Double-elimination tournament

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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 of course 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 2 (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, the first stage consisting of the winners of the previous stage (or losers of the very first round of competition) playing their matches, the second stage consisting of the winners of the first stage against the losers of that same round of the W Bracket playing their matches. This is to allow the losers of each stage of the W Bracket to "filter down" into the L Bracket.

For example, in an eight-competitor double-elimination tournament, the losers of the first round enter the first stage of the L Bracket – the L Bracket pre-quarter-finals – and compete against each other. The losers are eliminated, while the winners proceed to the second stage of the L Bracket – the L Bracket quarter-finals – to face the losers of the W Bracket semifinals. The winners of the L Bracket semifinals proceed to the L Bracket semi-final, with the winner of that game playing against the winners final losers in the L bracket 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 Winners' Bracket champion eliminated with its first loss. Therefore, while the Winners' Bracket champion needs to beat the Losers' Bracket champion only once to win the tournament, the Losers' Bracket champion must beat the Winners' Bracket champion twice. Some tournaments, however, ignore this advantage for the Winners' Bracket champion and make the final game winner-take-all or always a best-of-three set of games.

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 life event. A second grid is then produced with the competitors placed in a fixed arrangement which ensures that they cannot play the same opponents as they met in the draw. This is also played out as a single life competition. If the same person wins both 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 both halves play each other for first place.[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. Additionally, in a double-elimination format better teams are likely to progress further in the tournament. Suppose in a single-elimination tournament the best team plays the second best team in the first round—the second best team will be eliminated right away, having only played one game. Then, a more mediocre team with a more favorable seeding could potentially win several games, play the best team in the finals, and come away with second place. (Usually, good seeding would help avoid this, but it is an issue nonetheless.) A double-elimination tournament would allow the second best team to keep winning (in the loser's bracket) and eventually work their way back up to their rightful position of second place.

Another advantage of the double-elimination format is the fact that all competitors will play at least twice and most 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 a considerably greater 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 tournament for $n$ competitors there will be $2n-1$ (or $2(n-1)$ in case the winner was undefeated during the tournament) games; 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. The fact that the final game in the tournament may be unnecessary is also a disadvantage, particularly if broadcasting and ticket sales companies have an interest in the tournament. Another alternative is a "modified single elimination" format which guarantees at least two games for each participant, but does not guarantee two losses for elimination.

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 computer gaming tournaments (most famously by the Cyberathlete Professional League) 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

Some variations on double elimination are used. For example, in Judo, players that end up in the L bracket can finish third 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 first stage of the final, resulting in two 3rd placed players. Thus, compared to the standard double elimination, there is no second stage of the final of the L bracket played, and there is no game between the winners of the W and L bracket.

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.).

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 Losers' Bracket. What would be the Losers' Bracket semifinals (i.e., the round where the Winners' Bracket semifinal losers dropped down) became the Losers' Bracket quarterfinals, with the Losers' Bracket semifinals having the two participants in the Winners' Bracket final (i.e., the WINNERS of the Winners' Bracket semifinals) drop down. This thus left open the possibility that the Winners' Bracket champion would pick up a loss, albeit in the Losers' Bracket semifinal. If, however, the Winners' Bracket champion prevailed in the Losers' Bracket semifinal, the same two-game final setup existed in effect, albeit not in practice ... for under the CWS pre-1988 version, the unbeaten Winners' Bracket champion would be playing a once-beaten Losers' Bracket opponent in the Losers' Bracket final, with the winner to advance to play the unbeaten Winners' 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 Upper Bracket final join the third round of the Lower Bracket, the winner facing the lowest-seeded Loser's Bracket team or crossing inversely how winners bracket semifinal losers are placed in losers bracket. If the Winner's Bracket team wins, there will be two teams left and they will go straight to the finals (with the Winner's Bracket team having a one game advantage as usual). However, if the Winner's 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 Winner's 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 Winner's 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