only position a single-elimination tournament can reliably determine is first - for example, if sorting the numbers 1-4 ascending, if 4 and 3 meet in the first round, 3 and 1 will lose in the first round and 2 will lose in the second, selecting 4 as the largest number in the set, but insufficient comparisons have been performed to determine which is greater, 2 or 3. Despite this, the candidate that loses in the final round is commonly considered to have taken second place (in this case, 2). When matches are held to determine places or prizes lower than first and second, these typically include a match between the losers of the semifinal matches called third place playoffs, the winner therein placing third and the loser fourth. Many Olympic single-elimination tournaments feature the bronze medal match if they do not award bronze medals to both losing semifinalists. The FIFA World Cup has long featured the third place match (since 1934), though the UEFA Euro has not held one since the 1980 edition.

Sometimes, contests are also held among the losers of the quarterfinal matches to determine fifth to eighth places. In one scenario, two "consolation semifinal" matches may be conducted, with the winners of these then facing off to determine fifth and sixth places and the losers playing for seventh and eighth; those are used often in qualifying tournaments where only the top five teams advance to the next round; or some method of ranking the four quarterfinal losers might be employed, in which case only one round of additional matches would be held among them, the two highest-ranked therein then playing for fifth and sixth places and the two lowest for seventh and eighth.

The number of distinct ways of arranging a single-elimination tournament (as an abstract structure, prior to seeding the players into the tournament) is given by the Wedderburn–Etherington numbers. [7] Thus, for instance, there are three different arrangements for five players:

However, the number of arrangements grows quickly for larger numbers of players and not all of them are commonly used.

Seeding

Opponents may be allocated randomly (such as in the FA Cup); however, since the "luck of the draw" may result in the highest-rated competitors being scheduled to face each other early in the competition, seeding is often used to prevent this. Brackets are set up so that the top two seeds could not possibly meet until the final round (should both advance that far), none of the top four can meet prior to the semifinals, and so on. If no seeding is used, the tournament is called a random knockout tournament.

Standard seeding pairs the highest and lowest, then second highest and second lowest and so on, for an 8 seed tournament this is 1 v 8, 2 v 7, 3 v 6 and 4 v 5, for example this is used for 16 seeds in the World Snooker Championship and 32 seeds in the World Darts Championship. Some tournaments stray from this, for example it is not the procedure that is followed in most tennis tournaments, where the 1 and 2 seeds are placed in separate brackets, but then the 3 and 4 seeds are assigned to their brackets randomly, and so too are seeds 5 through 8, and so on. This may result in some brackets consisting of stronger players than other brackets, and since only the top 32 players of 128 are seeded in Tennis Grand Slam tournaments, it can happen that the 33rd-best player in a 128-player field could end up playing the top seed in the first round. An example of this occurring was when World No. 33 Florian Mayer was drawn against, and defeated by, World No. 1 Novak Djokovic in the first round of the 2013 Wimbledon Championships, [8] in what was also a rematch of a quarter-final from the previous year. [9]

Sometimes the remaining competitors in a single-elimination tournament will be "re-seeded" so that the highest surviving seed is made to play the lowest surviving seed in the next round, the second-highest plays the second-lowest, etc. This may be done after each round, or only at selected intervals. In American team sports, for example, the NFL employs this tactic, but MLS, NHL and the NBA do not (and neither does the NCAA college basketball tournament). Although MLB does have enough teams (12) in its playoff tournament where re-seeding would have made a large difference in the matchups; only the WNBA's at the minimum, which is at least four from each conference for a total of 8. The NBA's format calls for the winner of the first-round series between the first and eighth seeds (within each of the two conferences the league has) to face the winner of the first-round series between the fourth and fifth seeds in the next round, even if one or more of the top three seeds had been upset in their first-round series; critics have claimed that this gives a team fighting for the fifth and sixth seeding positions near the end of the regular season an incentive to tank (deliberately lose) games, so as to finish sixth and thus avoid a possible match-up with the top seed until one round later. MLS' format is identical, except that the conference quarterfinals is a best-of-three series.

In some situations, a seeding restriction may be implemented; from 1975 until 1989 in the NFL, and from 1994 until 2011 in MLB there was a rule where at the conference or league semifinal, should the top seed and last seed (wild card) be from the same division, they cannot play each other; in that case, the top seed plays the worst division champion; the second-best division champion plays the wild card team. This is due to the scheduling employed for the regular season, in which a team faces any given divisional opponent more often than any given non-divisional opponent – the tournament favors match-ups that took place fewer times in the regular season (or did not take place, in some cases). [1]

In international fencing competitions, it is common to have a group stage. Participants are divided in groups of 6–7 fencers who play a round-robin tournament, and a ranking is calculated from the consolidated group results. Single elimination is seeded from this ranking.

Evaluation

The single-elimination format enables a relatively large number of competitors to participate. There are no "dead" matches (perhaps excluding "classification" matches), and no matches where one competitor has more to play for than the other.

The format is less suited to games where draws are frequent. In chess, each fixture in a single-elimination tournament must be played over multiple matches, because draws are common, and because white has an advantage over black. In association football, games ending in a draw may be settled in extra time and eventually by a penalty shootout or by replaying the fixture.

Another perceived disadvantage is that most competitors are eliminated after relatively few games. Variations such as the double-elimination tournament allow competitors a single loss while remaining eligible for overall victory. However, losing one game requires the competitor to win more games in order to win the tournament.

In a random knockout tournament (single-elimination without any seeding), awarding the second place to the loser of the final is unjustified: any of the competitors knocked out by the tournament winner might have been the second strongest one, but they never got the chance to play against the losing finalist. In general, it is only fair to use a single-elimination tournament to determine first place. To fairly determine lower places requires some form of round-robin in which each player/team gets the opportunity to face every other player/team.

Also, if the competitors' performance is variable, that is, it depends on a small, varying factor in addition to the actual strength of the competitors, then not only will it become less likely that the strongest competitor actually wins the tournament, in addition the seeding done by the tournament organizers will play a major part in deciding the winner. [10] [11] As a random factor is always present in a real-world competition, this might easily cause accusations of unfairness.

Other tournament systems

Variations of the single-elimination tournament include:

Other common tournament types include:

Related Research Articles

The playoffs, play-offs, postseason or finals of a sports league are a competition played after the regular season by the top competitors to determine the league champion or a similar accolade. Depending on the league, the playoffs may be either a single game, a series of games, or a tournament, and may use a single-elimination system or one of several other different playoff formats. Playoff, in regard to international fixtures, is to qualify or progress to the next round of a competition or tournament.

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:

  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.
<span class="mw-page-title-main">Bracket (tournament)</span> Diagram of a tournament

A bracket or tournament bracket is a tree diagram that represents the series of games played during a knockout tournament. Different knockout tournament formats have different brackets; the simplest and most common is that of the single-elimination tournament. The name "bracket" is American English, derived from the resemblance of the links in the tree diagram to the bracket punctuation symbol ] or [. The closest British term is draw, although this implies an element of chance, whereas some brackets are determined entirely by seeding.

<span class="mw-page-title-main">Archery at the Summer Olympics</span>

Archery had its debut at the 1900 Summer Olympics and has been contested in 17 Olympiads. 105 nations have competed in the Olympic archery events, with France appearing the most often at 15 times. The most noticeable trend has been the excellence of South Korean archers, who have won 27 out of 39 gold medals in events since 1984. It is governed by the World Archery Federation. Recurve archery is the only discipline of archery featured at the Olympic Games. Archery is also an event at the Summer Paralympics.

<span class="mw-page-title-main">Double-elimination tournament</span> Type of elimination competition

A double-elimination tournament is a type of elimination tournament competition in which a participant ceases to be eligible to win the tournament's championship upon having lost two games or matches. It stands in contrast to a single-elimination tournament, in which only one defeat results in elimination.

<span class="mw-page-title-main">Repechage</span> Practice amongst ladder competitions

Repechage is a practice in series competitions that allows participants who failed to meet qualifying standards by a small margin to continue to the next round. A well-known example is the wild card system.

A Swiss-system tournament is a non-eliminating tournament format that features a fixed number of rounds of competition, but considerably fewer than for a round-robin tournament; thus each competitor does not play all the other competitors. Competitors meet one-on-one in each round and are paired using a set of rules designed to ensure that each competitor plays opponents with a similar running score, but does not play the same opponent more than once. The winner is the competitor with the highest aggregate points earned in all rounds. With an even number of participants, all competitors play in each round.

A seed is a competitor or team in a sport or other tournament who is given a preliminary ranking for the purposes of the draw. Players/teams are "planted" into the bracket in a manner that is typically intended so that the best do not meet until later in the competition, usually based on regular season. The term was first used in tennis, and is based on the idea of laying out a tournament ladder by arranging slips of paper with the names of players on them the way seeds or seedlings are arranged in a garden: smaller plants up front, larger ones behind.

There are a number of formats used in various levels of competition in sports and the[game]]s to determine an overall champion. Some of the most common are the single elimination, the best-of- series, the total points series more commonly known as on aggregate, and the round-robin tournament.

A wild card is a tournament or playoff berth awarded to an individual or team that fails to qualify in the normal way; for example, by having a high ranking or winning a qualifying stage. In some events, wildcards are chosen freely by the organizers. Other events have fixed rules. Some North American professional sports leagues compare the records of teams which did not qualify directly by winning a division or conference.

The Page playoff system is a playoff format used primarily in softball and curling at the championship level, and the Indian Premier League and Pakistan Super League cricket tournaments. Teams are seeded using a round-robin tournament and the top four play a mix of a single-elimination and double-elimination tournament to determine the winner. It is identical to a four-team McIntyre system playoff, first used by the WANFL, SANFL and VFL in Australia in 1931, originally called the Page–McIntyre system, after the VFL delegate, the Richmond Football Club's Secretary, Percy "Pip" Page, who had advocated its use. A form has been adopted in the Canadian Premier League national soccer competition.

In sports, a bye is the preferential status of a player or team that is automatically advanced to the next round of a tournament without having to play an opponent in an early round.

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The Atlantic Coast Conference baseball tournament, sometimes referred to simply as the ACC tournament, is the conference championship tournament in baseball for the Atlantic Coast Conference (ACC). In 2017, the event adopted a modified twelve-team pool play format. The winner receives the conference's automatic bid to the NCAA Division I baseball tournament.

The National Basketball Association (NBA) playoffs is the annual elimination tournament held to determine the league champion. The four-round, best-of-seven tournament is held after the league's regular season and its preliminary postseason tournament, the NBA play-in tournament. Six teams from each of the two conferences automatically advance to the playoffs based on regular season winning percentage, while those teams finishing seven through 10 from each conference compete in the play-in tournament to determine the final two playoff seeds.

The Inline Hockey World Championship is an annual inline hockey tournament organized by World Skate. Prior to the creation of World Skate in September 2017, the championship was administrated by the Comité International Roller In-Line Hockey (CIRILH), an organization and discipline of Fédération Internationale de Roller Sports (FIRS). It is the sport's highest-profile annual international tournament.

<span class="mw-page-title-main">Fencing at the 1992 Summer Olympics – Men's épée</span> Olympic fencing event

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The PBA Tour Playoffs is an annual invitational event on the PBA Tour in North America that debuted in the 2019 season. After two years as a 24-player tournament, the event was set up in a 16-player bracket-style format since 2021.

The Ontario University Athletic Association ice hockey tournament was an annual conference championship held between member teams.

References

  1. 1 2 "Knock-Out tournament". Sport Science Corner. Retrieved 31 August 2023.
  2. "Coupe de France : football, résultats, calendrier, reportage, photos" (in French). French Football Federation. Archived from the original on 19 July 2012. Retrieved 16 July 2012.
  3. "Premier League clubs want the FA Cup moved to midweek and replays scrapped". talkSPORT. 31 May 2018 [2017]. Retrieved 31 March 2019.; Emirates FA Cup (17 February 2017). "We do now! The sixth round has been renamed as the quarter-finals from this season". @EmiratesFACup. Twitter. Retrieved 31 March 2019.
  4. "2012 Tournament Schedule". US Open. Archived from the original on 17 July 2012. Retrieved 16 July 2012.
  5. "Gentlemen's Singles – 2012 Official Site by IBM". Wimbledon Championships Website. Retrieved 16 July 2012.
  6. Cary, Tim (21 November 2014). "What's in a Name? March Madness First Round Is the 'First Round' Again". The Cheat Sheet. Retrieved 6 June 2015.
  7. Maurer, Willi (1975), "On most effective tournament plans with fewer games than competitors", The Annals of Statistics, 3 (3): 717–727, doi: 10.1214/aos/1176343135 , JSTOR   2958441, MR   0371712 .
  8. Wimbledon: Novak vs Mayer in R1; Andy, Roger, Rafa all in bottom half, Novak Djokovic official website, 21 June 2013
  9. Wimbledon 2013: Men's matches to watch out for, The Roar, 22 June 2013
  10. Ryvkin, Dmitry (March 2005). "The Predictive Power of Noisy Elimination Tournaments" (PDF). CERGE-EI. Archived (PDF) from the original on 22 October 2007. Retrieved 21 October 2010.
  11. Kim, Michael P.; Suksompong, Warut; Vassilevska Williams, Virginia (2017). "Who Can Win a Single-Elimination Tournament?". SIAM Journal on Discrete Mathematics. 31 (3): 1751–1764. arXiv: 1511.08416 . doi:10.1137/16M1061783. hdl:1721.1/125608. S2CID   1251470.