Tournament system with elimination after two defeats

Initial conditions

The number of tournament participants should be a power of two (8, 16, 32, 64, 128, and so on). If the number of participants differs from the correct one, you can apply this tournament scheme with the addition of fictitious ("empty") participants, to the nearest correct number. A participant who gets a game with an “empty” gets a technical victory in this round. In practice, the use of this scheme is convenient when the number of participants is exactly 8, 16, or more than 20. With less than 8 participants, it is better to play a round- robin tournament (the number of games will be acceptable), and for 9-15 or 17-19 players it is better use the Swiss system .

The tournament is divided into two grids - upper and lower (winners grid and losers grid). All participants start the tournament in the upper bracket. Participants are divided into pairs, who spend in the first round of the game among themselves. The selection procedure for pairs can be either random (by lot) or by ratings (in this case, usually pairs are made on the principle of “strong versus weak” so that the weakest participants drop out in the first rounds and the strongest play among themselves at the end of the tournament). In the presence of “empty” participants and selection by ratings, technical victories are awarded to the strongest participants.

Upper and Lower Grid Games

1. The winners of the first round go to the second round of the upper bracket. Losers go to the bottom grid.
2. In the lower bracket, the tournament starts from the second round. The selection of pairs of the second and next rounds can be built either “according to a rigid grid” (tournament grids are formed in advance and uniquely determine the formation of pairs), or selection by game results in this tournament (points, points, difference between goals scored and missed, etc.), or again by lot, with a mandatory limit: no one should play with the same opponent twice.
3. Starting from the second round, the game is played simultaneously in both grids:
   • The winner in the upper bracket moves to the next round in it.
   • The loser in the upper bracket moves to the next round in the lower bracket.
   • The winner in the lower bracket moves to the next round in it.
   • The loser in the lower bracket drops out of the tournament.
4. Games in both nets are held, depending on the rules, up to “rule 1-2” (when one participant remains in the upper bracket, two or more remain in the lower bracket) or to “2-2 rule” (two players in the upper bracket at the bottom - two or more). (“Rules” are designed to be better remembered by judges) .
   • "Rule 1-2." The winner of the upper bracket reaches the final. In the lower bracket, the players play the elimination, the winner of the lower bracket reaches the final, the loser of the last game in the lower bracket gets 3rd place.
   • "Rule 2-2." In the bottom bracket, up to 2 players are eliminated. Then the pairs in the upper and lower grid play among themselves. The winner of the upper bracket reaches the final. The loser in the bottom bracket gets 4th place. After that, the loser in the upper bracket plays with the winner from the bottom. The loser of this match takes third place, the winner - goes to the finals.
   • The rule of equality is an additional one, applied if necessary. In some rounds, games are held only in the lower bracket, until the number of participants in it becomes equal to the number of participants in the upper bracket (4-4, 8-8, 16-16 ...). Then the games in both grids continue until the rules “1-2” or “2-2”. Used with a large number of participants to avoid the award of technical victories.

Games in the upper and lower grids (option)

There is another version of the regulation. In it, the first three rules exactly correspond to the previous ones, but the organization of games in the second grid is fundamentally different. For each round in the upper grid in the bottom two are held:

• The first (of a pair) round of the lower bracket is held simultaneously with the round of the upper: players who remain in the bracket after the previous round play among themselves. Losers in the bottom bracket drop out of the tournament. Losers in the upper grid go to the bottom. As a result, there are half as few players in the upper bracket, and in the lower bracket their number remains the same (half dropped out, half moved from the upper bracket).
• Couples are made up of those who won the previous round of the lower bracket and those who crossed from the top. Between them is another round of elimination. The upper net does not play at this time. As a result, as many players remain in the lower grid as in the upper.

At the end of each round of the upper bracket and the corresponding pair of rounds of the lower bracket, an equal number of players appear in both grids. After the final rounds in both grids, there is one player each, they play the super final among themselves. The advantage of this system is that it works the same way for any number of participants, the disadvantage is the big difference in the number of parties that a participant must play in order to reach the final on the lower and upper grid.

Super Final

The final round is held between the winners of both grids, which may also be called the “super final” (then the last matches in each of the grids are called the “finals”). There are two options for the super final.

1. Game with handicap ( full double elimination ). The final round is held in one or two games, its goal is to ensure that one of the finalists has two defeats in the tournament.
   • If the winner of the upper bracket wins the first game, then he gets the first place, and his opponent - the second.
   • If the winner of the upper bracket loses the first game, the second game is held, the winner of which gets the first place, the loser - the second.
2. Playing without a handicap is a regular match (a series of several matches), the winner of the series becomes the winner of the tournament. Applied, for example, to The International .

Here is how the distribution of the number of participants in the grids looks for some variants of the number of participants (when using the first version of the regulation).

• (*) - rule 1-2 or 2-2 is reached, this and subsequent games, until the final ones, are held only in the lower bracket.
• (**) - after this round, if you follow the general rule, in the lower grid through the round you will have to assign technical victories. Therefore, here, according to the rule of equality, two rounds are held only in the lower grid - to position 4-4.
• (***) - according to the rule of equality, one round is conducted only in the lower grid; after it, the rest of the tournament repeats the tournament for 64 players.

In a tournament with up to two defeats, 2 n −1 or 2 n −2 games are played, ^[1] depending on the results of the super final. This is at least twice as much as in the Olympic system, and the number of tours is at least one more. In terms of speed, this tournament significantly exceeds the round robin and lags behind the playoffs a little. In terms of objectivity in the distribution of prizes, the double elimination tournament is better than the playoffs: if a participant who is objectively second in strength may not be among the winners in a knockout tournament, if he meets the strongest in the first rounds, then in a similar situation he will fall into the second bracket and, having passed it to the final, will be able to take the second or third place and even fight for the victory.

You may notice that in order to reach the super final in the lower bracket it is necessary to play more games than in the upper bracket (as shown in the examples above, for a tournament with 16 participants, the finalist of the lower bracket must play one game more, with 32 participants - already two, with 64 - by three, with 128 - by four). However, the top bracket is played by those who did not lose to anyone, and we can assume that a higher level of rivals compensates for the difference in the number of games. This drawback can be eliminated only by switching to spectacle systems; there is a theorem. ^[2]

Benefits

• Some holding systems automatically set a bronze medalist; you do not need a match for third place .
• It decreases the likelihood that a strong player, by some chance, prematurely leaves the tournament.
• Each, even the weakest outsider, before leaving the championship, will play two matches, and ¾ of all participants - three matches. In the Olympic system, it can be disappointing that a participant had to travel far and pay for the transportation of equipment, and as a result, he played only once - and there are half of them!
• It makes no sense for an athlete to lose; match-fixing is not encouraged.
• Extremely few matches between teams of different strengths; finals will be between two strong participants, and not between little-known outsiders.

Weaknesses

• Special requirements for the number of participants (ideally, the degree of two ). When using computer systems for conducting competitions, problems with the number of participants usually do not arise.
• Two athletes can meet each other twice (and sometimes even thrice).
• Most matches are held between outsiders and middle peasants and are interesting only for a narrow group of fans.
• It is difficult to ensure the transportation of participants from one sports arena to another. In the Olympic system, for example, four stadiums host different tournament branches up to the quarter finals, and then they are all taken to one stadium, where the semi-finals and the final play.
• In the handicap mode, one or two final matches are possible, therefore, if the match is long, there will be problems with pre-selling tickets to the finals, broadcast rights.
• Each match must end in victory or defeat. If, as in football , draws are frequent, you have to connect the mechanisms for resolving draws. However, the loss is not as fatal as in the Olympic system.

Resourcefulness

• Compared with the Swiss system, it is not necessary to use platforms, computers, etc., equal to half the number of participants. Practice has shown that if all participants cannot play at the same time, the first two days it is better to conduct qualifying rounds, due to the seeding of participants it is also possible to schedule a time that is more convenient for them. From the third day, 75% of the participants played continuously (and 25% took off).
• In Russian e-sports, this system is popular due to the use of sorting functions by random number RND in Microsoft Excel. However, the requirement of inadmissibility of re-play to the final (in the grid of participants with one defeat) was often not paid attention
• If 1-2 matches are delayed, then the draw can already be carried out, while the participants of the protracted match and their opponents are given a break. There is a possibility that the next matches will end earlier, and the delay will be leveled (or the game day will end). The rush is also associated with the fact that for computer sports the playground is rented for hours, but funds are not provided ^[3] . There were no significant prizes in the evening tournaments, and the absence of a break was less evil than disrupting the schedule of the tournament participants.

The two-defeat system is used in those sports where it is easy to play twice as many matches as in the Olympic system: either due to a short match, or due to the large number of arenas running in parallel. The system has become widespread in the following types of competitions:

• motor sports and motor sports ,
• darts
• judo
• eSports
• table tennis
• beach volleyball
• Russian billiards.

There is interest in it in other individual sports.

With a large number of participants it is rather difficult to make a competitive grid manually; you have to turn to computer systems for conducting competitions .