Read Files in a Round Dobin Fashion

Type of sports tournament

Example of a circular-robin tournament with x participators

A circular-robin tournament (or all-play-all tournament) is a competition in which each contestant meets every other participant, usually in plough.^{[i] [2]} A round-robin contrasts with an emptying tournament, in which participants are eliminated subsequently a certain number of losses.

Terminology [edit]

The term round-robin is derived from the French term ruban, meaning "ribbon". Over a long menstruation of time, the term was corrupted and idiomized to robin.^{[3] [iv]}

In a unmarried 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,^[1] and is never used when one participant plays others an diff number of times (as is the case in almost all of the major United States professional person sports leagues – see AFL (1940–41) and All-America Football Conference for exceptions). In the United Kingdom, a round-robin tournament has been called an American tournament in sports such as tennis or billiards which unremarkably have knockout tournaments, although this is now rarely, if always, done.^{[five] [6] [7]} In Italian it is chosen girone all'italiana (literally "Italian-fashion group"). In Serbian information technology is called the Berger system ( Бергеров систем , Bergerov sistem ), afterward chess actor Johann Berger.

A round-robin tournament with four players is sometimes chosen "quad" or "foursome".^[viii]

Employ [edit]

In sports with a large number of competitive matches per season, double circular-robins are mutual. Most association football game leagues in the globe are organized on a double round-robin footing, in which every team plays all others in its league once at home and once away. This system is too used in qualification for major tournaments such equally the FIFA World Cup and the continental tournaments (e.grand. UEFA European Championship, CONCACAF Gilt Cup, AFC Asian Cup, CONMEBOL Copa América and CAF Cup of Nations). There are likewise circular-robin span, chess, draughts, become, water ice hockey, curling, and Scrabble tournaments. The World Chess Title decided in 2005 and in 2007 on an viii-player double round-robin tournament where each player faces every other player once as white and once as blackness.

In a more farthermost example, the KBO League of baseball game plays a xvi-fold circular robin, with each of the 10 teams playing each other xvi times for a total of 144 games per squad.

Group tournaments rankings unremarkably go by number of matches won and drawn, with any of a multifariousness of tiebreaker criteria.

Often, pool stages within a wider tournament are conducted on a circular-robin ground. 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 xiv (simply not in its later xv- and 18-team formats), the Cricket Earth Cup along with Indian Premier League, major Twenty-20 Cricket tournament, and many American Football college conferences, such as the Big 12 (which currently has ten members). The group phases of the UEFA club competitions and Copa Libertadores are contested every bit a double round-robin, equally are most basketball game leagues outside the U.s., including the regular season of the EuroLeague (besides equally its former Top 16 stage); the United Football League has used a double round-robin for both its 2009 and 2010 seasons.

Season ending tennis tournaments also employ a round robin format prior to the semi on stages.

Evaluation [edit]

Advantages of the format [edit]

The champion in a circular-robin tournament is the contestant that wins the near games, except when draws are possible.

In theory, a round-robin tournament is the fairest style to determine the champion from amid a known and fixed number of contestants. Each contestant, whether actor or team, has equal chances against all other opponents because in that location is no prior seeding of contestants that will preclude a match between any given pair. The element of luck is seen to be reduced every bit compared to a knockout system since 1 or 2 bad performances need not ruin a competitor'southward chance of ultimate victory. Final records of participants are more accurate, in the sense that they represent the results over a longer period confronting 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 every bit well as for prize money.

In team sport the (circular-robin) major league champions are generally regarded as the "best" squad in the land, rather than the (elimination) loving cup winners.

Moreover, in tournaments such as the FIFA or ICC World Cups, a first round stage consisting of a number of mini circular robins between groups of 4 teams guards confronting the possibility of a team travelling possibly thousands of miles merely to be eliminated later just one poor performance in a straight knockout system. The summit one, 2, or occasionally iii teams in these groups so proceed to a straight knockout stage for the remainder of the tournament.

In the circle of death (run into below), it is possible that no champion emerges from a circular-robin tournament, fifty-fifty if there is no describe. Nonetheless, most sports have tie-breaker systems which resolve this.

Disadvantages of the format [edit]

Round-robins can endure from being too long compared to other tournament types, and with subsequently scheduled games potentially not having any substantial meaning. They may as well require tiebreaking procedures.

Swiss system tournaments effort to combine elements of the circular-robin and elimination formats, to provide a worthy champion using fewer rounds than a circular-robin, while assuasive draws and losses.

Tournament length [edit]

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 later each round, a circular robin requires one round less than the number of participants. For example, a tournament of xvi teams tin 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 one time.

Other bug stem from the difference between the theoretical fairness of the round robin format and practise in a real event. Since the victor is gradually arrived at through multiple rounds of play, teams who perform poorly, who might take been quickly eliminated from championship contention, are forced to play out their remaining games. Thus games are played late in the competition betwixt competitors with no remaining chance of success. Moreover, some subsequently matches will pair one competitor who has something left to play for against another who does non. It may also exist 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 disproportion means that playing the same opponents is not necessarily completely equitable.

There is besides no scheduled showcase terminal match unless (past coincidence) ii competitors run across in the terminal match of the tournament, with the outcome of that friction match determining the title. A notable instance of such an event was the May 26, 1989 match betwixt Arsenal and Liverpool.

Qualified teams [edit]

Further problems 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 non try hard (in order to conserve resources for the side by side stage) or even deliberately lose (if the scheduled adjacent-stage opponent for a lower-placed qualifier is perceived to exist easier than for a higher-placed one).

Four pairs in the 2012 Olympics Women'southward doubles badminton, having qualified for the adjacent round, were ejected from the contest for attempting to lose in the round robin phase to avert compatriots and improve ranked opponents.^[ix] The round robin phase 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 [edit]

Another disadvantage, specially in smaller round-robins, is the "circumvolve of expiry", where teams cannot be separated on a caput-to-caput record. In a three-team circular-robin, where A defeats B, B defeats C, and C defeats A, all three competitors will have a tape of ane win and ane loss, and a tiebreaker will need to exist used to dissever the teams.^[10] This famously happened during the 1994 FIFA Globe Cup Group E, where all 4 teams finished with a record of one win, one draw, and one loss. This phenomenon is coordinating to the Condorcet paradox in voting theory.

Scheduling algorithm [edit]

If ${\displaystyle due north}$ is the number of competitors, a pure round robin tournament requires ${\displaystyle {\begin{matrix}{\frac {n}{two}}\end{matrix}}(n-ane)}$ games. If ${\displaystyle n}$ is even, then in each of ${\displaystyle (n-i)}$ rounds, ${\displaystyle {\begin{matrix}{\frac {n}{two}}\stop{matrix}}}$ games can be run concurrently, provided in that location exist sufficient resources (e.thou. courts for a lawn tennis tournament). If ${\displaystyle northward}$ is odd, at that place will be ${\displaystyle north}$ rounds, each with ${\displaystyle {\begin{matrix}{\frac {due north-one}{2}}\end{matrix}}}$ games, and i competitor having no game in that circular.

Circle method [edit]

The circumvolve method is the standard algorithm to create a schedule for a round-robin tournament^{[ citation needed ]}. All competitors are assigned to numbers, and and then paired in the showtime circular:

Circular i. (ane plays 14, 2 plays xiii, ... )

1	2	3	four	5	half dozen	seven
14	13	12	11	10	9	8

Adjacent, one of the competitors in the start or last column of the tabular array is stock-still (number one in this example) and the others rotated clockwise one position

Circular 2. (i plays 13, 14 plays 12, ... )

1	fourteen	2	3	4	5	6
13	12	11	10	9	eight	seven

Round 3. (i plays 12, xiii plays xi, ... )

1	thirteen	14	two	3	iv	5
12	xi	x	nine	eight	vii	6

This is repeated until you end upwards about dorsum at the initial position:

Round 13. (1 plays 2, iii plays 14, ... )

1	3	4	five	half-dozen	vii	8
two	14	thirteen	12	11	10	9

To see that - with an even number ${\displaystyle north}$ of competitors - this algorithm realizes every possible combination of them (equivalently, that all pairs realized are pairwise different), we argue equally follows.

Beginning, the algorithm patently realizes every pair of competitors if ane of them equals ${\displaystyle one}$ (the non-moving competitor).

Adjacent, for pairs of non- ${\displaystyle ane}$ competitors, allow their distance be the number ${\displaystyle k<{\frac {northward}{two}}}$ of times the rotation has to exist carried out in lodge that one competitor arrives at the position the other had.

In the example given ( ${\displaystyle n=xiv}$ ), ${\displaystyle two}$ has altitude ${\displaystyle one}$ to ${\displaystyle 3}$ and to ${\displaystyle 14}$ and information technology has distance ${\displaystyle 6}$ to ${\displaystyle 8}$ and to ${\displaystyle nine}$ .

In a circular, a non-leftmost position (not including ${\displaystyle 1}$ ) tin simply exist taken by competitors of a fixed distance. In round ${\displaystyle 1}$ of the case, in the second position competitor ${\displaystyle 2}$ plays against ${\displaystyle thirteen}$ , their distance is ${\displaystyle two}$ . In circular ${\displaystyle 2}$ , this position is held past competitors ${\displaystyle 14}$ and ${\displaystyle 12}$ , also having distance ${\displaystyle 2}$ , etc. Similarly, the next position ( ${\displaystyle 3}$ against ${\displaystyle 12}$ in round ${\displaystyle 1}$ , ${\displaystyle 2}$ against ${\displaystyle 11}$ in round ${\displaystyle ii}$ , etc.) can but hold distance- ${\displaystyle 4}$ competitors.

For every ${\displaystyle k<{\frac {n}{ii}}}$ , there are exactly ${\displaystyle due north-i}$ pairs of distance ${\displaystyle k}$ . At that place are ${\displaystyle n-1}$ rounds and they all realize one distance- ${\displaystyle k}$ pair at the same position. Conspicuously, these pairs are pairwise dissimilar. The conclusion is that every distance- ${\displaystyle yard}$ pair is realized.

This holds for every ${\displaystyle g}$ , hence, every pair is realized.

If there are an odd number of competitors, a dummy competitor can exist added, whose scheduled opponent in a given circular does not play and has a goodbye. The schedule can therefore be computed as though the dummy were an ordinary player, either stock-still or rotating. Instead of rotating one position, whatsoever number relatively prime number to ${\displaystyle (north-i)}$ 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 e'er on the kickoff row. If, say, competitors 3 and 8 were unable to fulfil their fixture in the third round, it would demand to be rescheduled exterior the other rounds, since both competitors would already be facing other opponents in those rounds. More complex scheduling constraints may crave more than complex algorithms.^[11] This schedule is applied in chess and draughts tournaments of rapid games, where players physically movement round a table. In French republic this is chosen the Carousel-Berger system (Système Rutch-Berger).^[12]

The schedule can also be used for "asynchronous" round-robin tournaments where all games take place at different times (for example, considering there is but ane venue). The games are played from left to correct in each round, and from the first circular to the last. When the number of competitors is even, this schedule performs well with respect to quality and fairness measures such every bit the amount of residuum betwixt games. On the other hand, when the number of competitors is odd, it does not perform and so well and a different schedule is superior with respect to these measures.^[13]

Berger tables [edit]

Alternatively Berger tables,^[14] named afterwards the Austrian chess master Johann Berger, are widely used in the planning of tournaments ^[15] . Berger published the pairing tables in his two Schach-Jahrbücher (Chess Annals),^{[xvi] [17]} with due reference to its inventor Richard Schurig.^{[18] [19]}

Circular 1	1 – 14	ii – 13	3 – 12	4 – 11	five – 10	six – 9	7 – 8
Round 2	xiv – 8	nine – 7	10 – 6	11 – 5	12 – 4	13 – 3	1 – 2
Circular three	2 – 14	3 – 1	four – thirteen	5 – 12	half dozen – 11	7 – 10	viii – 9
...	...
Round 13	7 – xiv	8 – 6	ix – 5	10 – 4	eleven – iii	12 – two	13 – ane

This constitutes a schedule where player fourteen has a fixed position, and all other players are rotated counterclockwise ${\displaystyle {\frac {due north}{2}}}$ positions. This schedule is easily generated manually. To construct the next circular, the last player, number 8 in the first circular, moves to the caput of the table, followed past player 9 confronting histrion seven, player 10 against 6, until player 1 against player 2. Arithmetically, this equates to adding ${\displaystyle {\frac {n}{2}}}$ to the previous row, with the exception of player ${\displaystyle due north}$ . When the result of the addition is greater than ${\displaystyle (north-1)}$ , then subtract ${\displaystyle (n-1)}$ .

This schedule tin also be represented equally a (north-1, northward-ane) table, expressing a round in which players meets each other. For example, player 7 plays against role player 11 in circular 4. If a player meets itself, so this shows a bye or a game against player northward. All games in a round constitutes a diagonal in the tabular array.

Diagonal Scheme × 2 three four five 6 vii 8 9 10 xi 12 13 1 ii iii iv v 6 seven 8 nine 10 eleven 12 13 one 1 2 3 4 five vi seven 8 9 10 11 12 thirteen 2 one ii 3 4 v 6 7 8 9 x 11 12 13 3 1 2 3 4 5 half dozen 7 8 9 ten 11 12 thirteen 4 1 2 3 4 v 6 seven 8 9 x xi 12 13 5 ane 2 iii iv five half-dozen vii 8 9 ten 11 12 xiii 6 1 ii 3 4 five 6 7 8 9 10 xi 12 13 7 1 2 three four 5 6 7 viii nine 10 11 12 13 8 1 ii 3 4 five half-dozen vii eight ix 10 xi 12 13 9 1 2 iii 4 v 6 7 8 ix 10 xi 12 13 x 1 2 iii 4 5 6 7 8 9 10 11 12 13 xi 1 2 three iv v six 7 eight nine 10 11 12 13 12 1 2 3 iv 5 half dozen 7 8 nine 10 11 12 thirteen xiii 1 ii 3 4 5 vi 7 8 ix 10 11 12 xiii

Round Robin Schedule × 1 2 3 four v 6 7 8 ix 10 eleven 12 13 ane 1 2 3 four v half-dozen 7 viii 9 ten xi 12 13 2 2 three 4 v 6 seven 8 9 10 xi 12 xiii ane three 3 iv 5 vi 7 8 9 10 11 12 13 1 two four 4 5 6 7 viii 9 10 xi 12 13 1 2 3 v 5 6 7 8 ix 10 11 12 thirteen i 2 three 4 6 6 seven eight ix 10 xi 12 13 1 two 3 4 5 7 7 8 9 x 11 12 xiii 1 2 3 four five 6 eight 8 9 x 11 12 xiii 1 2 iii four 5 vi vii 9 9 10 11 12 13 1 two 3 iv 5 vi 7 8 10 10 11 12 13 1 2 3 iv 5 6 7 8 9 eleven 11 12 13 1 two 3 4 5 half-dozen 7 8 9 10 12 12 13 i 2 iii four 5 6 7 viii 9 10 11 13 13 1 2 3 4 5 6 7 viii ix ten eleven 12

The higher up schedule can also be represented past a graph, as shown below:

Circular Robin Schedule Bridge Diagram

Both the graph and the schedule were reported by Édouard Lucas in^[20] as a recreational mathematics puzzle. Lucas, who describes the method as elementary and ingenious, attributes the solution to Felix Walecki, a teacher at Lycée Condorcet. Lucas also included an culling solution by means of a sliding puzzle.

Original construction of pairing tables by Richard Schurig (1886) [edit]

For an fifty-fifty number ${\displaystyle n}$ or an odd number ${\displaystyle n-1}$ of competitors, Schurig^[nineteen] builds a table with ${\displaystyle north/two}$ vertical rows and ${\displaystyle northward-i}$ horizontal rows. Then he populates it starting from the top left corner by repeating the sequence of numbers from 1 up to ${\displaystyle n-1}$ . Hither is an example tabular array for 7 or 8 competitors:

Circular 1	i	ii	3	4
Round ii	5	6	7	1
Round three	2	3	4	v
Round 4	6	7	1	ii
Round 5	iii	iv	5	vi
Circular half-dozen	vii	1	2	3
Circular 7	iv	5	6	7

And so to become the opponents a 2nd table is constructed. Every horizontal row ${\displaystyle ten}$ is populated with the same numbers equally row ${\displaystyle ten+1}$ in the previous table (the last row is populated with numbers from the kickoff row in the original table), but in the reverse social club (right to left).

Round 1	– 1	– 7	– 6	– 5
Round two	– 5	– 4	– 3	– 2
Circular 3	– 2	– 1	– 7	– 6
Round 4	– 6	– 5	– four	– 3
Round 5	– three	– ii	– 1	– seven
Round vi	– 7	– 6	– 5	– 4
Circular vii	– 4	– 3	– ii	– one

Past merging above tables we arrive at:

Circular 1	1 – 1	two – 7	3 – 6	4 – 5
Round ii	5 – 5	6 – 4	7 – 3	i – ii
Round 3	ii – ii	3 – 1	4 – 7	5 – 6
Round 4	6 – 6	7 – v	ane – iv	two – 3
Round five	3 – 3	4 – 2	five – 1	half dozen – vii
Round 6	7 – 7	1 – 6	two – 5	3 – 4
Circular 7	4 – four	v – three	vi – 2	7 – ane

And so the outset column is updated: if the number of competitors is even, player number ${\displaystyle due north}$ is alternatingly substituted for the first and 2d positions, whereas if the number of competitors is odd a bye is used instead.

The pairing tables were published as an addendum concerning the arrangements for the belongings of master tournaments. Schurig did not provide a proof nor a motivation for his algorithm. For more historical details, see Ahrens.^[21]

Come across also [edit]

• Group tournament ranking system, including details of necktie-breaking systems
• Combinatorial design, a balanced tournament pattern of lodge n (a BTD(n))
• Tournament (graph theory), mathematical model of a round-robin tournament
• Other tournament systems:
  • Swiss organization tournament
    • McMahon system tournament, a variation of the Swiss system that incorporates pre-tournament rankings to preclude early lopsided pairings
  • Single-emptying tournament
    • Shaughnessy playoff system, a type of single-elimination tournament featuring 4 teams
  • Double-elimination tournament
  • McIntyre System, a serial of tournament formats that combine features of single- and double-elimination tournaments
• Span:
  • Duplicate bridge movements
• Chess:
  • List of round-robin chess tournaments
  • Scheveningen organisation, where each member of one team plays each member of the other
• Voting:
  • Condorcet method
  • Condorcet benchmark

References [edit]

1. ^ ^{a b} Webster's Third New International Dictionary of the English language Language, Entire (1971, G. & C. Merriam Co), p.1980.
2. ^ Orcutt, William Dana (1895). Official Lawn Lawn tennis Message. Vol. 2. New York: The Editors. pp. 1, iii.
3. ^ Strehlov, Richard A; Wright, Sue Ellen, eds. (1993). Standardizing Terminology for Better Communication: Practice, Practical Theory, and Results. Vol. 1166. ASTM. pp. 336–337. ISBN0-8031-1493-1.
4. ^ Brewer's Dictionary of Phrase & Fable. New York: Harper & Blood brother Publishers. p. 786.
5. ^ "A Glossary of Terms Used in Connexion with Billiards". Billiard Monthly. English Amateur Billiards Association. Feb 1912. American Tournament: A tournament in which each player must run into in plough every other player.
6. ^ Allied. "American tournament". Chambers 21st Century Dictionary. Allied Publishers. p. 38. ISBN978-0550106254 . Retrieved August 1, 2012.
7. ^ Mead, Shepherd (1977). How to succeed in tennis without actually trying: the easy tennismanship way to do all the things no lawn tennis pro tin can teach y'all. McKay. p. 130. ISBN9780679507499 . Retrieved Baronial 1, 2012.
8. ^ "An Introduction to USCF-Rated Tournaments" (PDF). The United states Chess Federation. Feb 23, 2006.
9. ^ "Eight Olympic badminton players disqualified for 'throwing games'". The Guardian. August 1, 2012. Retrieved August i, 2012.
10. ^ "UC Berkeley Quiz Basin: How To Brand Schedules". www.ocf.berkeley.edu.
11. ^ Dinitz, Jeff (November 13, 2004). "Designing Schedules for Leagues and Tournaments" (PDF). Dwelling house Page for Jeff Dinitz. Mount Saint Mary Higher: GRAPH THEORY DAY 48.
12. ^ Le livre de l'arbitre : édition 2008 (PDF) (in French). Fédération Française des Échecs. 2008. p. 56. ISBN978-2-915853-01-eight.
13. ^ Suksompong, Warut (2016). "Scheduling asynchronous circular-robin tournaments". Operations Enquiry Letters. 44 (1): 96–100. arXiv:1804.04504. doi:x.1016/j.orl.2015.12.008. S2CID 4931332.
14. ^ Table de Berger (in French), examples of round robin schedules up to 30 participants.
15. ^ "C. General Rules and Technical Recommendations for Tournaments / 05. General Regulations for Competitions / Full general Regulations for Competitions. Annex 1: Details of Berger Table /". FIDE Handbook. FIDE. (contents page)
16. ^ Berger, Johann (1893). Schach-Jahrbuch für 1892/93 (in High german). Leipzig. pp. 26–31. OCLC 651254787.
17. ^ Berger, Johann (1899). Schach-Jahrbuch für 1899/1900 : Fortsetzung des Schach-Jahrbuches für 1892/93 (in German). Leipzig. pp. 21–27. OCLC 651254792.
18. ^ Richard Schurig (in French)
19. ^ ^{a b} Schurig, Richard (1886). "Die Paarung der Theilnehmer eines Turniers". Deutsche Schachzeitung (in German). 41: 134–137. OCLC 556959107.
20. ^ Lucas, Edouard (1883). "Les jeux de demoiselles". Récréations Mathématiques (in French). Paris: Gauthier-Villars. pp. 161–197.
21. ^ Ahrens, Wilhelm (1901). "Anordnungs Probleme, Aufgabe 2". Mathematische Unterhaltungen und Spiele (in High german). Leipzig: B. M. Teubner. ark:/13960/t2w37mv93.

External links [edit]

• Round Robin Discussion Lath link to a give-and-take community and schedules (balanced,cyclic,first-fit,whist).
• Circular Robin System Tables (Scoring - Program)
• Free Printable Circular Robin Brackets

bunkerpliteruning.blogspot.com

Source: https://en.wikipedia.org/wiki/Round-robin_tournament

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