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[[File:Placeholderright300px]]{{refimprovedate=May 2011}}<br />[[Image:Mitbat2007bracketlarge.pngthumb250pxExample of a singleelimination tournament bracket]]

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{{refimprovedate=May 2011}} 

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[[Image:Mitbat2007bracketlarge.pngthumb250pxExample of a singleelimination tournament bracket]] 

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A '''singleelimination 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]]. 

A '''singleelimination 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]]. 

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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. 

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. 

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A simple way to describe a singleelimination tournament is that the winner of each match moves on and the loser goes home. 

A simple way to describe a singleelimination tournament is that the winner of each match moves on and the loser goes home. 

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Some competitions are held with a pure singleelimination tournament system. Others have many phases, with the last being a singleelimination final stage called [[playoffs]]. 

Some competitions are held with a pure singleelimination tournament system. Others have many phases, with the last being a singleelimination final stage called [[playoffs]]. 
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==Brackets==<br />Assuming two competitors per match, if there are <math>n</math> competitors, there will be <math>r = \left \lceil \log_{2} n \right \rceil </math> rounds required, or if there are <math>r</math> rounds, there will be <math>n= 2^r</math> competitors.

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==Brackets== 

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Assuming two competitors per match, if there are <math>n</math> competitors, there will be <math>r = \left \lceil \log_{2} n \right \rceil </math> rounds required, or if there are <math>r</math> rounds, there will be <math>n= 2^r</math> competitors. 

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In the opening round, <math>2^r  n</math> competitors will get a ''[[bye (sports)bye]]''. Often, the number of participants in a singleelimination tournament is fixed as a [[power of two]], so that nobody gets a bye. For example, the tennis [[Grand Slam (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. 

In the opening round, <math>2^r  n</math> competitors will get a ''[[bye (sports)bye]]''. Often, the number of participants in a singleelimination tournament is fixed as a [[power of two]], so that nobody gets a bye. For example, the tennis [[Grand Slam (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. 

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The full schedule of pairings across all rounds (the ''[[bracket (tournament)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. 

The full schedule of pairings across all rounds (the ''[[bracket (tournament)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. 
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==Byes==<br />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 ''[[bye (sports)bye]]'' 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 highestrated competitors in the event as a reward for some previous accomplishment; indeed, in some [[United StatesAmerican]] 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 highachieving team in the justcompleted 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)

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==Byes== 

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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 ''[[bye (sports)bye]]'' 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 highestrated competitors in the event as a reward for some previous accomplishment; indeed, in some [[United StatesAmerican]] 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 highachieving team in the justcompleted 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) 

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Multiple rounds of byes are also possible: in the [[FA Cup]], the teams in the top two [[English football league system#The systemleague divisions]] enter in the third round "proper" (of eight); the two nexthighest divisions' teams will have entered in the first round; lowerdivision teams in one of 6 preliminary rounds. Another example is the [[UEFA Europa League]]. 

Multiple rounds of byes are also possible: in the [[FA Cup]], the teams in the top two [[English football league system#The systemleague divisions]] enter in the third round "proper" (of eight); the two nexthighest divisions' teams will have entered in the first round; lowerdivision teams in one of 6 preliminary rounds. Another example is the [[UEFA Europa League]]. 
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==Nomenclature==<br />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 ''quarterfinal'' round; this is followed by the ''semifinal'' round in which only four are left, the two winners of which then meet in the final or ''championship round''.

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==Nomenclature== 

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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 ''quarterfinal'' round; this is followed by the ''semifinal'' round in which only four are left, the two winners of which then meet in the final or ''championship round''. 

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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 "playin games". 

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 "playin games". 
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Names of rounds in various systems and competitions:<br />{class="wikitable"<br /><br />! Competitor count<br />! Fraction of final<br />! [[Grand Slam tennis]]<br/>singles<br />! [[FA Cup]]<br />! [[NCAA Men's Division I Basketball ChampionshipNCAA Men's Basketball<br/>Championship]]<br />! [[NCAA Women's Division I Basketball ChampionshipNCAA Women's Basketball<br/>Championship]]<br />! [[North American Debating ChampionshipNADC]]<br/>playoffs<br /><br /> Round of 2<br /> [[Final (competition)Final]]<br /> Final<br /> [[FA Cup Final]]<br /> Championship game<br /> Championship game<br /> Final<br /><br /> Round of 4<br /> Semifinals<br /> Semifinals<br /> Semifinals<br /> [[Final Four]]<br /> [[Final Four]]<br /> Semifinals<br /><br /> Round of 8<br /> Quarterfinals<br /> Quarterfinals<br /> 6th Round<br /> [[Elite Eight]]<br/>(Regional finals)<br /> [[Elite Eight]]<br/>(Regional finals)<br /> Quarterfinals<br /><br /> Round of 16<br /> Eighthfinals<br /> 4th round<br /> 5th round<br /> Sweet Sixteen<br/>(Regional Semifinals)<br /> Sweet Sixteen<br/>(Regional Semifinals)<br /> Octofinals<br /><br /> Round of 32<br /> 16thfinals<br /> 3rd round<br /> 4th round<br /> 3rd round<br /> 2nd round<br /> Doubleoctofinals<br /><br /> Round of 64<br /> 32ndfinals<br /> 2nd round<br /> 3rd round<br /> 2nd round<br /> 1st round<br /> Tripleoctofinals<br /><br /> Round of 128<br /> 64thfinals<br /> 1st round<br /> 2nd round<ref group="t">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.</ref><br /> [[NCAA Men's Division I Basketball Opening Round gameFirst Four]]<ref group="t">Starting in 2011, 68 teams will play in the Championship, with four "playin games" before the 64team first round.</ref><br /> N/A<br /> Quadoctofinals<ref group="t">The number of eligible teams is typically less than 128, but more than 64, so not all teams play this round</ref><br />}

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Names of rounds in various systems and competitions: 

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{class="wikitable" 

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! Competitor count 

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! Fraction of final 

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! [[Grand Slam tennis]]<br/>singles 

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! [[FA Cup]] 

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! [[NCAA Men's Division I Basketball ChampionshipNCAA Men's Basketball<br/>Championship]] 

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! [[NCAA Women's Division I Basketball ChampionshipNCAA Women's Basketball<br/>Championship]] 

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! [[North American Debating ChampionshipNADC]]<br/>playoffs 

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 Round of 2 

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 [[Final (competition)Final]] 

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 Final 

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 [[FA Cup Final]] 

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 Championship game 

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 Championship game 

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 Final 

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 Round of 4 

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 Semifinals 

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 Semifinals 

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 Semifinals 

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 [[Final Four]] 

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 [[Final Four]] 

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 Semifinals 

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 Round of 8 

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 Quarterfinals 

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 Quarterfinals 

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 6th Round 

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 [[Elite Eight]]<br/>(Regional finals) 

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 [[Elite Eight]]<br/>(Regional finals) 

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 Quarterfinals 

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 Round of 16 

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 Eighthfinals 

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 4th round 

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 5th round 

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 Sweet Sixteen<br/>(Regional Semifinals) 

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 Sweet Sixteen<br/>(Regional Semifinals) 

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 Octofinals 

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 Round of 32 

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 16thfinals 

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 3rd round 

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 4th round 

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 3rd round 

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 2nd round 

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 Doubleoctofinals 

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 Round of 64 

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 32ndfinals 

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 2nd round 

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 3rd round 

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 2nd round 

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 1st round 

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 Tripleoctofinals 

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 Round of 128 

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 64thfinals 

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 1st round 

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 2nd round<ref group="t">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.</ref> 

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 [[NCAA Men's Division I Basketball Opening Round gameFirst Four]]<ref group="t">Starting in 2011, 68 teams will play in the Championship, with four "playin games" before the 64team first round.</ref> 

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 N/A 

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 Quadoctofinals<ref group="t">The number of eligible teams is typically less than 128, but more than 64, so not all teams play this round</ref> 

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} 

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{{reflistgroup="t"}} 

{{reflistgroup="t"}} 
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==Classification==<br />When matches are held to determine places or prizes lower than first and second (the loser of the finalround match gaining the latter position), these typically include a match between the losers of the semifinal matches called [[third place playoff]], 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 highestranked therein then playing for fifth and sixth places and the two lowest for seventh and eighth.

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==Seeding==<! This section is linked from [[FA Cup]] ><br />{{mainSeed (sports)}} 
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==Classification== 

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When matches are held to determine places or prizes lower than first and second (the loser of the finalround match gaining the latter position), these typically include a match between the losers of the semifinal matches called [[third place playoff]], 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 highestranked therein then playing for fifth and sixth places and the two lowest for seventh and eighth. 

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==Seeding==<! This section is linked from [[FA Cup]] > 

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{{mainSeed (sports)}} 

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Opponents may be allocated randomly (such as in the FA Cup); however, since the "luck of the draw" may result in the highestrated 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. 

Opponents may be allocated randomly (such as in the FA Cup); however, since the "luck of the draw" may result in the highestrated 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. 
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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 [[Grand Slam (tennis)Tennis Grand Slam]] tournaments, it is conceivable that the 33rdbest player in a 128player 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 headtohead matchups being repeated over and over again in successive tournaments.

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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 [[Grand Slam (tennis)Tennis Grand Slam]] tournaments, it is conceivable that the 33rdbest player in a 128player 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 headtohead matchups being repeated over and over again in successive tournaments. 

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Sometimes the remaining competitors in a singleelimination tournament will be "reseeded" so that the highest surviving seed is made to play the lowest surviving seed in the next round, the secondhighest plays the secondlowest, etc. This may be done after each round, or only at selected intervals. In American team sports, for example, both the [[NFL]] and [[National Hockey LeagueNHL]] employ this tactic, but the [[NBA]] does not (and neither does the [[NCAA Men's Division I Basketball ChampionshipNCAA college basketball tournament]]). [[Major League BaseballMLB]] does not have enough teams in its playoff tournament where reseeding 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 firstround series between the first and eighth seeds (within each of the two conferences the league has) to face the winner of the firstround 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 firstround 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 [[match fixingtank]] (deliberately lose) games, so as to finish sixth and thus avoid a possible matchup with the top seed until one round later. 

Sometimes the remaining competitors in a singleelimination tournament will be "reseeded" so that the highest surviving seed is made to play the lowest surviving seed in the next round, the secondhighest plays the secondlowest, etc. This may be done after each round, or only at selected intervals. In American team sports, for example, both the [[NFL]] and [[National Hockey LeagueNHL]] employ this tactic, but the [[NBA]] does not (and neither does the [[NCAA Men's Division I Basketball ChampionshipNCAA college basketball tournament]]). [[Major League BaseballMLB]] does not have enough teams in its playoff tournament where reseeding 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 firstround series between the first and eighth seeds (within each of the two conferences the league has) to face the winner of the firstround 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 firstround 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 [[match fixingtank]] (deliberately lose) games, so as to finish sixth and thus avoid a possible matchup with the top seed until one round later. 

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In some situations, a seeding restriction will be implemented; from 1975 until 1989, the [[National Football LeagueNFL]], and, since 1998, [[Major League BaseballMLB]] 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 secondbest division champion plays the wild card team. 

In some situations, a seeding restriction will be implemented; from 1975 until 1989, the [[National Football LeagueNFL]], and, since 1998, [[Major League BaseballMLB]] 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 secondbest division champion plays the wild card team. 
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==Evaluation==<br />The singleelimination 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.

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==Evaluation== 

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The singleelimination 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. 

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The format is less suited to games where [[tie (draw)draw]]s are frequent. In [[chess]], each fixture in a singleelimination tournament must be played over multiple matches, because [[draw (chess)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 (football)penalty shootout]], viewed by many fans as an unsatisfactory conclusion to a fixture, or by replaying the fixture. In various forms of [[limited overs cricketoneday]] [[cricket]], a [[bowlout]] has been used in recent years to settle tied matches. 

The format is less suited to games where [[tie (draw)draw]]s are frequent. In [[chess]], each fixture in a singleelimination tournament must be played over multiple matches, because [[draw (chess)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 (football)penalty shootout]], viewed by many fans as an unsatisfactory conclusion to a fixture, or by replaying the fixture. In various forms of [[limited overs cricketoneday]] [[cricket]], a [[bowlout]] has been used in recent years to settle tied matches. 

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Another perceived disadvantage is that most competitors are eliminated after relatively few games. Variations such as the [[doubleelimination tournament]] allow competitors a single loss while remaining eligible for overall victory. 

Another perceived disadvantage is that most competitors are eliminated after relatively few games. Variations such as the [[doubleelimination tournament]] allow competitors a single loss while remaining eligible for overall victory. 

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In a random knockout tournament (singleelimination 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 a random knockout tournament (singleelimination 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. 

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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.<ref name="ryv">{{cite weburl=http://www.cerge.cuni.cz/pdf/wp/Wp252.pdftitle=The Predictive Power of Noisy Elimination Tournamentslast=Ryvkinfirst=Dmitrydate=March 2005publisher=CERGEEIaccessdate=21 October 2010}}</ref> As a random factor is always present in a real world competition, this might easily cause accusations of unfairness. 

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.<ref name="ryv">{{cite weburl=http://www.cerge.cuni.cz/pdf/wp/Wp252.pdftitle=The Predictive Power of Noisy Elimination Tournamentslast=Ryvkinfirst=Dmitrydate=March 2005publisher=CERGEEIaccessdate=21 October 2010}}</ref> As a random factor is always present in a real world competition, this might easily cause accusations of unfairness. 
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==Other tournament systems==<br />Variations of the singleelimination tournament include:<br />*[[Doubleelimination tournament]]<br />Other common tournament types are<br />*[[Roundrobin tournament]]<br />*[[Swiss system tournament]]

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==References==<br />{{Reflist}}<br />{{competition}}<br />[[Category:Tournament systems]] 
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==Other tournament systems== 
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[[ca:Eliminació directa]]<br />[[cs:Vyřazovací systém]]<br />[[de:K.o.System]]<br />[[es:Eliminación directa]]<br />[[eo:Pokalo (konkurso)]]<br />[[ko:싱글 엘리미네이션 토너먼트]]<br />[[id:Sistem gugur]]<br />[[he:שיטת גביע]]<br />[[lt:Vieno minuso sistema]]<br />[[mr:नॉक आउट फेरी]]<br />[[nl:Knockoutsysteem]]<br />[[ja:トーナメント方式#勝ち残り式トーナメント]]<br />[[no:Cup]]<br />[[pl:System pucharowy]]<br />[[fi:Cup]]<br />[[sv:Cup]]<br />[[ta:ஒற்றை வெளியேற்றப் போட்டி]]<br />[[th:การแข่งขันแบบแพ้คัดออก]]<br />[[zh:单败淘汰制]]<br /> 

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Variations of the singleelimination tournament include: 

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*[[Doubleelimination tournament]] 

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Other common tournament types are 

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*[[Roundrobin tournament]] 

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*[[Swiss system tournament]] 

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==References== 

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{{Reflist}} 

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{{competition}} 

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[[Category:Tournament systems]] 

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[[Category:Tournament systems]] 

[[Category:National Football League]] 

[[Category:National Football League]] 