Unit 2 Notes:
Single Elimination Tournament Introduction
also see: Recreational Sport Management by Mull, Bayless, Ross &
Jamieson, pp. 108-109
Single elimination tournaments are one of the most well-known types of tournament formats that sport programmers use. There are many advantages to programming a single elimination tournament, but like round robin tournaments, single elimination tournaments also have some disadvantages. Participants generally understand single elimination tournaments, and they produce a true winner at the end of tournament play.
Single elimination tournaments also work well as post-season playoff formats after round robin tournaments are played. Programmers are able to seed teams/players based on their performance in the round robin, allowing for better competition as the tournament progresses. If the highest seeds all "take care of business" and win their games, the #1 and #2 seeded teams will face each other in the final. Something a tournament programmer wants to avoid, however, is having the #1 and #2 seeds face each other in a round OTHER THAN the finals. Sometimes, it is not always apparent to the programmer how teams should be seeded. The programmer might not have insight regarding the teams' ability, or past performance. In these cases, it might be necessary to do a random draw to determine seeds, or the programmer may choose to seed based on order of entry.
We will see later that single elimination tournaments are based on powers of 2. That is, when the tournament size is a power of 2 (2, 4, 8, 16, 32, 64, 128, 256, ...) there will be NO first round byes. A "bye" game in a single elimination tournament only occurs in the first round, and byes are generally awarded to the highest seeded teams. Teams who receive a first round "bye" will play their first game in the second round. Byes are determined by taking the number of teams in the tournament (n) and subtracting the number from the NEXT HIGHEST power of 2. For example, in a single elimination tournament with 14 teams, you would take the next highest power of 2 (16) and subtract 14 from it:
16-14 = 2
Therefore, there will be 2 byes in the first round for your single elimination tournament with 14 teams.
Some advantages of single elimination tournaments are:
the participants understand them easily
they are the simplest tournaments to conduct
they are useful in determining a champion for preliminary tournaments, such as a round robin
they determine the champion in the shortest time compared with other tournaments
they can be conducted with limited facilities
they can accommodate a large number of entries
they are interesting for spectators
they are the most appropriate for a one-day event
they are economical to conduct
Some disadvantages of single elimination tournaments are:
they involve minimum participation
they place maximum emphasis on winning
the champion may not represent the best team or player...this also applies to the second place finisher because entries in the other half of the bracket may be better (if you have no true method for seeding)
they do not allow for an off-day
competition may become too intense because the entry must win every contest or face elimination
outdoor sport programs, with their potential for weather-related postponements, cause scheduling problems because contests must be played sequentially
they provide the least flexibility for the participant
Formulas for Single Elimination Tournaments:
with N= total number of entries, you can use the following formulas:
Formula
Number of games = N-1 13-1 =
12 games
Number of 2 - number of times 2 has to
be multiplied to equal or exceed the number
of entries
2x2 = 4
2x2x2 = 8
2x2x2x2 = 16
2x2x2x2x2 = 32
Number of Byes = Next Highest Power of 2 - N 16-13 = 3 byes
Number of Rounds = the power to which 2 must be
raised 2x2x2x2 = 4 rounds
to equal or exceed "N"
Number of first round games = N- (next lowest power of 2) 13-8 = 5 first round games