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55-564: The tournament is held under round-robin rules, with 2 points for a win, 1 for a draw, and 0 for a loss; in earlier tournaments, only a time limit draw would provide the one point, with other methods (such as a Double Disqualification and Double Countouts) providing nothing for either team. The name "Real World Tag League" was a mistranslation by AJPW promoter Giant Baba ; "saikyō" in Japanese means "strongest," not "real", but Baba used Engrish for promotional material. Between 1988 and 1994,

110-463: A bye . The schedule can therefore be computed as though the dummy were an ordinary player, either fixed or rotating. Instead of rotating one position, any number relatively prime to ( n − 1 ) {\displaystyle (n-1)} will generate a complete schedule. The upper and lower rows can indicate home/away in sports, white/black in chess , etc.; to ensure fairness, this must alternate between rounds since competitor 1

165-464: A bye. If the number is even, an added player (ω) becomes the opponent. For an even number n {\displaystyle n} or an odd number n − 1 {\displaystyle n-1} of competitors, Schurig builds a table with n / 2 {\displaystyle n/2} vertical rows and n − 1 {\displaystyle n-1} horizontal rows. Then he populates it starting from

220-411: A competitor to play the strongest opponents in a round robin in quick succession while others play them intermittently with weaker opposition. This asymmetry means that playing the same opponents is not necessarily completely equitable. There is also no scheduled showcase final match unless (by coincidence) two competitors meet in the last match of the tournament, with the result of that match determining

275-477: A competitor's chance of ultimate victory. Final records of participants are more accurate, in the sense that they represent the results over a longer period against the same opposition. The system is also better for ranking all participants, not just determining the winner. This is helpful to determine the final rank of all competitors, from strongest to weakest, for purposes of qualification for another stage or competition as well as for prize money. In team sports,

330-998: A large number of competitive matches per season, double round-robins are common. Most association football leagues in the world are organized on a double round-robin basis, in which every team plays all others in its league once at home and once away. This system is also used in qualification for major tournaments such as the FIFA World Cup and the continental tournaments (e.g. UEFA European Championship , CONCACAF Gold Cup , AFC Asian Cup , CONMEBOL Copa América and CAF Cup of Nations ). There are also round-robin cricket , bridge , chess , draughts , go , ice hockey , curling , and Scrabble tournaments. The World Chess Championship decided in 2005 and in 2007 on an eight-player double round-robin tournament where each player faces every other player once as white and once as black. There has been several major international cricket tournaments held in this format including ICC events, including

385-489: A lower-placed qualifier is perceived to be easier than for a higher-placed one). Four pairs in the 2012 Olympics Women's doubles badminton , having qualified for the next round, were ejected from the competition for attempting to lose in the round robin stage to avoid compatriots and better ranked opponents. The round robin stage at the Olympics was a new introduction, and these potential problems were readily known prior to

440-719: A neck injury and was replaced by Kenso . The 2014 Tag League, featuring 8 teams, took place from November 16 to December 6. Atsushi Aoki and Hikaru Sato earned a spot in the tournament by winning the 2014 Jr. Tag Battle of Glory in October. The tournament was contested for the World Tag Team Championship , which Jun Akiyama and Takao Omori vacated on October 23 in time for the tournament. The 2015 World's Strongest Tag Determination League took place from November 23 to December 6. After their win, Suwama and Miyahara turned on each other. The 2016 edition of

495-437: A round in which players meets each other. For example, player 7 plays against player 11 in round 4. If a player meets itself, then this shows a bye or a game against player n. All games in a round constitutes a diagonal in the table. The above schedule can also be represented by a graph, as shown below: Both the graph and the schedule were reported by Édouard Lucas in as a recreational mathematics puzzle. Lucas, who describes

550-497: A round, a non-leftmost position (not including 1 {\displaystyle 1} ) can only be taken by competitors of a fixed distance. In round 1 {\displaystyle 1} of the example, in the second position competitor 2 {\displaystyle 2} plays against 13 {\displaystyle 13} , their distance is 2 {\displaystyle 2} . In round 2 {\displaystyle 2} , this position

605-540: A schedule where player 14 has a fixed position, and all other players are rotated counterclockwise n 2 {\displaystyle {\frac {n}{2}}} positions. This schedule is easily generated manually. To construct the next round, the last player, number 8 in the first round, moves to the head of the table, followed by player 9 against player 7, player 10 against 6, until player 1 against player 2. Arithmetically, this equates to adding n 2 {\displaystyle {\frac {n}{2}}} to

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660-619: A straight knockout system. The top one, two, or occasionally three teams in these groups then proceed to a straight knockout stage for the remainder of the tournament. In the circle of death it is possible that no champion emerges from a round-robin tournament, even if there is no draw, but most sports have tie-breaker systems which resolve this. Round-robins can suffer from being too long compared to other tournament types, and with later scheduled games potentially not having any substantial meaning. They may also require tie-breaking procedures. Swiss system tournaments attempt to combine elements of

715-526: A table. In France this is called the Carousel -Berger system (Système Rutch-Berger). The schedule can also be used for "asynchronous" round-robin tournaments where all games take place at different times (for example, because there is only one venue). The games are played from left to right in each round, and from the first round to the last. When the number of competitors is even, this schedule performs well with respect to quality and fairness measures such as

770-416: A tournament of 16 teams can be completed in just 4 rounds (i.e. 15 matches) in a knockout format; a double elimination tournament format requires 30 (or 31) matches, but a round-robin would require 15 rounds (i.e. 120 matches) to finish if each competitor faces each other once. Other issues stem from the difference between the theoretical fairness of the round robin format and practice in a real event. Since

825-508: A variety of tiebreaker criteria. Frequently, pool stages within a wider tournament are conducted on a round-robin basis. Examples with single round-robin scheduling include the FIFA World Cup , UEFA European Football Championship , and UEFA Cup (2004–2009) in football, Super Rugby ( rugby union ) in the Southern Hemisphere during its past iterations as Super 12 and Super 14 (but not in its later 15- and 18-team formats),

880-613: Is a simple algorithm to create a schedule for a round-robin tournament. All competitors are assigned to numbers, and then paired in the first round: Next, one of the competitors in the first or last column of the table is fixed (number one in this example) and the others rotated clockwise one position: This is repeated until when the next iteration would lead back to the initial pairings: With an even number n {\displaystyle n} of competitors this algorithm realizes every possible combination of them (equivalently, that all pairs realized are pairwise different). First,

935-435: Is always on the first row. If, say, competitors 3 and 8 were unable to fulfil their fixture in the third round, it would need to be rescheduled outside the other rounds, since both competitors would already be facing other opponents in those rounds. More complex scheduling constraints may require more complex algorithms. This schedule is applied in chess and draughts tournaments of rapid games, where players physically move round

990-507: Is derived from the French term ruban ('ribbon'). Over time, the term became idiomized to robin . In a single round-robin schedule, each participant plays every other participant once. If each participant plays all others twice, this is frequently called a double round-robin . The term is rarely used when all participants play one another more than twice, and is never used when one participant plays others an unequal number of times, as

1045-691: Is even, then in each of ( n − 1 ) {\displaystyle (n-1)} rounds, n 2 {\displaystyle {\begin{matrix}{\frac {n}{2}}\end{matrix}}} games can be run concurrently, provided there exist sufficient resources (e.g. courts for a tennis tournament). If n {\displaystyle n} is odd, there will be n {\displaystyle n} rounds, each with n − 1 2 {\displaystyle {\begin{matrix}{\frac {n-1}{2}}\end{matrix}}} games, and one competitor having no game in that round. The circle method

1100-1054: Is held by competitors 14 {\displaystyle 14} and 12 {\displaystyle 12} , also having distance 2 {\displaystyle 2} , etc. Similarly, the next position ( 3 {\displaystyle 3} against 12 {\displaystyle 12} in round 1 {\displaystyle 1} , 2 {\displaystyle 2} against 11 {\displaystyle 11} in round 2 {\displaystyle 2} , etc.) can only hold distance- 4 {\displaystyle 4} competitors. For every k < n 2 {\displaystyle k<{\frac {n}{2}}} , there are exactly n − 1 {\displaystyle n-1} pairs of distance k {\displaystyle k} . There are n − 1 {\displaystyle n-1} rounds and they all realize one distance- k {\displaystyle k} pair at

1155-485: Is the case in almost all of the major North American professional sports leagues. In the United Kingdom , a round-robin tournament has been called an American tournament in sports such as tennis or billiards which usually have single-elimination (or "knockout") tournaments, although this is now rarely done. A round-robin tournament with four players is sometimes called "quad" or "foursome". In sports with

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1210-408: Is the fairest way to determine the champion from among a known and fixed number of contestants. Each contestant, whether player or team, has equal chances against all other opponents because there is no prior seeding of contestants that will preclude a match between any given pair. The element of luck is seen to be reduced as compared to a knockout system since one or two bad performances need not ruin

1265-574: The 2025 ICC Champions Trophy . In a more extreme example, the KBO League in baseball plays a 16-fold round robin, with each of the 10 teams playing each other 16 times for a total of 144 games per team. LIDOM (Baseball Winter League in the Dominican Republic) plays an 18-fold round robin as a semi final tournament between four classified teams. Group tournaments rankings usually go by number of matches won and drawn, with any of

1320-656: The Cricket World Cup along with Indian Premier League , major Twenty-20 Cricket tournament, and many American football college conferences , such as the Conference USA (which currently has 9 members). The group phases of the UEFA club competitions and Copa Libertadores are contested as a double round-robin, as are most basketball leagues outside the United States, including the regular season of

1375-536: The EuroLeague (as well as its former Top 16 phase); the United Football League has used a double round-robin for both its 2009 and 2010 seasons. Season ending tennis tournaments also use a round robin format prior to the semi on stages. The champion in a round-robin tournament is the contestant that wins the most games, except when draws are possible. In theory, a round-robin tournament

1430-425: The World Tag Team Championship was annually vacated in time for the tournament, which would be used to determine the new champions. The rule was reinstated for the 2012 tournament, but was again ignored the following year, but was reinstated in 2014. In 2000 and 2015 the vacancy was determined by separate post-tournament playoffs between the 2nd and 3rd places. Ten-Koji ( Hiroyoshi Tenzan and Satoshi Kojima ) are

1485-560: The World Strongest Tag Determination League took place from December 3 through December 18. The 2017 edition of the World Strongest Tag Determination League took place from November 19 through December 12. The 2018 edition of the World Strongest Tag Determination League took place from November 13 through December 11. The 2019 edition of the World Strongest Tag Determination League took place from November 11 through December 9. The 2020 edition of

1540-419: The World Strongest Tag Determination League, featured 8 teams in a single block, taking place from November 18 to December 7. The tournament featured outside participation from Big Japan Pro Wrestling 's Daisuke Sekimoto and Abdullah Kobayashi and from Pro Wrestling Zero1 's Masato Tanaka . On November 17, it was announced that Zeus had tested positive for coronavirus (COVID-19), leading him to pull out of

1595-446: The algorithm obviously realizes every pair of competitors if one of them equals 1 {\displaystyle 1} (the non-moving competitor). Next, for pairs of non- 1 {\displaystyle 1} competitors, let their distance be the number k < n 2 {\displaystyle k<{\frac {n}{2}}} of times the rotation has to be carried out in order that one competitor arrives at

1650-540: The amount of rest between games. On the other hand, when the number of competitors is odd, it does not perform so well and a different schedule is superior with respect to these measures. Alternatively Berger tables, named after the Austrian chess master Johann Berger , are widely used in the planning of tournaments. Berger published the pairing tables in his two Schach-Jahrbücher (Chess Annals), with due reference to its inventor Richard Schurig. This constitutes

1705-435: The championship. A notable instance of such an event was the 1950 FIFA World Cup match between Uruguay and Brazil . Further issues arise where a round-robin is used as a qualifying round within a larger tournament. A competitor already qualified for the next stage before its last game may either not try hard (in order to conserve resources for the next phase) or even deliberately lose (if the scheduled next-phase opponent for

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1760-462: The final, became Brody's new regular tag team partner beginning the following year. The 1982 Tag League, featuring 7 teams, was held from November 26 to December 13. The 1983 Tag League, featuring 8 teams, was held from November 25 to December 12. The 1984 Tag League, featuring 8 teams, was held from November 22 to December 12. The 1985 Tag League, featuring 8 teams, was held from November 23 to December 12. The 1986 Tag League, featuring 9 teams,

1815-402: The final, contested for the vacant World Tag Team Championship . Kenso and Great Sasuke were forced to pull out of the tournament and forfeit all of their matches after Sasuke suffered a shoulder injury. The 2013 Tag League, featuring 8 teams, will be held from November 30 to December 8. Bambi Killer was originally scheduled to take part in the tournament, but was forced to pull out due to

1870-403: The method as simple and ingenious , attributes the solution to Felix Walecki, a teacher at Lycée Condorcet . Lucas also included an alternative solution by means of a sliding puzzle . To easily remember this method, the following mnemonic can be used. Starting from the first round, the next round is constructed: and then, If the number of players is odd, the player in the first venue gets

1925-751: The only team to win both the World's Strongest Tag Determination League and its counterpart in New Japan Pro-Wrestling , the World Tag League , as well as the only team to win both tournaments in the same year (2008). The 1977 Tag League, featuring 9 teams, was held from December 2 to December 15. The 1978 Tag League, featuring 6 teams, was held from December 1 to December 15. Abdullah the Butcher used both The Sheik and Tor Kamata as partners. The 1979 Tag League, featuring 7 teams,

1980-496: The position the other had. In the example given ( n = 14 {\displaystyle n=14} ), 2 {\displaystyle 2} has distance 1 {\displaystyle 1} to 3 {\displaystyle 3} and to 14 {\displaystyle 14} and it has distance 6 {\displaystyle 6} to 8 {\displaystyle 8} and to 9 {\displaystyle 9} . In

2035-400: The previous row, with the exception of player n {\displaystyle n} . When the result of the addition is greater than ( n − 1 ) {\displaystyle (n-1)} , then subtract ( n − 1 ) {\displaystyle (n-1)} from the sum. This schedule can also be represented as a (n-1, n-1) table, expressing

2090-414: The previous year, the top four teams faced off in the semifinals as a result of a four-way tie. The 2002 Tag League, featuring 8 teams, was held from November 23 to December 6. The 2003 Tag League, featuring 7 teams, was held from November 22 to December 2. The 2004 Tag League was held from November 21 to December 1. It was the first to utilize a multi-block system, featuring 10 teams in two blocks, with

2145-406: The round-robin and elimination formats, to provide a worthy champion using fewer rounds than a round-robin, while allowing draws and losses. The main disadvantage of a round robin tournament is the time needed to complete it. Unlike a knockout tournament where half of the participants are eliminated after each round, a round robin requires one round less than the number of participants. For instance,

2200-525: The round-robin major league champions are generally regarded as the "best" team in the land, rather than the cup winners, whose tournaments usually follow a single-elimination format. Moreover, in tournaments such as the FIFA or ICC World Cups, a first round stage consisting of a number of mini round robins between groups of 4 teams guards against the possibility of a team travelling possibly thousands of miles only to be eliminated after just one poor performance in

2255-408: The same position. Clearly, these pairs are pairwise different. The conclusion is that every distance- k {\displaystyle k} pair is realized. This holds for every k {\displaystyle k} , hence, every pair is realized. If there are an odd number of competitors, a dummy competitor can be added, whose scheduled opponent in a given round does not play and has

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2310-608: The teams. This famously happened during the 1994 FIFA World Cup Group E , where all four teams finished with a record of one win, one draw, and one loss. This phenomenon is analogous to the Condorcet paradox in voting theory. If n {\displaystyle n} is the number of competitors, a pure round robin tournament requires n 2 ( n − 1 ) {\displaystyle {\begin{matrix}{\frac {n}{2}}\end{matrix}}(n-1)} games. If n {\displaystyle n}

2365-417: The top left corner by repeating the sequence of numbers from 1 up to n − 1 {\displaystyle n-1} . Here is an example table for 7 or 8 competitors: World Tag Team Championship (AJPW) The World Tag Team Championship ( 世界タッグ王座 , sekai taggu ōza ) is a professional wrestling World tag team championship in Japanese promotion All Japan Pro Wrestling . It

2420-424: The tournament and be replaced by his Purple Haze stablemate Izanagi . Round-robin tournament A round-robin tournament or all-play-all tournament is a competition format in which each contestant meets every other participant, usually in turn. A round-robin contrasts with an elimination tournament , wherein participants are eliminated after a certain number of wins or losses. The term round-robin

2475-435: The tournament; changes were made prior to the next Olympics to prevent a repeat of these events. Another disadvantage, especially in smaller round-robins, is the "circle of death", where teams cannot be separated on a head-to-head record. In a three-team round-robin, where A defeats B, B defeats C, and C defeats A, all three competitors will have a record of one win and one loss, and a tiebreaker will need to be used to separate

2530-451: The victor is gradually arrived at through multiple rounds of play, teams who perform poorly, who might have been quickly eliminated from title contention, are forced to play out their remaining games. Thus games are played late in the competition between competitors with no remaining chance of success. Moreover, some later matches will pair one competitor who has something left to play for against another who does not. It may also be possible for

2585-444: The winners of each block facing each other in the final. The 2005 Tag League, featuring 10 teams in two blocks, was held from November 20 to December 5. The 2006 Tag League, featuring 7 teams, was held from November 19 to December 2. The 2007 Tag League featured 8 teams and was held from November 23 to December 9. The 2008 league was held from November 22 to December 8 and featured 8 teams. The 2009 Tag League, featuring 9 teams,

2640-446: Was also to decide the vacant World Tag Team Championship . The 1995 Tag League, featuring 10 teams, was held from November 18 to December 9. The 1996 Tag League, featuring 7 teams, was held from November 16 to December 6. In an alteration of previous years, each team faced each other twice during the group stage. The 1997 Tag League, featuring 10 teams, was held from November 15 to December 5. The 1998 Tag League, featuring 8 teams,

2695-775: Was created on June 10, 1988 as a unification of two previous tag team titles in All Japan; the PWF Tag Team Championship , and the NWA International Tag Team Championship ; when the PWF champions Jumbo Tsuruta and Yoshiaki Yatsu defeated NWA champions The Road Warriors . As with the Triple Crown Heavyweight Championship , it is symbolized by four belts, two for each wrestler, representing

2750-428: Was held from November 13 to December 2. It was also to decide the vacant World Tag Team Championship . Giant Baba replaced Ted DiBiase as Stan Hansen 's partner after one match due to injury. Hansen and Ted DiBiase originally defeated Slinger and Smothers in 7:11; however, when Baba replaced DiBiase, the teams wrestled a rematch. The 1994 Tag League, featuring 10 teams, was held from November 19 to December 10. It

2805-425: Was held from November 14 to December 5. The 1999 Tag League, featuring 8 teams, was held from November 13 to December 3. The 2000 Tag League, featuring 8 teams, was held from November 19 to December 9. Due to a four-way tie for first place, the four teams were placed into a semifinals instead of the traditional one-match final. The 2001 Tag League, featuring 8 teams, was held from November 24 to December 7. As with

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2860-442: Was held from November 15 to December 7. It was also to decide the vacant World Tag Team Championship . The 1991 Tag League, featuring 13 teams, was held from November 16 to December 6. It was also to decide the vacant World Tag Team Championship . The 1992 Tag League, featuring 11 teams, was held from November 14 to December 4. It was also to decide the vacant World Tag Team Championship . The 1993 Tag League, featuring 8 teams,

2915-466: Was held from November 22 to December 12. The 1987 Tag League, featuring 12 teams, was held from November 21 to December 11. The 1988 Tag League, featuring 11 teams, was held from November 19 to December 16. It was also to decide the vacant World Tag Team Championship . The 1989 Tag League, featuring 10 teams, was held from November 17 to December 6. It was also to decide the vacant World Tag Team Championship . The 1990 Tag League, featuring 13 teams,

2970-412: Was held from November 23 to December 6. The 2010 Tag League, featuring 9 teams, was held from November 20 to December 7. The 2011 Tag League, featuring 9 teams, was held from November 19 to December 4. The 2012 Tag League was held from November 17 to November 30. It was only the second to utilize a multi-block system, featuring 10 teams in two blocks, with the winners of each block facing each other in

3025-616: Was held from November 30 to December 13. The 1980 Tag League, featuring 7 teams, was held from November 28 to December 11. The 1981 Tag League, featuring 9 teams, was held from November 27 to December 13. Winners Bruiser Brody and Jimmy Snuka were the first winners to never win the World Tag Team Championship or its predecessors the International or PWF titles, as Stan Hansen , who had recently jumped from New Japan Pro-Wrestling and helped Brody and Snuka win

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