Double-elimination tournament

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A double elimination bracket from the 2004 National Science Bowl

A double-elimination tournament is a 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.

A double-elimination tournament is broken 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 winners proceed into the W Bracket and the losers proceed 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.

As with single-elimination tournaments, most often the number of competitors is equal to a power of 2 (4, 8, 16, etc) so that there are an even number of competitors at every round.

1 Conducting the tournament
2 Pros and cons
3 Variations
4 Other tournament systems
5 References
6 External links

[edit] Conducting the tournament

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), the second stage consisting of the winners of the first stage against the losers of that same round of the W Bracket. This is to allow the losers of each stage of the W Bracket to "filter down" into the L Bracket.

For example, in an 8-competitor double-elimination tournament, the losers of the first round enter the first stage of the L Bracket --- the L Bracket quarterfinals --- and compete against each other. The losers are eliminated, while the winners proceed to the second stage of the L Bracket --- the L Bracket semifinals --- to face the losers of the W Bracket semifinals. The winners of the L Bracket semifinals proceed to the L Bracket finals, with the winner of that game being the Losers' Bracket champion.

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.

In some tournaments, however, the final game is always winner-take-all, or always a best-of-three set of games, with the usual advantage of the last Winner's Bracket team ignored. If the losers bracket champion should win the final, the rationale is that while both teams lost only a single game in the tournament, the losers bracket champion defeated the winners bracket champion, and is thus the better team.

[edit] 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 better 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.

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 2*N-1 (or 2*N-2 in case the winner was undefeated during the tourney) games; a plausible 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 disavantage, particularly if broadcasting and ticket sales companies have an interest in the tournament.

The most well-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 2-of-3 series, College World Series, and then championship 2-of-3 series). 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 as well as Curling bonspiels (where triple-elimination is also used).

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

[edit] 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^[1]. 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.).

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 one-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. 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.