Asingle-elimination knockout, orsudden-death tournament is a type ofelimination tournament where the loser of a 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(s). Some match-ups may be a single match or several, for exampletwo-legged ties in European sports orbest-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, athird place playoff between losing semi-finalists. In a shootoutpoker 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 calledplayoffs.[1]
InEnglish, the round in which only eight competitors remain is generally called (with or without hyphenation) thequarter-final round; this is followed by thesemi-final round, in which only four are left, the two winners of which then meet in thefinal orchampionship round.
The round before the quarterfinals has multiple designations. Often it is called theround of sixteen,last sixteen, or (in South Asia)pre-quarterfinals. In many other languages the term for these eight matches translates toeighth-final (e.g., in these European languages: "huitième de finale" inFrench, "achtste finale" in Dutch,octavos de final inSpanish,Achtelfinale inGerman,åttondelsfinal inSwedish,ottavi di finale inItalian,oitavos-de-final inPortuguese,optimi de finală inRomanian,osmifinále inCzech,osemfinále inSlovak, andosmina finala inSerbo-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 calledround 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 abye, the round at which they enter may be named thefirst round, with the earlier matches called apreliminary round,qualifying round,opening round, or theplay-in games.
Examples of the diverse names given to concurrent rounds in various select disciplines:
| By competitors | Fraction of final | Grand Slam tennis[t 1] | FA Cup football | Coupe de France[2] | NCAA Men's Basketball | North American Debating Championship | Snooker |
|---|---|---|---|---|---|---|---|
| Round of 2 | Final | Final | Final | Final | National Championship | Final | Final |
| Round of 4 | Semifinals | Semifinals | Semi-finals | Semifinals | Final Four (National semifinals)[t 2] | Semifinals | Semi-finals |
| Round of 8 | Quarterfinals | Quarterfinals | quarter-finals[t 3] | Quarterfinals | Elite Eight (Regional finals)[t 4] | Quarterfinals | Quarter-finals |
| Round of 16 | Octofinals | Round of 16 (US Open[4]), 4th round[5][citation needed] | 5th round[t 5] | 8th-finals | Sweet Sixteen (Regional semifinals)[t 6] | Round 7 | Last 16, 4th Round[citation needed] |
| Round of 32 | 16th-finals | 3rd round | 4th round[t 5] | 16th-finals | 3rd/2nd round[t 7][t 8] | Round 6 | Last 32, 3rd Round |
| Round of 64 | 32nd-finals | 2nd round | 3rd round[t 5] | 32nd-finals | 2nd/1st round[t 7][t 8] | Round 5 | Last 64, 2nd Round |
| Round of 128 | 64th-finals | 1st round | 2nd round[t 9][t 5] | 8th qualifying round[t 10] | First Four[t 7] | Round 4[t 11] | Last 128, 1st Round |
Notes:
The knockout round of the2002 FIFA World Cup tournament:
| Round of 16 | Quarter-finals | Semi-finals | Final | |||||||||||
| 15 June –Seogwipo | ||||||||||||||
 Germany | 1 | |||||||||||||
| 21 June –Ulsan | ||||||||||||||
 Paraguay | 0 | |||||||||||||
| Germany | 1 | |||||||||||||
| 17 June –Jeonju | ||||||||||||||
 United States | 0 | |||||||||||||
 Mexico | 0 | |||||||||||||
| 25 June –Seoul | ||||||||||||||
| United States | 2 | |||||||||||||
| Germany | 1 | |||||||||||||
| 16 June –Suwon | ||||||||||||||
 South Korea | 0 | |||||||||||||
 Spain (p) | 1 (3) | |||||||||||||
| 22 June –Gwangju | ||||||||||||||
 Republic of Ireland | 1 (2) | |||||||||||||
| Spain | 0 (3) | |||||||||||||
| 18 June –Daejeon | ||||||||||||||
| South Korea (p) | 0 (5) | |||||||||||||
| South Korea (a.s.d.e.t.) | 2 | |||||||||||||
| 30 June –Yokohama | ||||||||||||||
 Italy | 1 | |||||||||||||
| Germany | 0 | |||||||||||||
| 15 June –Niigata | ||||||||||||||
 Brazil | 2 | |||||||||||||
 Denmark | 0 | |||||||||||||
| 21 June –Shizuoka | ||||||||||||||
 England | 3 | |||||||||||||
| England | 1 | |||||||||||||
| 17 June –Kobe | ||||||||||||||
| Brazil | 2 | |||||||||||||
| Brazil | 2 | |||||||||||||
| 26 June –Saitama | ||||||||||||||
 Belgium | 0 | |||||||||||||
| Brazil | 1 | |||||||||||||
| 16 June –Ōita | ||||||||||||||
 Turkey | 0 | Third place play-off | ||||||||||||
 Sweden | 1 | |||||||||||||
| 22 June –Osaka | 29 June –Daegu | |||||||||||||
 Senegal (a.s.d.e.t.) | 2 | |||||||||||||
| Senegal | 0 | South Korea | 2 | |||||||||||
| 18 June –Miyagi | ||||||||||||||
| Turkey (a.s.d.e.t.) | 1 | Turkey | 3 | |||||||||||
 Japan | 0 | |||||||||||||
| Turkey | 1 | |||||||||||||
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, 1 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 calledthird 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. TheFIFA World Cup has long featured the third place match (since1934), though theUEFA Euro has not held one since the1980 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 theWedderburn–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.
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.[citation needed]
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 theWorld Snooker Championship and 32 seeds in theWorld Darts Championship.[citation needed] 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.[citation needed] This may result in some brackets consisting of stronger players than other brackets, and since only the top 32 players of 128 are seeded inTennis 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. 33Florian Mayer was drawn against, and defeated by, World No. 1Novak Djokovic in the first round of the2013 Wimbledon Championships,[8] in what was also a rematch of a quarter-final from the previous year.[citation needed]
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, theNFL employs this tactic, butMLS,NHL and theNBA do not (and neither does theNCAA college basketball tournament).[citation needed] AlthoughMLB does have enough teams (12) in its playoff tournament where re-seeding would have made a large difference in the match-ups; 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 totank (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.[citation needed]
In some situations, a seeding restriction may be implemented; from 1975 until 1989 in theNFL, and from 1994 until 2011 inMLB 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 internationalfencing competitions, it is common to have agroup 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.
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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. If a small number of teams play in a single elimination tournament, sometimes a consolation bracket is included to allow the eliminated teams to play more than once. This was the format of theLittle League World Series until 1992.
The format is less suited to games wheredraws are frequent. Inchess, each fixture in a single-elimination tournament must be played over multiple matches, becausedraws are common, and because white has an advantage over black. Inassociation football, games ending in a draw may be settled in extra time and eventually by apenalty shootout or by replaying the fixture.
Another perceived disadvantage is that most competitors are eliminated after relatively few games. Variations such as thedouble-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 single-elimination tournament without any seeding, awarding the second place to the loser of the final is unjustified: any of the competitors knocked out before getting to play the losing finalist might have been stronger than the actual 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 ofround-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.[9][10] As a random factor is always present in a real-world competition, this might easily cause accusations of unfairness.
Variations of the single-elimination tournament include:
Other common tournament types include: