Transcript Round Robin Scheduling - Indiana University Bloomington

Round Robin Scheduling
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Round Robin
• Each entry plays all other entries in their
league at least ONCE
• Wins and losses do not affect participation
• Winner determined from win-loss percentage
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Terminology
• Tournament:
We will use the word "tournament" when we are
referring to the overall event.
– For example, we might program an intramural basketball
tournament for 100 teams.
– We will always use the word "tournament" when we are referring
to the largest unit which we are programming.
• League (aka - division, pool): We will use the
word "league" when we are referring to the
different "groups" that we put our entries into.
– For example, if we are programming an intramural basketball
tournament for 100 teams, we might choose to break down our
tournament into 20 leagues with 5 teams in each league.
– This means that not all 100 teams will play each other.
– Teams will only play other teams within their particular league.
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Round Robin Basics -- Total Number
of Games
• For example, if you are programming an
intramural singles tennis tournament in
round robin format and you have 30 people
entered, you need to place these people into
different leagues.
• You have several choices that you can make:
– You could offer one big league of 30 teams and have every
tennis player play everyone else.
– You could offer ten small leagues with 3 teams in each
league, where teams will only play the other teams in their
particular league.
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• How do you choose?
• What is the difference between one BIG 30 team
league and ten small leagues of 3 teams?
• You still have the same number of TOTAL teams,
you are just formatting them differently.
– Major differences lie in:
– the number of games that EACH TEAM will play
– depending on the number of teams in their league
– and the number of games that it will take to complete EACH
LEAGUE
– depending on the number of teams in their league.
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We use some simple formulas to
arrive at each answer:
• Where "n" = the number of teams in a
LEAGUE:
– Number of games per team/entry = n - 1
– Number of games per league = n(n-1)/2
– Number of games needed to complete the tournament =
n(n-1)/2 * number of leagues
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Lets look at some examples:
Ex. 1: Four leagues of 8 teams each
• number of games per team: 8 - 1 = 7
– each team will play 7 games
• number of games per league: 8(8-1)/2 = 28
• number of games to complete the tournament =
28 * 4 = 112 games
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Ex. 2: Three leagues of 7 teams each and ten
leagues of 6 teams each
Hint: when you have leagues with unequal
numbers of teams, treat these as separate
problems.
• number of games per team: 7 - 1 = 6
– each team will play 6 games in these league
number of games per league: 7(7-1)/2 = 21 games
number of games to complete the tournament: 21 * 3 = 63
games
• REMEMBER: You aren't done....you need to
figure out the second half of the problem!
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• number of games per team: 6 - 1 = 5
– each team will play 5 games in these leagues
• number of games per league: 6(6-1)/2 = 15
games
• number of games to complete the
tournament: 15 * 10 = 150 games
REMEMBER: You STILL aren't done...in order
to figure out TOTAL games, add both
answers together:
– 63 + 150 = 213; in this example, it will take 213
games to complete this tournament!
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• Lets go back to our tennis tournament that we
are programming from above!
If you were to use the formulas, you would
find the following information regarding some
different scheduling combinations involving
30 total teams:
• Go to overheads
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