# Double-elimination tournament

A double elimination bracket from the 2004 National Science Bowl

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.

One method of arranging a double-elimination tournament is to break the competitors into two sets of brackets, the Winners Bracket and Losers Bracket (W and L Brackets for short; also sometimes Upper Bracket and Lower Bracket, respectively) after the first round. The first round winners proceeding into the W Bracket and the losers proceeding into the L Bracket. The W Bracket is conducted in the same manner as a single-elimination tournament, except that the losers of each round "drop down" into the L Bracket. Another method of double elimination tournament management is the Draw and Process.

As with single-elimination tournaments, most often the number of competitors is equal to a power of two (8, 16, 32, etc.) so that each round there are an even number of competitors and never any byes. The maximum number of games in a double elimination tournament is one less than twice the number of teams participating (e.g., 8 teams – 15 games). The minimum number is two less than twice the number of teams (e.g., 8 teams – 14 games).

## Conducting the tournament

If the Bracket arrangement is being used then each round of the L Bracket is conducted in two stages; a minor stage followed by a major stage. Both contain the same number of matches (assuming there are no byes) which is the same again as the number of matches in the corresponding round of the W Bracket. If the minor stage of an L Bracket round contains $N$ matches, it will produce $N$ winners. Meanwhile, the $N$ matches in the corresponding round of the W Bracket will produce $N$ losers. These $2N$ competitors will then pair off in the $N$ matches of the corresponding major stage of the L Bracket.

For example, in an eight-competitor double-elimination tournament, the four losers of the first round, W Bracket quarter finals, pair off in the first stage of the L Bracket, the L Bracket minor semifinals. The two losers are eliminated, while the two winners proceed to the L Bracket major semifinals. Here they will contest the two losers of the W Bracket semifinals. The winners of the L Bracket major semifinals contest the L Bracket minor-final, with the winner playing the loser of the W Bracket final in the L Bracket major final.

The championship finals of a double elimination tournament is usually set up to be a possible two games. The rationale is that since the tournament is indeed double elimination, it is unfair to have the W Bracket champion eliminated with its first loss. Therefore, while the W Bracket champion needs to beat the L Bracket champion only once to win the tournament, the L Bracket champion must beat the Winners' Bracket champion twice.

A Draw and Process tournament requires less intervention by the manager. The competitors are allocated their first round positions on the competition grid and this is played as if it were a single elimination event. This grid is called the "Draw". A second competition grid called the "Process" is then produced and again playes as a single elimination event. The fixed arrangement of the Process ensures that players who met in the first round of the Draw cannot meet until the final of the Process. Similarly, players who meet in the second round of the Draw cannot meet until the semi finals of the Process. If the same person wins both the Draw and Process then they are the overall winner and the losing finalists will play each other for second and third place. Otherwise the winners of the Draw and Process will play off to determine the winner.[1]

## Pros and cons

The double-elimination format has some advantages over the single-elimination format, most notably the fact that third and fourth places can be determined without the use of a consolation or "classification" match involving two contestants who have already been eliminated from winning the championship.

Some tournaments, such as in tennis, will use "seeding" to prevent the strongest contestants from meeting until the later round. However, in tournaments where contestants are placed randomly in the draw, or in situations where seeding is not available, it is possible for 2 of the strongest teams to meet in the early rounds rather than a final or semifinal as would be expected in a seeded draw. Double elimination overcomes this shortfall by allowing a strong team which loses early to work their way through the L Bracket and progress to the later rounds, despite meeting the strongest team in the early rounds of competition.

Another advantage of the double-elimination format is the fact that all competitors will play at least twice and approximately three quarters will play three games or more. In a single-elimination tournament with no byes, half of the competitors will be eliminated after their first game. This can be disappointing to those who had to travel to the tournament and were only able to play once.

A disadvantage compared to the single-elimination format is that at least twice the number of matches have to be conducted. Since each player has to lose twice and since the tournament ends when only one player remains, in a tournament for $n$ competitors there will be either $2n-2$ or $2n-1$ games depending on whether or not the winner was undefeated during the tournament.

It is possible for the Championship finals to be determined by just a single match if the W Bracket winner defeats the L Bracket winner. It is therefore unknown, until this match has been concluded, whether the final scheduled match will in fact be required. This can be seen as a disadvantage of the system, particularly if broadcasting and ticket sales companies have an interest in the tournament.

## Examples of use

The best-known athletic event that employs a double-elimination format is the NCAA baseball tournament, including the College World Series, where a team is not eliminated until it loses twice in each of the four rounds (regional, super regional, College World Series, and CWS championship, with the super regional and CWS championship series featuring two teams in a best 2-of-3 format). The NCAA softball tournament (including the Women's College World Series) uses the same format.

It is also extensively used in video game tournaments and table football tournaments. Double-elimination brackets are also popular in amateur wrestling of all levels, surfing and kiteboarding freestyle competitions, as well as Curling bonspiels (where triple-elimination is also used), Hardcourt Bike Polo. The World Baseball Classic used a double-elimination format for its second rounds of the tournament in 2009 and 2013, as well as in its first round in 2009. The Little League World Series also switched from round-robin to double-elimination formats for each of its pools starting in 2010 in an effort to eliminate meaningless games.

It is also used, in modified form, in the All-Ireland Senior Gaelic Football Championship and All-Ireland Senior Hurling Championship.

## Variations

In Judo, players that end up in the L bracket can finish in third place at best. The winner of the W bracket will win the tournament, with the losing finalist finishing second. The other losers of the W bracket will end up in the L bracket, which will only be played to the minor stage of the final, resulting in two 3rd placed players. Thus, compared to double elimination, there is no major stage of the L Bracket final played, and there is no game between the winners of the W and L Brackets.

Another aspect of the system used in Judo is that losers of the first round (of the W bracket) only advance to the L bracket if the player they lost to wins his or her second round match. If a player loses to a second round loser, they are eliminated from the tournament.

Another variant, called the (third-place) challenge, is used, particularly in scholastic wrestling. The winner of the L bracket may challenge the loser of the finals in the W bracket, if and only if the two contestants had not faced each other previously; if the challenger (the winner of the L bracket) wins, he is awarded second place, and the loser of the W final is dropped to third place. This system is used particularly where the top two places advance to a higher level of competition (example: advancement from a regional tournament to a state tournament).

Another is the balanced variant which is a bracket arrangement that is not strictly divided into two brackets based on number of losses.[2] Players with different numbers of losses can play each other in any round. A goal of the variant is that no player sits idle for more than one round consecutively. The added complexity of the brackets is handled by using "if necessary" matches. The flexible approach allows practical bracket designs to be made for any number of competitors including odd numbers (9, 10, 11, 12, 13, etc.).

A possible alternative is a single-elimination format where each match is a best-of-5 or best-of-7 series. This format still allows a competitor to lose (perhaps multiple times) while still remaining eligible to win the tournament. Of course, having multiple games in each series also requires considerably more games to be conducted.

Another is the modified single elimination tournament which guarantees at least two games per competitor, but not necessarily two losses for elimination. The brackets are similar to the double elimination format, except the two finalists from the L bracket (each with one loss) face the two finalists from the W bracket (neither with a loss) in a single elimination semi-final and final.

The College World Series has frequently tried to modify the double-elimination format to set up, if possible, a single championship game. Until 1988, the College World Series did this by adding an extra round to the L Bracket. What would be the L Bracket major semifinals (i.e. the round where the W Bracket semifinal losers dropped down) became the L Bracket quarterfinals. The winners would then progress to the L Bracket semifinals against the two participants in the W Bracket final (i.e. the WINNERS of the W Bracket semifinals drop down). This thus left open the possibility that the W Bracket champion would pick up a loss, albeit in the L Bracket semifinal. If, however, the W Bracket champion prevailed in the L Bracket semifinal, the same two-game final setup existed in effect, albeit not in practice ... for under the CWS pre-1988 version, the unbeaten W Bracket champion would be playing a once-beaten L Bracket opponent in the L Bracket final, with the winner to advance to play the unbeaten W Bracket champion in the finals (if necessary). The CWS subsequently broke up its eight-team field into two four-team double elimination tournaments, with the winners meeting in either a sudden-death or, currently, a best-of-three final.

A way to reduce the number of rounds is to do cross-bracket elimination in the last rounds. For instance, in a double-elimination tournament of eight teams, you could have both the winner and the loser of the W Bracket final join the third round of the L Bracket, the winner facing the lowest-seeded L Bracket team or crossing inversely how W Bracket semifinal losers are placed in L Bracket. If the W Bracket team wins, there will be two teams left and they will go straight to the finals (with the W Bracket team having a one game advantage as usual). However, if the W Bracket team loses then three teams will still be in the tournament, all with one loss. Usually in the subsequent fifth round either the last W Bracket team that just lost has a bye round or the top seed remaining will have a bye, while the other two teams square off. This leaves two teams for a one game final in the sixth and last round. Whether the W Bracket team wins or loses in round four, this cross-bracket procedure shortens an eight team double elimination tournament from 6–7 rounds to 5–6 rounds. This system also gives more odds to a single game final (75% of situations, instead the ordinary 50%)

## Other tournament systems

Variations of the double-elimination tournament include:

Other common tournament types are