Example of a single-elimination
tournament bracket
A
single-elimination tournament, also called a
knockout,
cup or
sudden
death tournament, is a type of
elimination tournament where the
loser of each match is immediately eliminated from winning the
championship or first prize in the event. (However, it does not
always mean that the defeated competitor will not participate
further in the tournament: in some such tournaments, consolation or
"classification" contests are subsequently held among those already
defeated to determine the awarding of lesser places, for example, a
Third place playoff.)
Format
Often, the number of participants in a single-elimination
tournament is fixed as a
power of two;
for example, the tennis
Grand
Slam singles championships are tournaments of 128 players. This
ensures all competitors will face opponents who have previously
played the same number of matches. The full schedule of pairings
across all rounds (the
bracket) may be allocated before
the start of the tournament; or each round may be allocated at the
end of the preceding round. Each successive round halves the number
of competitors remaining (assuming there are no
byes — see
below). The round in which only sixteen remain is sometimes called
the "Round of Sixteen" or "Last Sixteen", when eight remain at the
start it is generally called the
quarter-final round; this
is followed by the
semi-final round in which only four are
left, the two winners of which then meet in the final or
championship round.
In cases where the number of competitive entities at the start of
the tournament is not a power of two, some competitors may receive
a
bye in the first round,
which entitles these competitors to advance to the second round
automatically without playing.
Often, these byes will be awarded to the
highest-rated competitors in the event as a reward for some
previous accomplishment; indeed, in some American team sports
- most notably American football -
the number of teams qualifying for the postseason tournament will
be intentionally set at a number which is not a power of two, in
order to provide such an advantage to a high-achieving team in the
just-completed regular season.
Multiple rounds of byes are also possible: in the
FA Cup, the teams in the top two
league divisions
enter in the third round "proper" (of eight); the two next-highest
divisions' teams will have entered in the first round;
lower-division teams in one of 6 preliminary rounds.
When matches are held to determine places or prizes lower than
first and second (the loser of the final-round match gaining the
latter position), these typically include a match between the
losers of the semifinal matches, the winner therein placing third
and the loser fourth; sometimes contests are also held among the
losers of the quarterfinal matches to determine fifth through
eighth places (this is most commonly encountered in the
Olympic Games, with the exception of
boxing, where both fighters are deemed to be third
place). In one scenario, two "consolation semifinal" matches may be
conducted, with the winners of these then facing off to determine
fifth and sixth places and the losers playing for seventh and
eighth; those are used often in qualifying tournaments where only
the top five teams advance to the next round; or some method of
ranking the four quarterfinal losers might be employed, in which
case only one round of additional matches would be held among them,
the two highest-ranked therein then playing for fifth and sixth
places and the two lowest for seventh and eighth.
In a tournament where more than two opponents or teams can play
together at once, such as in a shootout
poker tournament, players are removed when
they can no longer play until one player remains from the group.
This player moves on to the next round.
SOP for tournament brackets.
N = the number of teams in the tournament
Start with x = 1; Repeat x = 2*x (i.e. keep doubling x) until x
exceeds N.
The number of teams with a bye for the play-in bracket, B = x –
N;
The number of teams in the play-in bracket, N – B (which also
equals 2*N-x) will be an even number. It is possible for B to equal
N, in which case there will be no play-in games.
For the play-in bracket, the team in position B+1 plays team N with
the winner taking position B+1, team B+2 plays team N-1 with the
winner taking position B+2, etc.
After the play-in games are complete, the number of teams left, F =
x/2 (N- (2*N-x)/2), will be a number for a normal bracket (2, 4, 8,
16, etc)
In the next round, team 1 plays team F with the winner taking
position 1, team 2 play team F-1 with the winner taking position 2,
etc.
Subsequent rounds proceed likewise.
Seeding
Opponents may be allocated randomly (such as in the FA Cup);
however, since the "luck of the draw" may result in the
highest-rated competitors being scheduled to face each other early
in the competition,
seeding is often used to prevent this.
Brackets are set up so that the top two seeds could not possibly
meet until the final round (should both advance that far), none of
the top four can meet prior to the semifinals, and so on.
One version of seeding is where brackets are set up so that the
quarterfinal pairings (barring any upsets) would be the 1 seed vs.
the 8 seed, 2 vs. 7, 3 vs. 6 and 4 vs. 5; however, this is not the
procedure that is followed in most tennis tournaments, where the 1
and 2 seeds are placed in separate brackets, but then the 3 and 4
seeds are assigned to their brackets randomly, and so too are seeds
5 through 8, and so on. This may result in some brackets consisting
of stronger players than other brackets, and since only the top 32
players are seeded at all in
Tennis
Grand Slam tournaments, it is conceivable that the 33rd-best
player in a 128-player field could end up playing the top seed in
the first round. While this may seem unfair to a casual observer,
it should be pointed out that rankings of tennis players are
generated by computers, and players tend to change ranking
positions very gradually, so that a more equitable method of
determining the pairings might result in many of the same
head-to-head matchups being repeated over and over again in
successive tournaments.
Sometimes the remaining competitors in a single-elimination
tournament will be "re-seeded" so that the highest surviving seed
is made to play the lowest surviving seed in the next round, the
second-highest plays the second-lowest, etc. This may be done after
each round, or only at selected intervals. In American team sports,
for example, both the
NFL and
NHL employ this tactic, but the
NBA does not (and neither does the
NCAA college
basketball tournament).
MLB does not have enough teams in its
playoff tournament where re-seeding would make a difference in the
matchups, (The NFL is at the minimum, which is 6 from each league
(or conference in the NFL, NBA or NHL) for a total of 12) . The
NBA's format calls for the winner of the first-round series between
the first and eighth seeds (within each of the two conferences the
league has) to face the winner of the first-round series between
the fourth and fifth seeds in the next round, even if one or more
of the top three seeds had been upset in their first-round series;
critics have claimed that this gives a team fighting for the fifth
and sixth seeding positions near the end of the regular season an
incentive to
tank (deliberately lose)
games, so as to finish sixth and thus avoid a possible matchup with
the top seed until one round later.
In some situations, a seeding restriction will be implemented; from
1975 until 1989, the
NFL,
and, since 1998,
MLB have a
rule where at the conference or league semifinal, should the top
seed and last seed (wild card) be from the same division, they may
not play each other; in that case, the top seed plays the worst
division champion; the second-best division champion plays the wild
card team.
Evaluation
The single-elimination format enables a relatively large number of
competitors to participate. There are no "dead" matches (perhaps
excluding "classification" matches), and no matches where one
competitor has more to play for than the other.
The format is less suited to games where
draw are frequent. In
chess,
each fixture in a single-elimination tournament must be played over
multiple matches, because
draws are
common, and because white has an advantage over black. In
association football, games
ending in a draw may be settled in extra time and eventually by a
penalty shootout, viewed
by many fans as an unsatisfactory conclusion to a fixture, or by
replaying the fixture. In various forms of
one-day cricket, a
bowl-out has been
used in recent years to settle tied matches.
Another perceived disadvantage is that most competitors are
eliminated after relatively few games. Variations such as the
double-elimination
tournament allow competitors a single loss while remaining
eligible for overall victory.
Other tournament systems
Variations of the single-elimination tournament include:
Other common tournament types are
External links
- Challonge.com Free single elimination bracket
generator and hosting/management
References