Single-elimination tournament
Encyclopedia
A single-elimination tournament, also called a knockout, cup or sudden death tournament, is a type of elimination tournament
where the loser of each match or bracket is immediately eliminated from winning the championship or first prize in the event. This does not always mean that the defeated competitor will not participate further in the tournament: in some such tournaments, consolation or "classification" contests are subsequently held among those already defeated to determine the awarding of lesser places, for example, a third place playoff
.
Where more than two competitors can play in each match, such as in a shootout poker tournament
, players are removed when they can no longer play until one player remains from the group. This player moves on to the next round.
A simple way to describe a single-elimination tournament is that the winner of each match moves on and the loser goes home.
Some competitions are held with a pure single-elimination tournament system. Others have many phases, with the last being a single-elimination final stage called playoffs.
In the opening round, competitors will get a bye
. Often, the number of participants in a single-elimination tournament is fixed as a power of two
, so that nobody gets a bye. For example, the tennis Grand Slam
singles championships are tournaments of 128 players. This ensures all competitors will face opponents who have previously played the same number of matches.
The full schedule of pairings across all rounds (the bracket
) may be allocated before the start of the tournament, or each round may be allocated at the end of the preceding round. Each successive round halves the number of competitors remaining, assuming there are no byes.
in the first round, which entitles these competitors to advance to the second round automatically without playing. Often, these byes will be awarded to the highest-rated competitors in the event as a reward for some previous accomplishment; indeed, in some American
team sports—most notably American football
— the number of teams qualifying for the postseason tournament will be intentionally set at a number which is not a power of two, in order to provide such an advantage to a high-achieving team in the just-completed regular season. Additionally, the player/team getting byes may get them exclusively by luck or random chance (i.e. if there are 7 competitors, one random one will automatically advance to the next round)
Multiple rounds of byes are also possible: in the FA Cup
, the teams in the top two league divisions enter in the third round "proper" (of eight); the two next-highest divisions' teams will have entered in the first round; lower-division teams in one of 6 preliminary rounds. Another example is the UEFA Europa League.
If some teams get a bye, the round at which they enter may be named the "first" round, with the earlier matches called a "preliminary" round, or "play-in games".
Names of rounds in various systems and competitions:
, the winner therein placing third and the loser fourth. Sometimes, contests are also held among the losers of the quarterfinal matches to determine fifth through eighth places - this is most commonly encountered in the Olympic Games
, with the exception of boxing
, where both fighters are deemed to be third place. 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.
One version of seeding is where brackets are set up so that the quarterfinal pairings (barring any upsets) would be the 1 seed vs. the 8 seed, 2 vs. 7, 3 vs. 6 and 4 vs. 5; however, this 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 are seeded at all in Tennis Grand Slam
tournaments, it is conceivable that the 33rd-best player in a 128-player field could end up playing the top seed in the first round. While this may seem unfair to a casual observer, it should be pointed out that rankings of tennis players are generated by computers, and players tend to change ranking positions very gradually, so that a more equitable method of determining the pairings might result in many of the same head-to-head matchups being repeated over and over again in successive tournaments.
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, both the NFL and NHL
employ this tactic, but the NBA does not (and neither does the NCAA college basketball tournament
). MLB
does not have enough teams in its playoff tournament where re-seeding would make a difference in the matchups, (The NFL is at the minimum, which is 6 from each league (or conference in the NFL, NBA or NHL) for a total of 12). 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 matchup with the top seed until one round later.
In some situations, a seeding restriction will be implemented; from 1975 until 1989, the NFL
, and, since 1998, MLB
have a rule where at the conference or league semifinal, should the top seed and last seed (wild card) be from the same division, they may not play each other; in that case, the top seed plays the worst division champion; the second-best division champion plays the wild card team.
The format is less suited to games where draw
s 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
, viewed by many fans as an unsatisfactory conclusion to a fixture, or by replaying the fixture. In various forms of one-day cricket
, a bowl-out
has been used in recent years to settle tied matches.
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.
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.
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. As a random factor is always present in a real world competition, this might easily cause accusations of unfairness.
Other common tournament types are
Elimination tournament
Elimination tournament may refer to any of several types of tournament in which each player has a set number of loses before elimination from the competition.*Single-elimination tournament, in which a player is eliminated after losing to a single opponent...
where the loser of each match or bracket is immediately eliminated from winning the championship or first prize in the event. This does not always mean that the defeated competitor will not participate further in the tournament: in some such tournaments, consolation or "classification" contests are subsequently held among those already defeated to determine the awarding of lesser places, for example, a third place playoff
Third place playoff
The third place playoff is a single match that is included in many sporting knockout tournaments to decide which competitor or team will be credited with finishing third and fourth. The teams that compete in the third place playoffs are usually the two losing semi-finalists in a particular...
.
Where more than two competitors can play in each match, such as in a shootout poker tournament
Poker tournament
A poker tournament is a tournament where players compete by playing poker. It can feature as few as two players playing on a single table , and as many as tens of thousands of players playing on thousands of tables...
, players are removed when they can no longer play until one player remains from the group. This player moves on to the next round.
A simple way to describe a single-elimination tournament is that the winner of each match moves on and the loser goes home.
Some competitions are held with a pure single-elimination tournament system. Others have many phases, with the last being a single-elimination final stage called playoffs.
Brackets
Assuming two competitors per match, if there are competitors, there will be rounds required, or if there are rounds, there will be competitors.In the opening round, competitors will get a bye
Bye (sports)
A bye, in sports and other competitive activities, most commonly refers to the practice of allowing a player or team to advance to the next round of a playoff tournament without playing...
. Often, the number of participants in a single-elimination tournament is fixed as a power of two
Power of two
In mathematics, a power of two means a number of the form 2n where n is an integer, i.e. the result of exponentiation with as base the number two and as exponent the integer n....
, so that nobody gets a bye. For example, the tennis Grand Slam
Grand Slam (tennis)
The four Major tennis tournaments, also called the Slams, are the most important tennis events of the year in terms of world tour ranking points, tradition, prize-money awarded, strength and size of player field, and public attention. They are the Australian Open, the French Open, Wimbledon, and...
singles championships are tournaments of 128 players. This ensures all competitors will face opponents who have previously played the same number of matches.
The full schedule of pairings across all rounds (the bracket
Bracket (tournament)
A bracket is a tree diagram that represents the series of games played during a tournament, named as such because it appears to be a large number of interconnected brackets....
) may be allocated before the start of the tournament, or each round may be allocated at the end of the preceding round. Each successive round halves the number of competitors remaining, assuming there are no byes.
Byes
In cases where the number of competitive entities at the start of the tournament is not a power of two, some competitors may receive a byeBye (sports)
A bye, in sports and other competitive activities, most commonly refers to the practice of allowing a player or team to advance to the next round of a playoff tournament without playing...
in the first round, which entitles these competitors to advance to the second round automatically without playing. Often, these byes will be awarded to the highest-rated competitors in the event as a reward for some previous accomplishment; indeed, in some American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
team sports—most notably American football
American football
American football is a sport played between two teams of eleven with the objective of scoring points by advancing the ball into the opposing team's end zone. Known in the United States simply as football, it may also be referred to informally as gridiron football. The ball can be advanced by...
— the number of teams qualifying for the postseason tournament will be intentionally set at a number which is not a power of two, in order to provide such an advantage to a high-achieving team in the just-completed regular season. Additionally, the player/team getting byes may get them exclusively by luck or random chance (i.e. if there are 7 competitors, one random one will automatically advance to the next round)
Multiple rounds of byes are also possible: in the FA Cup
FA Cup
The Football Association Challenge Cup, commonly known as the FA Cup, is a knockout cup competition in English football and is the oldest association football competition in the world. The "FA Cup" is run by and named after The Football Association and usually refers to the English men's...
, the teams in the top two league divisions enter in the third round "proper" (of eight); the two next-highest divisions' teams will have entered in the first round; lower-division teams in one of 6 preliminary rounds. Another example is the UEFA Europa League.
Nomenclature
The round in which only sixteen remain is sometimes called the "Round of Sixteen" or "Last Sixteen", when eight remain at the start it is generally called 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.If some teams get a bye, the round at which they enter may be named the "first" round, with the earlier matches called a "preliminary" round, or "play-in games".
Names of rounds in various systems and competitions:
Competitor count | Fraction of final | Grand Slam tennis singles |
FA Cup FA Cup The Football Association Challenge Cup, commonly known as the FA Cup, is a knockout cup competition in English football and is the oldest association football competition in the world. The "FA Cup" is run by and named after The Football Association and usually refers to the English men's... |
NCAA Men's Basketball Championship NCAA Men's Division I Basketball Championship The NCAA Men's Division I Basketball Championship is a single-elimination tournament held each spring in the United States, featuring 68 college basketball teams, to determine the national championship in the top tier of college basketball... |
NCAA Women's Basketball Championship NCAA Women's Division I Basketball Championship The NCAA Women's Division I Championship is an annual college basketball tournament for women. Held each April, the Women's Championship was inaugurated in the 1981–82 season... |
NADC North American Debating Championship The North American Debating Championship is the official university debating championship of North America, sanctioned by the national university debating associations in the United States and Canada, the American Parliamentary Debate Association and the Canadian University Society for... playoffs |
---|---|---|---|---|---|---|
Round of 2 | Final Final (competition) The final of a competition is the match or round in which the winner of the entire event is decided.In sports competitions following a knockout system, where only two individuals or teams compete in each match, the final is usually played between the winners of two semi-finals... |
Final | FA Cup Final FA Cup Final The FA Cup Final, commonly referred to in England as just the Cup Final, is the last match in the Football Association Challenge Cup. With an official attendance of 89,826 at the 2007 FA Cup Final, it is the fourth best attended domestic club championship event in the world and the second most... |
Championship game | Championship game | Final |
Round of 4 | Semi-finals | Semi-finals | Semi-finals | Final Four Final four Final Four isa sports term that is commonly applied to the last four teams remaining in a playoff tournament, most notably NCAA Division I college basketball tournaments. The term usually refers to the four teams who compete in the two games of a single-elimination tournament's semi-final round... |
Final Four Final four Final Four isa sports term that is commonly applied to the last four teams remaining in a playoff tournament, most notably NCAA Division I college basketball tournaments. The term usually refers to the four teams who compete in the two games of a single-elimination tournament's semi-final round... |
Semi-finals |
Round of 8 | Quarter-finals | Quarter-finals | 6th Round | Elite Eight Elite Eight The term Elite Eight, or less commonly called "Great Eight", refers to the final eight teams in the NCAA Men's Division I Basketball Championship or the NCAA Women's Division I Basketball Championship; and, thus, represents the national quarterfinals. In Division I, the Elite Eight consists of the... (Regional finals) |
Elite Eight Elite Eight The term Elite Eight, or less commonly called "Great Eight", refers to the final eight teams in the NCAA Men's Division I Basketball Championship or the NCAA Women's Division I Basketball Championship; and, thus, represents the national quarterfinals. In Division I, the Elite Eight consists of the... (Regional finals) |
Quarter-finals |
Round of 16 | Eighth-finals | 4th round | 5th round | Sweet Sixteen (Regional Semi-finals) |
Sweet Sixteen (Regional Semi-finals) |
Octofinals |
Round of 32 | 16th-finals | 3rd round | 4th round | 3rd round | 2nd round | Double-octofinals |
Round of 64 | 32nd-finals | 2nd round | 3rd round | 2nd round | 1st round | Triple-octofinals |
Round of 128 | 64th-finals | 1st round | 2nd roundThe 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. | First FourStarting in 2011, 68 teams will play in the Championship, with four "play-in games" before the 64-team first round. | N/A | Quad-octofinalsThe number of eligible teams is typically less than 128, but more than 64, so not all teams play this round |
Classification
When matches are held to determine places or prizes lower than first and second (the loser of the final-round match gaining the latter position), these typically include a match between the losers of the semifinal matches called third place playoffThird place playoff
The third place playoff is a single match that is included in many sporting knockout tournaments to decide which competitor or team will be credited with finishing third and fourth. The teams that compete in the third place playoffs are usually the two losing semi-finalists in a particular...
, the winner therein placing third and the loser fourth. Sometimes, contests are also held among the losers of the quarterfinal matches to determine fifth through eighth places - this is most commonly encountered in the Olympic Games
Olympic Games
The Olympic Games is a major international event featuring summer and winter sports, in which thousands of athletes participate in a variety of competitions. The Olympic Games have come to be regarded as the world’s foremost sports competition where more than 200 nations participate...
, with the exception of boxing
Boxing
Boxing, also called pugilism, is a combat sport in which two people fight each other using their fists. Boxing is supervised by a referee over a series of between one to three minute intervals called rounds...
, where both fighters are deemed to be third place. 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.
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.One version of seeding is where brackets are set up so that the quarterfinal pairings (barring any upsets) would be the 1 seed vs. the 8 seed, 2 vs. 7, 3 vs. 6 and 4 vs. 5; however, this 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 are seeded at all in Tennis Grand Slam
Grand Slam (tennis)
The four Major tennis tournaments, also called the Slams, are the most important tennis events of the year in terms of world tour ranking points, tradition, prize-money awarded, strength and size of player field, and public attention. They are the Australian Open, the French Open, Wimbledon, and...
tournaments, it is conceivable that the 33rd-best player in a 128-player field could end up playing the top seed in the first round. While this may seem unfair to a casual observer, it should be pointed out that rankings of tennis players are generated by computers, and players tend to change ranking positions very gradually, so that a more equitable method of determining the pairings might result in many of the same head-to-head matchups being repeated over and over again in successive tournaments.
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, both the NFL and NHL
National Hockey League
The National Hockey League is an unincorporated not-for-profit association which operates a major professional ice hockey league of 30 franchised member clubs, of which 7 are currently located in Canada and 23 in the United States...
employ this tactic, but the NBA does not (and neither does the NCAA college basketball tournament
NCAA Men's Division I Basketball Championship
The NCAA Men's Division I Basketball Championship is a single-elimination tournament held each spring in the United States, featuring 68 college basketball teams, to determine the national championship in the top tier of college basketball...
). MLB
Major League Baseball
Major League Baseball is the highest level of professional baseball in the United States and Canada, consisting of teams that play in the National League and the American League...
does not have enough teams in its playoff tournament where re-seeding would make a difference in the matchups, (The NFL is at the minimum, which is 6 from each league (or conference in the NFL, NBA or NHL) for a total of 12). 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
Match fixing
In organised sports, match fixing, game fixing, race fixing, or sports fixing occurs as a match is played to a completely or partially pre-determined result, violating the rules of the game and often the law. Where the sporting competition in question is a race then the incident is referred to as...
(deliberately lose) games, so as to finish sixth and thus avoid a possible matchup with the top seed until one round later.
In some situations, a seeding restriction will be implemented; from 1975 until 1989, the NFL
National Football League
The National Football League is the highest level of professional American football in the United States, and is considered the top professional American football league in the world. It was formed by eleven teams in 1920 as the American Professional Football Association, with the league changing...
, and, since 1998, MLB
Major League Baseball
Major League Baseball is the highest level of professional baseball in the United States and Canada, consisting of teams that play in the National League and the American League...
have a rule where at the conference or league semifinal, should the top seed and last seed (wild card) be from the same division, they may not play each other; in that case, the top seed plays the worst division champion; the second-best division champion plays the wild card team.
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 draw
Tie (draw)
To tie or draw is to finish a competition with identical or inconclusive results. The word "tie" is usually used in North America for sports such as American football. "Draw" is usually used in the United Kingdom, Ireland and the Commonwealth of Nations and it is usually used for sports such as...
s are frequent. In chess
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...
, each fixture in a single-elimination tournament must be played over multiple matches, because draws are common
Draw (chess)
In chess, a draw is when a game ends in a tie. It is one of the possible outcomes of a game, along with a win for White and a win for Black . Usually, in tournaments a draw is worth a half point to each player, while a win is worth one point to the victor and none to the loser.For the most part,...
, 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
Penalty shootout (football)
A penalty shoot-out, referred to as kicks from the penalty mark in the Laws of the Game, is the FIFA official term for a method used in association football to decide which team progresses to the next stage of a tournament following a tied game...
, viewed by many fans as an unsatisfactory conclusion to a fixture, or by replaying the fixture. In various forms of one-day cricket
Cricket
Cricket is a bat-and-ball game played between two teams of 11 players on an oval-shaped field, at the centre of which is a rectangular 22-yard long pitch. One team bats, trying to score as many runs as possible while the other team bowls and fields, trying to dismiss the batsmen and thus limit the...
, a bowl-out
Bowl-out
A bowl-out is used in various forms of limited overs cricket to decide a match that would otherwise end in a tie. The procedure is similar to a penalty shootout in association football. Five bowlers from each side deliver one or two balls each at an unguarded wicket...
has been used in recent years to settle tied matches.
Another perceived disadvantage is that most competitors are eliminated after relatively few games. Variations such as the double-elimination tournament
Double-elimination tournament
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...
allow competitors a single loss while remaining eligible for overall victory.
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.
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. 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:- Double-elimination tournamentDouble-elimination tournamentA 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...
Other common tournament types are
- Round-robin tournamentRound-robin tournamentA round-robin tournament is a competition "in which each contestant meets all other contestants in turn".-Terminology:...
- Swiss system tournamentSwiss system tournamentA Swiss-system tournament is a commonly used type of tournament where players or teams need to be paired to face each other for several rounds of competition. This type of tournament was first used in a Zurich chess tournament in 1895, hence the name "Swiss system". The Swiss system is used when...