A
round-robin tournament or
all-play-all
tournament is a type of
tournament "in which each contestant meets every
other contestant in turn". 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 III and All America Football
Conference for exceptions).
A round-robin tournament with four players is sometimes called a
"quad".
In
croquet and tennis
clubs in Great
Britain
, a round-robin tournament is often called an
American tournament. The term
round-robin is derived from the French term
ruban, meaning "ribbon". Over a long period of time, the
term was corrupted and idiomized to
robin.
Use
In sports with a large number of competitive matches per season,
double round-robins are common. Many
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. There are also
round-robin
chess and
go tournaments; the
World Chess Championship was
decided in 2005 and in 2007 by an eight-player double round-robin
tournament, where each player faces every other player once as
white and once as black.
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 pure round-robin scheduling include the FIFA World Cup, UEFA European Football
Championship and UEFA Cup (since
2004–05) in football, the Super 14 of
rugby union in the Southern
Hemisphere
, the Cricket World
Cup and many American Football
college
conferences, such as the Pacific
10. The group phase of the UEFA Champions League is contested as
a double round-robin, as are most basketball leagues outside the United States, including the regular-season and Top 16 phases of
the Euroleague.
Evaluation
In a round-robin format, the element of luck is seen to be reduced,
given that all competitors face the same opponents, and a few bad
performances need not cripple a competitor's chances of ultimate
victory. In
English football,
although the
FA Cup was founded before the
Football League, the (round-robin)
League champions have always been regarded as the "best" team in
the land, rather than the (
knockout) Cup winners.Disadvantages
include the existence of games 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. This asymmetry means that
playing the same opponents is not necessarily equitable: the same
opponents in a different order may play harder or easier matches.
There is also no showcase final match. Conversely, the ability to
recover from defeats, while rewarding overall consistency, may also
be seen as a crutch for competitors who lack the temperament to
handle the pressure of a knockout tournament.
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).
Swiss system tournaments
attempt to combine elements of the round-robin and elimination
formats, to provide a reliable champion using fewer rounds than a
round-robin, while allowing draws and losses.
Scheduling algorithm
If n is the number of competitors, a pure round robin tournament
requires \begin{matrix} \frac{n}{2} \end{matrix}(n - 1) games. 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.
The standard
algorithm for round-robins is
to assign each competitor a number, and pair them off 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
… then fix one competitor (number one in this example) and rotate
the others clockwise …
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
… until you end up almost back at the initial position
Round 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 and has a
bye. 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.
Footnotes
See also
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