Talk:Round-robin tournament

Creating

I replaced the following section because I find it hard to follow. My version is not as pretty, but I reckon it makes sense. It's based on the last post here: Mon, 03 Nov 1997 16:39:06. Joestynes

A pure round robin grid requires ${\frac {1}{2}}n(n-1)$ games, where $n$ is the number of teams in the tournament. In many cases (e.g. football), ${\frac {1}{2}}n$ games can be run in parallel.

To create a round robin grid, break it conceptually into a number of rounds. In the first round, each participant plays the participants immediately above and below them in the list of teams. In the second round, each participant plays the participants two spots above and below them; and so on for subsequent rounds. If there are an even number of teams, it will be necessary to finish with a half-length round, in which each team plays the team ${\frac {1}{2}}n$ spots above/below them. A sample for 6 teams is shown below.

Each row in this grid is a participant, and each column is a game. For example, looking at the first column, we can see that in the first game team A plays team B. The colors represent whatever is appropriate for your sport: red is home and green is away; upwind and downwind; left end and right end, etc.

Each participant plays twice in each round (except the final half-length round, if there is one). Each participant is red once and green once in each round (except in the half-length).

You can scale this to any number of teams, in a way which hopefully is obvious from the example. You can rearrange games to suit; in particular in some sports you will want to rearrange so that no participant plays twice in a row. In any given round, the games can be arranged into two groups which can be run in parallel; for example in the first round above, games 1, 3 and 5 can be run in parallel, as can games 2, 4 and 6.

Replaced with

The standard algorithm for round-robins is to assign each competitor a number, and pair them off in the first round …

1. (1 plays 14, 2 plays 13, ... )
 1  2  3  4  5  6  7  
 14 13 12 11 10 9  8

… then fix one competitor (number one in this example) and rotate the others clockwise …

2. (1 plays 13, 14 plays 12, ... )
 1  14 2  3  4  5  6
 13 12 11 10 9  8  7

3. (1 plays 12, 13 plays 11, ... )
 1  13 14 2  3  4  5
 12 11 10 9  8  7  6

… until you end up almost back at the initial position

13. (1 plays 2, 3 plays 14, ... )
 1  3  4  5  6  7  8
 2 14  13 12 11 10 9

If there are an odd number of competitors, a dummy competitor can be added, whose scheduled opponent in a given round does not play. The upper and lower rows can indicate home/away in sports, white/black in chess, etc (this must alternate between rounds since competitor 1 is always on the first row). If, say, competitors 3 and 8 were unable to fulfill 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.

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Hi, Joe. If you reckon yours is clearer, I'm happy to leave it up. What do you think about adding back in the initial paragraph from my version about the number of games required? DougBurbidge

Yep: done, more or less. Proofreading and maths-checking encouraged. Joestynes 10:06, 11 Apr 2005 (UTC) [P.S. name's Jöstij, actually :)]

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Hey, sorry about my etiquette, but I just wanted to mention that something seems to be wrong here.

For 8 participants …

8/2(8-1)=28

1 2-3-4-|
 /	| (1)
8-7-6-5-|

1 8-2-3-|
 /	| (2)
7-6-5-4-|

1 7-8-2-|
 /	| (3)
6-5-4-3-|

1 6-7-8-|
 /	| (4)
5-4-3-2-|

1 5-6-7-|
 /	| (5)
4-3-2-8-|

1 4-5-6-|
 /	| (6)
3-2-8-7-|

1 3-4-5-|
 / 	| (7)
2-8-7-6-|

I just realized in composing this that the total number of matches would be 28, but it wasn't apparent to me at first however. I don't know if it needs clarification or not it could just be me being stupid. Perhaps it could be said the total number of rounds or least possible amount of rounds, assuming the most possible matches per round played, would be n-1?

The least possible amount of rounds is n-1 if n is even, and n if n is odd. This is already stated in the article:

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

Joestynes 16:54, 10 January 2006 (UTC)

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I think that the picture with the green and red is elegant. I read the article because I'm using the principle (I couldn't figure it out on my own) and I am greatly edified by seeing that picture of the grid of players. Consider leaving it (both explanations). Aaron Laws dartme@live.com

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I find the picture much clearer. Also, it gets the math right (14 teams end up with not 13 rounds, but 7). OmmadawnDK (talk) 17:55, 1 February 2010 (UTC)

The red/green diagrams and the text of the article are not describing the same thing. The red/green diagrams could be used if the games were played sequentially. But in many instances, you want to have everyone playing at the same time (except one if there are an odd number of players). The red/green diagrams don't show how to do that whereas the text in the article does. And you can't arbitrarily have several games going on at once - you need a method, which I found out in a scholastic chess tournament once. It was to be a 5-round Swiss system tournament but only six teams showed up. So we played a round-robin. The director didn't know how to do a round-robin so he just arbitrarily assigned th games in the early rounds, thinking that it would work itself out if each round someone played someone they hadn't played before. Well, in the third or fourth round there was no correct pairing. Bubba73 ^{(You talkin' to me?)}, 21:05, 1 February 2010 (UTC)

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Slept on it, drew a few pictures etc. I think both the text and the pictures should be included, they advise different ways of attacking the problem, but they both work. In the text version, the rounds drop out of the model directly. In the picture version, you have to dissect the picture to find the rounds, but the square pictures each have 2 rounds embedded. So actually, they both end up having 13 rounds (6 square pictures for 12 rounds, and one more). OmmadawnDK (talk) 14:15, 2 February 2010 (UTC)

The red/green chart shows a way of doing it if you aren't playing more than one game at a time (or rather the maximum). But there is no reason for the chart to be broken up into three pieces the way it is - that is confusing.

The two red/green squares do not both have two rounds embedded. In the first square, you could play games 1, 3, and 5 together in a round and then 2, 4, and 6 in a round. But you can't break the second square up that way. You can play 7 and 8 together, but then there isn't another game from the second square that you can play at the same time. You can play 7 an 10 together, but again there isn't a third game from the second square that you can play at the same time. Bubba73 ^{(You talkin' to me?)}, 16:32, 2 February 2010 (UTC)

A red/green diagram showing the procedure described in the text of the article would be beneficial. Bubba73 ^{(You talkin' to me?)}, 16:57, 2 February 2010 (UTC)

Proposed move to Round-robin tournament

That was a short American-centric article with no edit history talk page. I incorporated its extra information to this article and redirected it here. Just need an administrator to rename. Joestynes 11:43, 6 Apr 2005 (UTC)

• Support move. Round-robin tournament will be easier to link to in running text. It's also a better title because the concept is not just in sports. It's used in table games, such as chess tournaments, for example. Jonathunder 01:18, 2005 Apr 7 (UTC)
• Support move, but I think we should merge the histories, and not leave a redirect at Round-robin (sports). We can edit the pages to point to the correct title. -- Netoholic @ 01:32, 2005 Apr 7 (UTC)
• Since the concept is used in other venues besides just sports, I support the move, and yes, we can eliminate the redirect too. -- TOttenville8 07:31, 2005 Apr 7 (UTC)
• Support. Even though most of the material I added has been cut out again. :-) DougBurbidge 07:16, 10 Apr 2005 (UTC)

It was requested that this article be renamed but there was no consensus for it to be moved. This is a page merge not a move. I do agree, though, that round-robin tournament is a better name. violet/riga (t) 11:14, 10 Apr 2005 (UTC)

I have overwritten the old content of Round-robin tournament with the old content of Round-robin (sports) and made the latter a redirect; the talk page now redirects in the opposite direction. I had already done my best to merge the content prior to the rejection of the move request. Not sure if this is procedurally kosher but nothing's been happening about clearing up the duplicacy. Joestynes 08:10, 25 May 2005 (UTC)

It seems to me that this article should be linked to Condorcet method.

The Condorcet method is a "choice voting" system that is oft compared to Round-robin. Voters mark ranked-ballots (same as with Instant-runoff voting) with their first preference marked "1", second choice "2", and so on. Tabulation and determination of the winner is different that IRV; a hypothetical 2-person race is run with every candidate pair in round-robin fashion. The candidate who beats every other candidate in the paired-off races (and there can be no more than one candidate who does that) is the Condorcet winner and is elected.

There is an oft repeated potential flaw or problem with Condorcet elections, the potential for a Condorcet paradox or |cycle which is a rock-paper-scissors problem. What happens in a Round-robin tournament if Wrestler A beats Wrestler B, Wrestler B beats Wrestler C, and Wrestler C beats Wrestler A? Then who is declared the winner? Or do they all come away from that with a tie? I think this ambiguity and how it has been resolved in Round-robin tournaments could be spelled out in the article, and this article should have Condorcet method put into the See also section.

Just a suggestion from an anonymous editor. 74.104.160.199 (talk) 19:05, 12 September 2009 (UTC)

Maybe it can be put under See Also, but it seems quite a bit different. In chess, round-robins are done with more than three players and the winner is the one with the most total points. In the event of that being tied, sometimes tie-breaking methods are used, usually they are co-champions. Bubba73 (talk), 19:46, 12 September 2009 (UTC)

Reference to Berger tables included + table

Construction of Berger table explained. Table shows logic of the Berger table construction. 217.123.83.212 (talk) 10:16, 26 August 2011 (UTC)

how is this type of tournament "ribbon-like" in the first place?

What is ribbon-like about this kind of tournament? The first sentences in the "Terminology" section beg that question. The section starts:

The term round-robin is derived from the term ruban, meaning "ribbon". Over a long period of time, the term was corrupted and idiomized to robin.

References

I could see a square shape involved, in a list of all players crossed with list of all players. Where is a "ribbon" involved? Maybe it is obvious to some, but not to me! --doncram 01:28, 12 April 2015 (UTC)

Parentheses?

Why are parentheses used in the following sentence? And shouldn't there be a comma after "in team sport"?
"In team sport the (round-robin) major league champions is generally regarded as the "best" team in the land, rather than the (elimination) cup winners."--Adûnâi (talk) 13:43, 12 January 2017 (UTC)

One winner

The article claims: The champion, in a round-robin tournament, is the contestant that wins the most games. Unless there is a draw, there can be no more than one contestant who emerges as champion because, if there were two, eventually they must meet each other and one contestant will be defeated by the other. But it isn't hard to come up with an example where this is not true. Consider a tournament with four entries, A, B, C, and D. A wins against B and C; B wins against C and D; C wins against D; D wins against A. We end up with A and B having 2 wins, C and D 1 win, and no draws. --2001:981:4B0C:1:7038:2583:C1D0:E0B8 (talk) 21:52, 5 March 2019 (UTC)

removed "dubious" tag

On 4-Jan-2019 a dubious tag was added to this sentence: "The element of luck is seen to be reduced as compared to a knockout system since one or two bad performances need not cripple a competitor's chance of ultimate victory.". The IP editor who put the tag wrote "If a contestant loses one game or match, that contestant will not be the champion unless there is a circle of death that later is resolved". But this is clearly not always true. e.g. a contestant can lose 1 game but still be outright winner. There are many examples of this actually happening. Adpete (talk) 01:40, 10 June 2019 (UTC)

Possible error

I believe the sentence "When the result of the addition is greater than $(n-1)$, then subtract $({\begin{matrix}{\frac {n}{2}}\end{matrix}}-1)$" is wrong and the last part of it should instead read "then subtract $(n-1)$". Rather than editing it myself, I'd like a second opinion on this. — Preceding unsigned comment added by Feasel (talk • contribs) 09:51, 17 February 2020 (UTC)

I think I understand the confusion. In the 14 player example shown, when we add n/2 (7) to player 7, we get 14. Since 14 > n+1, "then subtract (n-1)". This direction is ambiguous. Do we complete the addition first and then subtract? Or subtract in lieu of addition? If you complete the addition first, 14-(n-1)=1 (the result you want). If you do not complete the addition first, 7-((n/2)-1)=1 (again, the result you want). So, I think the best result would be to edit the language in one of the two following ways: "When the result of the addition is greater than (n-1), subtract (n-1) from the sum." or "When the result of the addition is greater than (n-1), subtract (n/2)-1 in lieu of the addition." Please pardon my lack of math formatting knowledge here, this is my first post. I think either one of these solutions would clarify the procedure to follow.Chief-jk (talk) 18:34, 12 April 2020 (UTC)

Break?

In the example for 10 teams diagram, top right, except for the first day two circles are coloured light blue and the legend for that says "break". It is not clear to me what that is and nothing seems to explain it. Petelomax (talk) 09:55, 15 November 2021 (UTC)

Confused over horizontal / vertical rows

In the "Original construction of pairing tables by Richard Schurig (1886)" section, why do we refer to "vertical rows" and "horizontal rows" instead of rows and columns?

Ted537 (talk) 18:28, 18 June 2022 (UTC)

"horizontal row" is a direct translation from "senkrechte Reihen" in the original text:

Zunächst sind ebenso viele Nummern zu verloosen, als Theilnehmer
vorhanden sein: bei 14 Theilnehmern z. B. die Nummern 1, 2, 3 bis 14.
  Die Paarung geschieht alsdann in folgender Weise: Man fertigt
ein Schema an, welches soviel senkrechte Reihen hat, als die Hälfte
der Theilnehmer beträgt. Bei einer ungeraden Anzähl ist die Anzahl
der senkrechten Reihen die Hälfte der um 1 vergrösserten Theilnemer-
zahl. Bei 14 Theilnehmern sind daher 14/2 = 7, bei 13 Theilnehmern
(13+1)/2= 14 / 2, also ebenfalls 7 senkrechte Reihen zu bilden.

KP (talk) 10:35, 28 July 2022 (UTC)

Possible error in the graphics

https://en.wikipedia.org/wiki/Round-robin_tournament#/media/File:Round-robin-schedule-span-diagram.svg Shouldn't this have been "rotate 13 times"? (maybe with total of 14 round ) Otherwise e.g. 14 never plays with 2. 212.160.155.132 (talk) 10:22, 2 March 2023 (UTC)