Single-elimination tournament
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]
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.
Variations of the single-elimination tournament include:
Other common tournament types include: