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A round-robin tournament (or all-go-away-tournament) is a competition in which each contestant meets every other participant, usually in turn.''Webster's Third New International Dictionary of the English Language, Unabridged'' (1971, G. & C. Merriam Co), p.1980. A round-robin contrasts with an elimination tournament, in which participants/teams are eliminated after a certain number of losses.


Terminology

The term ''round-robin'' is derived from the French term ''ruban'', meaning "
ribbon A ribbon or riband is a thin band of material, typically cloth but also plastic or sometimes metal, used primarily as decorative binding and tying. Cloth ribbons are made of natural materials such as silk, cotton, and jute and of synthetic mater ...
". Over a long period of time, the term was corrupted and 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 is the case in almost all of the major United States professional sports leagues – see AFL (1940–41) and
All-America Football Conference The All-America Football Conference (AAFC) was a professional American football league that challenged the established National Football League (NFL) from 1946 to 1949. One of the NFL's most formidable challengers, the AAFC attracted many of the ...
for exceptions). In the United Kingdom, a round-robin tournament has been called an American tournament in sports such as tennis or billiards which usually have
knockout A knockout (abbreviated to KO or K.O.) is a fight-ending, winning criterion in several full-contact combat sports, such as boxing, kickboxing, muay thai, mixed martial arts, karate, some forms of taekwondo and other sports involving striking, a ...
tournaments, although this is now rarely, if ever, done. In Italian it is called (literally "Italian-style group"). In
Serbian Serbian may refer to: * someone or something related to Serbia, a country in Southeastern Europe * someone or something related to the Serbs, a South Slavic people * Serbian language * Serbian names See also

* * * Old Serbian (disambiguat ...
it is called the Berger system (, ), after chess player Johann Berger. In Brazil it is called (), referring to the accumulation of accounted points as the determinant of each participant's final performance, once all participants have played their games. A round-robin tournament with four players is sometimes called "quad" or "foursome".


Use

In sports with 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 The AFC Asian Cup is the primary association football competition contested by the senior men's national teams of the members of the Asian Football Confederation (AFC), determining the continental champion of Asia. It is the second oldest cont ...
, CONMEBOL Copa América and
CAF Cup of Nations The Africa Cup of Nations referred to as AFCON (french: Coupe d'Afrique des Nations, sometimes referred to as CAN, or TotalEnergies Africa Cup of Nations for sponsorship reasons), and sometimes as African Cup of Nations, is the main internati ...
). There are also round-robin 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. In a more extreme example, the KBO League of 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 a 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 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 Super Rugby is a men's professional rugby union club competition involving teams from Australia, Fiji, New Zealand, and the Pacific Islands. It previously included teams from Argentina, Japan, and South Africa. Building on various Southern Hem ...
( 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), the
Cricket World Cup The Cricket World Cup (officially known as ICC Men's Cricket World Cup) is the international championship of One Day International (ODI) cricket. The event is organised by the sport's governing body, the International Cricket Council (ICC), e ...
along with Indian Premier League, major Twenty-20 Cricket tournament, and many American Football college conferences, such as the Big 12 (which currently has 10 members). The group phases of the UEFA club competitions and
Copa Libertadores The CONMEBOL Libertadores, also known as the Copa Libertadores de América ( pt, Copa Libertadores da América), is an annual international club football competition organized by CONMEBOL since 1960. It is the highest level of competition in S ...
are contested as a double round-robin, as are most basketball leagues outside the United States, including the regular season of the EuroLeague (as well as its former Top 16 phase); the United Football League has used a double round-robin for both its
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and
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seasons. Season ending tennis tournaments also use a round robin format prior to the semi on stages.


Evaluation


Advantages of the format

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 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 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 sport the (round-robin) major league champions are generally regarded as the "best" team in the land, rather than the (
elimination Elimination may refer to: Science and medicine * Elimination reaction, an organic reaction in which two functional groups split to form an organic product *Bodily waste elimination, discharging feces, urine, or foreign substances from the bo ...
) cup winners. 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 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 (see below), it is possible that no champion emerges from a round-robin tournament, even if there is no draw. However, most sports have tie-breaker systems which resolve this.


Disadvantages of the format

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 tiebreaking procedures.
Swiss system tournament A Swiss-system tournament is a non-eliminating tournament format that features a fixed number of rounds of competition, but considerably fewer than for a round-robin tournament; thus each competitor (team or individual) does not play all the other ...
s attempt to combine elements of the round-robin and elimination formats, to provide a worthy champion using fewer rounds than a round-robin, while allowing draws and losses.


Tournament length

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, a tournament of 16 teams can be completed in just 4 rounds (i.e. 15 matches) in a knockout ( single elimination) 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 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 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 the championship. A notable instance of such an event was the
1950 FIFA World Cup The 1950 FIFA World Cup was the fourth edition of the FIFA World Cup, the quadrennial international football championship for senior men's national teams and held in Brazil from 24 June to 16 July 1950. The planned 1942 and 1946 World Cups were ...
match between Uruguay and Brazil.


Qualified teams

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 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 the tournament; changes were made prior to the next Olympics to prevent a repeat of these events.


Circle of death

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 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.


Scheduling algorithm

If n is the number of competitors, a pure round robin tournament requires \begin \frac \end(n - 1) games. If n is even, then in each of (n - 1) rounds, \begin \frac \end games can be run concurrently, provided there exist sufficient resources (e.g. courts for a tennis tournament). If n is odd, there will be n rounds, each with \begin \frac \end games, and one competitor having no game in that round.


Circle method

The circle method is the standard 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 you end up almost back at the initial position: To see that - with an even number n of competitors - this algorithm realizes every possible combination of them (equivalently, that all pairs realized are pairwise different), we argue as follows. First, the algorithm obviously realizes every pair of competitors if one of them equals 1 (the non-moving competitor). Next, for pairs of non-1 competitors, let their distance be the number k<\frac of times the rotation has to be carried out in order that one competitor arrives at the position the other had. In the example given (n=14), 2 has distance 1 to 3 and to 14 and it has distance 6 to 8 and to 9. In a round, a non-leftmost position (not including 1) can only be taken by competitors of a fixed distance. In round 1 of the example, in the second position competitor 2 plays against 13, their distance is 2. In round 2, this position is held by competitors 14 and 12, also having distance 2, etc. Similarly, the next position (3 against 12 in round 1, 2 against 11 in round 2, etc.) can only hold distance-4 competitors. For every k<\frac, there are exactly n-1 pairs of distance k. There are n-1 rounds and they all realize one distance-k pair at the same position. Clearly, these pairs are pairwise different. The conclusion is that every distance-k pair is realized. This holds for every 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 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) 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 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 a table. In France this is called the
Carousel A carousel or carrousel (mainly North American English), merry-go-round (List of sovereign states, international), roundabout (British English), or hurdy-gurdy (an old term in Australian English, in South Australia, SA) is a type of amusement ...
-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 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.


Berger tables

Alternatively Berger tables, named after the Austrian
chess master A chess title is a title regulated by a chess governing body and bestowed upon players based on their performance and rank. Such titles are usually granted for life. The international chess governing body FIDE grants several titles, the most pres ...
Johann Berger, are widely used in the planning of tournaments (contents page) . Berger published the pairing tables in his two ''Schach-Jahrbücher'' (Chess Annals), with due reference to its inventor Richard Schurig. This constitutes a schedule where player 14 has a fixed position, and all other players are rotated counterclockwise \frac 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 \frac to the previous row, with the exception of player n. When the result of the addition is greater than (n-1), then subtract (n-1) from the sum. This schedule can also be represented as a (n-1, n-1) table, expressing 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 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.


Original construction of pairing tables by Richard Schurig (1886)

For an even number n or an odd number n - 1 of competitors, Schurig builds a table with n/2 vertical rows and n-1 horizontal rows. Then he populates it starting from the top left corner by repeating the sequence of numbers from 1 up to n-1. Here is an example table for 7 or 8 competitors: Then to get the opponents a second table is constructed. Every horizontal row x is populated with the same numbers as row x + 1 in the previous table (the last row is populated with numbers from the first row in the original table), but in the reverse order (from right to left). By merging above tables we arrive at: Then the first column is updated: if the number of competitors is even, player number n is alternatingly substituted for the first and second positions, whereas if the number of competitors is odd a bye is used instead. The pairing tables were published as an annex concerning the arrangements for the holding of master tournaments. Schurig did not provide a proof nor a motivation for his algorithm. For more historical details, see Ahrens.


See also

*
Group tournament ranking system In a group tournament, unlike a knockout tournament, there is no scheduled decisive final match. Instead, all the competitors are ranked by examining the results of all the matches played in the tournament. Typically, points are awarded for each m ...
, including details of tie-breaking systems * Combinatorial design, a balanced tournament design of order ''n'' (a BTD(''n'')) * Tournament (graph theory), mathematical model of a round-robin tournament * Other tournament systems: **
Swiss system tournament A Swiss-system tournament is a non-eliminating tournament format that features a fixed number of rounds of competition, but considerably fewer than for a round-robin tournament; thus each competitor (team or individual) does not play all the other ...
***
McMahon system tournament A McMahon system tournament is a tournament design for games such as go and chess that attempts to generalize and improve upon the Swiss system. As in a Swiss tournament, all players compete in the same number of rounds against various other player ...
, a variation of the Swiss system that incorporates pre-tournament rankings to prevent early lopsided pairings ** Single-elimination tournament *** Shaughnessy playoff system, a type of single-elimination tournament featuring four teams ** Double-elimination tournament ** McIntyre System, a series of tournament formats that combine features of single- and double-elimination tournaments * Bridge: ** Duplicate bridge movements * Chess: **
List of round-robin chess tournaments This is a list of chess round-robin tournaments. Major present round-robin tournaments * Candidates Tournament of the World Chess Championship (1950–1962, 1985, 2013–) * Russian Chess Championship (most years) * U.S. Chess Championship (most ...
**
Scheveningen system The Scheveningen system is a method of organizing a chess match between two teams. Each player on one team plays each player on the other team . The team with the highest number of games won is the winner. This system is a popular way to creat ...
, where each member of one team plays each member of the other *Voting: ** Condorcet method ** Condorcet criterion


References


External links


Round Robin Tournament Scheduling
link to schedules (balanced,cyclic,first-fit,whist).

{{DEFAULTSORT:Round-Robin Tournament Tournament systems Chess tournament systems