A round-robin tournament or all-play-all tournament is a competition format 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, where participants are eliminated after a certain number of wins or losses, as well as with a Swiss-system tournament, where participants are matched according to their running score.
Terminology The term round-robin is derived from French: ('round') ('ribbon') meant a petition signed in circular format, so no name is first or last. Over time, "ruban" became idiomized or corrupted 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. Equivalent terms are seldom used when all participants play one another more than twice, and rarely when one participant plays others an unequal number of times, as 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".
Applications Pure round-robin In sports with a large number of competitive matches per season, double round-robins with no post-seasons are common. Most domestic association football leagues in the world, as well as the CONMEBOL qualifiers for the FIFA World Cup, are organized on a double pure round-robin basis, in which every team plays all others in its league once at home and once away, with no conferences or post-seasons. The team with most points after the round-robin is declared the champion. If more than one team has the same amount of points, the most common tiebreakers are aggregate scores in matches between the tied teams, and aggregate scores across all matches in the tournament.
Triple or quadruple round-robins were traditionally used in leagues with few teams, including the Danish Superliga and the Scottish Premiership. Such leagues later changed to a modified triple round-robin, where the top teams enter a final phase to play one additional match against each other.
The format is also very common in rugby union, where it is used for domestic leagues and in national-team continental tournaments.
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.
Other round-robin formats Frequently, pool stages within a wider tournament are conducted on a round-robin basis, among them 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).
Group tournaments rankings usually go by number of matches won and drawn, with any of a variety of tiebreaker criteria.
Examples with single round-robin scheduling in groups 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), the Cricket World Cup along with Indian Premier League, a major Twenty20 Cricket tournament, and many American football college conferences, such as the Conference USA (which currently has 9 members). The group phases of the Copa Libertadores 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 2009 and 2010 seasons.
The ATP and WTA Finals, season ending tennis tournaments, also use a round robin format prior to the semi final stage.
In a more extreme example, the KBO League in baseball plays a 16-fold round robin before proceeding to the post-season, with each of the 10 teams playing each other 16 times for a total of 144 games per team, while the LIDOM (Baseball Winter League in the Dominican Republic) plays an 18-fold round robin as a semi final tournament between four classified teams.
There have been several major international cricket tournaments held in this format including ICC events, including a grouped format in the 2025 ICC Champions Trophy.
In competitive debating, a specialised form of round-robin is sometimes used as debates consist of 4 teams in each room. The most notable example of this is the HWS Round Robin. Round robins of this kind can be considered as a special case of the Social Golfer Problem.
Evaluation
Advantages 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 sports, 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 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.
Disadvantages 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 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 up to the same number of rounds as the number of participants. (If the number of participants is even, then usually a round robin only requires one less round.) For instance, 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 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 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. For instance, 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. The circle of death 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 is the number of competitors, a pure round robin tournament requires games. If is even, then in each of rounds, games can be run concurrently, provided there exist sufficient resources (e.g. courts for a tennis tournament). If is odd, there will be rounds, each with games, and one competitor having no game in that round.
Circle method The circle method 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:
Round 1. (1 plays 14, 2 plays 13, ... ) 1 2 3 4 5 6 7 14 13 12 11 10 9 8
Next, one of the competitors in the first or last column of the table is fixed (number one in this example) and the others are rotated one position in a fixed direction(clockwise in this example):
Round 2. (1 plays 13, 14 plays 12, ... ) 1 14 2 3 4 5 6 13 12 11 10 9 8 7
Round 3. (1 plays 12, 13 plays 11, ... ) 1 13 14 2 3 4 5 12 11 10 9 8 7 6
This is repeated until when the next iteration would lead back to the initial pairings:
Round 13. (1 plays 2, 3 plays 14, ... ) 1 3 4 5 6 7 8 2 14 13 12 11 10 9
With an even number of competitors this algorithm realizes every possible combination of them (equivalently, that all pairs realized are pairwise different).