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Please Note:

You are responsible for checking the course
website for course/assignment schedules.

You will still need to down load course notes from
the course website: www.mtsu.edu/~hjgray/4110.
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Round Robin Scheduling Introduction
So you've decided to schedule a round robin tournament. Chances are, your participants will be happy
because round robin tournaments provide maximum participation for your entries. This is because each
entry plays all of the other entries in their league, regardless of their record. Teams play the games on
their schedule until they have no more games left to play. This differs from single elimination
tournaments, where an entry must win in order to keep playing.
Some advantages and disadvantages associated with choosing round robin tournaments can be found on
the Round Robin lecture...these are important to understand, as they will have an impact on how you
run your particular tournament.
Terminology
This unit in the course always seems to confuse students due to a lack of consistency in terminology.
Oftentimes, administrators are inconsistent in the way they use certain words and phrases associated
with tournament scheduling. For example, programmers and administrators may use the words,
"tournament" or "league" (or may use the words division, pool or others) interchangeably. For the
purposes of this course, the following will serve as consistent definitions for this unit:
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:
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.
Round Robin Basics -- Total Number of Games
In order to schedule a round robin tournament, it is necessary to understand several basic pieces of
information. Because round robin tournaments generally take a longer amount of time to complete
(longer than single elimination tournaments or even double elimination tournaments), you need to figure
out how many games it will take to complete your tournament. 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. 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. The major differences between these choices 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. 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
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
Number of games needed to complete the tournament = n(n-1)/2 * number of leagues
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
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. For
example:
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!
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!
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:
Leagues Offered
Games per team
n-1
Games per league
n(n-1)/2
Games per tournament
n(n-1)/2 * # of leagues
One league of 30 teams
29
435
435
Two leagues of 15 teams
14
105
210
Three leagues of 10
teams
9
45
135
Five leagues of 6 teams
5
15
75
Six leagues of 5 teams
4
10
60
Ten leagues of 3 teams
2
3
30
Do you see that even though the total number of teams in our tournament remains constant (30 teams),
the league format that we choose has a big impact on the number of games it will take us to complete our
tournament? It also has a big impact on the number of games that each team will get to play. If you were
on a team in one big 30 team league, your team would get to play 29 games! However, if you were on a
team that was in a 3 team league, your team would only get to play 2 games. So it becomes apparent
that how you format your league will have a big impact on the time it takes to finish your tournament and
the number of games that each team in your tournament will get to play.
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Your decision to go with ten leagues of 3 rather than two leagues of 15 will be largely dependent on the
facility time that you have available in which to play. If you only have a total of 40 games available to you
on your facility, and you have 30 teams that have entered to play, you are limited in the choices that you
can make. Your only choice would be to program your tournament in ten leagues of 3 teams, because
the total number of games it will take to play under this format (30) is less than the total number of games
available to you (40). If you choose any other combination, you will not be able to play all of your games.
****Also, be sure to read the Adobe file: “Round Robin Scheduling” posted on the
course website before class.
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Round Robin Scheduling
Problem Type I: Forecasting Days
In-Class Problem #1
Under the conditions stated below, find the NUMBER OF WEEKS AND THE DAY OF THE WEEK in
which a round robin tournament should end.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday.
Postponed games can be completed on weekends. Two days are set
aside at the end of league play to cover the possibility of league ties.
N = 35 teams. There are five leagues of 7 teams. The first day of play is Wednesday and the
number of games played per day is 8.
Step 1. Determine the maximum number of games that can be scheduled per day without having a team
play twice in the same day. To do this, you must find the number of games per round for each of the
leagues and add them together. Once this is completed, the total number of games per round for all
leagues must be checked to make sure that it does not exceed the number of games available per day.
(Note: if the total number of games per round is less than the number of games available per day, an
adjustment is necessary in order to prevent a team playing more than one game per day. In other words,
the number of games per round would be reduced to equal the number of games available per day)
Odd number of teams per league
= ___ games/league X ___leagues = ___ games
(n-1) = ( - ) =
2
2
2
Since only 8 games are available per day, the number of games per round (15) exceeds the
number of games that could be scheduled in one day, so no adjustment is needed. It will take
almost 2 days before teams repeat.
Step 2. Determine the total number of league games.
n(n-1) =
2
( - ) =
2
( ) =
2
2
= ___ games/league X ___ leagues =
___ total games
Step 3. Determine the total number of days it will take to complete the tournament. Divide the total
number of league games (___) by the number of games that are available each day (___).
___/__ = ___ days. (Always round up)
Step 4. Since we must add two days to the tournament scheduling process to take care of league ties,
rainouts, etc., we add 2 to the total number of days figured in Step 3.
___ days + ___ days = ___ days are needed to schedule the tournament.
Step 5. The last step is to determine the actual number of playing weeks and the ending day of the
tournament. To accomplish this, divide the total number of tournament days (___) by the number of days
scheduled per week (4 days - Monday through Thursday). Remember the starting day of the tournament
was a Wednesday.
____ days/4 days per playing week
Answer: The tournament will be completed on __________ of the ____ calendar week.
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Round Robin Scheduling
Problem Type I: Forecasting Days
In-Class Problem #2
Under the conditions stated below, find the NUMBER OF WEEKS AND THE DAY OF THE WEEK in
which a round robin tournament should end.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday.
Postponed games can be completed on weekends. Two days are set
aside at the end of league play to cover the possibility of league ties.
N = 29 teams. There are three leagues of 7 teams and one league of 8 teams. The first day of play
is Monday, and the number of games played per day is 15.
Step 1. Determine the maximum number of games that can be scheduled per day without having a team
play twice in the same day. To do this, you must find the number of games per round for each of the
leagues and add them together. Once this is completed, the total number of games per round for all
leagues must be checked to make sure that it does not exceed the number of games available per day.
(Note: if the total number of games per round is less than the number of games available per day, an
adjustment is necessary in order to prevent a team playing more than one game per day. In other words,
the number of games per round would be reduced to equal the number of games available per day)
Odd number of teams per league
(n-1)
2
Even number of team per league
n
2
9 games + 4 games = 13 games per round. Since 15 games are available per day, the
number of games per round (13) is less than the number of games that could be scheduled
in one day, so the number of games scheduled per day must be reduced to 13 so no team
will be scheduled for more than one game per day.
Step 2. Determine the total number of league games.
Step 3. Determine the total number of days it will take to complete the tournament. Divide the total number
of league games (91) by the number of games that are available each day (13-remember to use the
adjusted number).
Step 4. Since we must add two days to the tournament scheduling process to take care of league ties,
rainouts, etc., we add 2 to the total number of days figured in Step 3.
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Step 5. The last step is to determine the actual number of playing weeks and the ending day of the
tournament. To accomplish this, divide the total number of tournament days (9) by the number of days
scheduled per week (4 days - Monday through Thursday). Remember the starting day of the tournament
was a Monday.
Answer: The tournament will be completed on ________ of the ___ calendar week.
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Round Robin Scheduling: Homework Assignment #1
Homework Assignments (Collected at the beginning of every class). Please make a copy of your
completed homework assignment before class if you wish to review your homework as we go over the
assignment in class.
Please answer the following questions regarding round robin tournament scheduling and show all of
your work and staple your pages together!
1.
Assuming no league ties, find the total number of games necessary to play the following round
robin tournaments:
A.
Four leagues of 8 teams each.
N(N-1) =
2
=
=
=
games per league
___ games per league X ___ leagues = ___ total games
B.
Three leagues of 7 teams each and ten leagues of 6 teams each.
N(N-1) =
2
=
=
=
games per league for 7 team league
N(N-1) =
2
=
=
=
games per league for 6 team league
games per league X 3 leagues
games per league X 10 leagues
C.
games
games
total games
Two leagues of 9 teams and three leagues of 10 teams each.
N(N-1) =
2
=
N(N-1) =
2
=
=
=
=
____ games per league for 9 team league
= ____ games per league for 10 team league
games per league X 2 leagues =
games per league X 3 leagues =
=
2.
=
=
=
games
games
total games
Determine the winning percentages and the number of games behind for each of the listed
teams:
Wins
Total # of games played
Winning Percentages
W
L
Pct
National League-East
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Atlanta
Philadelphia
Montreal
New York
Florida
45
40
34
27
25
26
31
38
44
43
45/71 = .634
45
39
37
30
32
25
31
35
38
41
45/70 = .643
National League-Central
Cincinnati
Houston
Chicago
Pittsburgh
St. Louis
Games Behind
To figure the number of games behind a team is, use the following formula:
Team A = 1st place team
Team B = Team in question
[(# of wins of Team A)-(# of wins of Team B)] + [(# of losses of Team B) - (# of losses of Team A)]
2
W
L
Atlanta
45
26
Philadelphia
40
31
Montreal
34
38
New York
27
44
Florida
25
43
Games Behind
National League-East
0
[(45)-(40)] + [(31)-(26)]/2
[(5)] + [(5)]/2
[10]/2 = 5
5
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Team A = 1st place team
Team B = Team in question
[(# of wins of Team A)-(# of wins of Team B)] + [(# of losses of Team B) - (# of losses of Team A)]
2
W
L
Games Behind
National League-Central
Cincinnati
45
25
Houston
39
31
Chicago
37
35
Pittsburgh
30
38
St. Louis
32
41
(Statistics as of July 15, 1995)
3.
Find the number of games that can be scheduled for each entry in a round robin league under the
following conditions:
A.
N = 7 teams and a maximum of 63 games can be played.
Step 1. Determine the number of league games that can be scheduled for a single round
robin league.
Step 2. Determine the number of complete round robin tournaments that can be
scheduled utilizing the maximum number of games available. To obtain this, divide the
maximum number of games that can be schedule (63) by the number of games per
league __ (answer of step 1).
Step 3. Determine the number of games scheduled per team (N-1) in a single round
robin and then multiply that times the number of round robins that can be scheduled __
(answer of step 2).
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Round Robin Scheduling Homework Assignment #2
(See Worksheet Provided for Help)
(Use additional paper if more space is needed)
Problem Type I: Forecasting Days
Homework Assignments (Collected at the beginning of every class). Please make a copy of your
completed homework assignment before class if you wish to review your homework as we go over the
assignment in class.
Please answer the following questions regarding round robin tournament scheduling and show all of
your work and staple your pages together! A worksheet is attached to help, but CAUTION: you will not
have a worksheet on the exam!!! You need to remember/know the “steps” for the exam.
Under the conditions stated below, find the NUMBER OF WEEKS AND THE DAYS OF THE WEEK in
which a round robin tournament should end.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. Postponed
games can be completed on weekends. Two days are set aside at the end of
league play to cover the possibility of league ties.
A.
N = 67 teams. There are three leagues of 9 teams and four leagues of 10 teams. The first
day of play is Tuesday, and the number of games played per day is 7.
B.
N = 45. There are nine leagues of 5 teams. The first day of play is Thursday and 5 games
can be played per day.
C.
N = 21 teams. There are three leagues of 7 teams. The first day of play is Monday, and the
number of games played per day is 6.
D.
N = 26. There are two leagues of 5 teams and four leagues of 4 teams. The first day of
play is Thursday and 24 games can be played per day.
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Worksheet for Homework Assignment #2
(Worksheet for Problem Type I: Number of Games)
(May be duplicated or use your own paper if additional space is needed)
Homework Assignments (Collected at the beginning of every class). Please make a copy of your completed
homework assignment before class if you wish to review your homework as we go over the assignment in class.
Please answer the following questions regarding round robin tournament scheduling and show all of your work and
staple your pages together!
Use this worksheet as a guide in determining the NUMBER OF WEEKS AND THE DAY OF THE WEEK in which a
round robin tournament should end.
Step 1. Determine the maximum number of games that can be scheduled per day without having a team play twice in
the same day. To do this, you must find the number of games per round for each of the leagues and add them
together. Once this is completed, the total number of games per round for all leagues must be checked to make sure
that it does not exceed the number of games available per day. (Note: if the total number of games per round is less than
the number of games available per day, an adjustment is necessary in order to prevent a team playing more than one
game per day. In other words, the number of games per round would be reduced to equal the number of games
available per day)
Odd number of teams per league
(n-1)
2
Even number of teams per league
n
2
(Total number of games-odd number of teams) + (Total number of games-even number of teams) = Total number
of games per round.
Step 2. Determine the total number of league games.
n(n-1) X the number of leagues = total league games
2
Step 3. Determine the total number of days it will take to complete the tournament. Divide the total number of league
games ( ) by the number of games that are available each day ( ). (Always round up)
Step 4. Since we must add two days to the tournament scheduling process to take care of league ties, rainouts, etc., we
add 2 to the total number of days figured in Step 3.
Step 5. The last step is to determine the actual number of playing weeks and the ending day of the tournament. To
accomplish this, divide the total number of tournament days ( ) by the number of days scheduled per week ( ).
Answer: The tournament will be completed on
of the
playing week or
calendar week.
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Round Robin Scheduling
Problem Type II: Number of Games
In-Class Problem #1
Under the conditions stated below, find the MINIMUM NUMBER OF GAMES that must be available for each day to
complete a round robin tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. Postponed games
can be completed on weekends. Two days are set aside at the end of league play to
cover the possibility of league ties, rainouts, etc.
N = 107 teams. There are three leagues of 9 teams and ten leagues of 8 teams. Five weeks are available for play.
Step 1. Determine the total number of league games.
Step 2. Determine the total number of days that are available to conduct the tournament using the number of weeks and
the number of days per week given.
Step 3. Since two days are set aside at the end of league play to cover the possibility of league ties, rainouts, etc. these
two days must be deducted from the total number of days determined in Step 2.
Step 4. Determine the minimum number of games that must be available per day. To find this figure, divide the total
number of league games (____) by the total adjusted days available for play (____).
Step 5. Check to make sure that teams will not play more than one game per day. In other words, the number of games
available per day (Step 4) must be less than or equal to the maximum total number of games per round. We must
determine the maximum number of games per round that can be scheduled before proceeding into round two of the
tournament. To figure the total number of games per round, use the following formulas:
Odd number of teams per league
n -1
2
Even number of teams per league
= ____ games/round
___ leagues x ___ games/round =
n = ____ games/round
2
games/rd
___ leagues x ___ games/round =
games/rd
Total number of games per round = 12 + 40 = 52 total games per round
Since our calculation of ____ games per day (Step 4) is less than the total number of games per round (____),
teams will not play more than once per day. (It will take ____ days for all teams to play at least once.)
Answer: A minimum of ____ games must be available per day in order to complete the tournament.
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Round Robin Scheduling
Problem Type II: Number of Games
In-Class Problem #2
Under the conditions stated below, find the MINIMUM NUMBER OF GAMES that must be available for each
day to complete a round robin tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday.
Postponed games can be completed on weekends. Two days are set aside
at the end of league play to cover the possibility of league ties, rainouts, etc.
N = 34 teams. There are six leagues of 5 teams and 1 league of 4 teams. Four weeks are available for
play.
Step 1. Determine the total number of league games.
Step 2. Determine the total number of days that are available to conduct the tournament using the number of
weeks and the number of days per week given.
Step 3. Since two days are set aside at the end of league play to cover the possibility of league ties, rainouts,
etc. these two days must be deducted from the total number of days determined in Step 2.
Step 4. Determine the minimum number of games that must be available per day. To find this figure, divide
the total number of league games (___) by the total adjusted days available for play (___).
Step 5. Check to make sure that teams will not play more than one game per day. In other words, the
number of games available per day (Step 4) must be less than or equal to the maximum total number of
games per round. We must determine the maximum number of games per round that can be scheduled
before proceeding into round two of the tournament. To figure the total number of games per round, use the
following formulas:
Answer: A minimum of ___ games must be available per day in order to complete the tournament.
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Round Robin Scheduling
Problem Type II: Number of Games
In-Class Problem #3
Under the conditions stated below, find the MINIMUM NUMBER OF GAMES that must be available for each
day to complete a round robin tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday.
Postponed games can be completed on weekends. Two days are set aside
at the end of league play to cover the possibility of league ties, rainouts, etc.
N = 67 teams. There are five leagues of 5 teams and seven leagues of 6 teams. Six weeks are
available for play.
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Answer: A minimum of _____ games must be available per day in order to complete the tournament.
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Round Robin Scheduling Homework Assignment #3
(See Worksheet Provided for Help)
(Use additional paper if more space is needed)
Problem Type II: Number of Games
Homework Assignments (Collected at the beginning of every class). Please make a copy of your
completed homework assignment before class if you wish to review your homework as we go over the
assignment in class.
Please answer the following questions regarding round robin tournament scheduling and show all of your
work and staple your pages together! A worksheet is attached to help, but CAUTION: you will not have a
worksheet on the exam!!! You need to remember/know the “steps” for the exam!
Under the conditions stated below, find the MINIMUM NUMBER OF GAMES that must be available for each
day to complete a round robin tournament.
ASSUMPTIONS:
A.
Regularly scheduled games are played Monday through Thursday. Postponed
games can be completed on weekends. Two days are set aside at the end of league
play to cover the possibility of league ties, rainouts, etc.
N = 25 teams. There are three leagues of 6 teams and one league of 7 teams. Five weeks are
available for play.
B.
N = 22. There are two leagues of 7 teams and one league of 8 teams. Four weeks are available
for play.
C.
N = 37 teams. There are three leagues of 7 teams and two leagues of 8 teams. Six weeks are
available for play.
D.
N = 43. There are two leagues of 8 teams and three leagues of 9 teams. Nine weeks are
available for play.
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Worksheet for Homework Assignment #3
(May be duplicated or use your own paper if additional space is needed)
(Worksheet for Problem Type II: Number of Games)
Homework Assignments (Collected at the beginning of every class). Please make a copy of your
completed homework assignment before class if you wish to review your homework as we go over the
assignment in class.
Please answer the following questions regarding round robin tournament scheduling and show all of your
work and staple your pages together!
Use this worksheet as a guide in determining the MINIMUM NUMBER OF GAMES that must be available for
each day to complete a round robin tournament.
Step 1. Determine the total number of league games.
n(n-1) =
_____ games per league X _____ leagues = _____ total
games
2
Step 2. Determine the total number of days that are available to conduct the tournament using the number of
weeks and the number of days per week given.
_____ days per week X _____ weeks = _____ days available for play
Step 3. Since two days are set aside at the end of league play to cover the possibility of league ties, rainouts,
etc. these two days must be deducted from the total number of days determined in Step 2.
_____ days - _____ days for league ties, rainouts, etc. = _____ total adjusted days available
for play
Step 4. Determine the minimum number of games that must be available per day. To find this figure, divide
the total number of league games (_____) by the total adjusted days available for play (_____). (Always
round up)
Step 5. Check to make sure that teams will not play more than one game per day. In other words, the
number of games available per day (Step 4) must be less than or equal to the maximum total number of
games per round. We must determine the maximum number of games per round that can be scheduled
before proceeding into round two of the tournament. To figure the total number of games per round, use the
following formulas:
Odd number of teams per league
n-1
2
=
Even number of teams per league
_____ games/round
_____ league x _____ games/round =
n
2
games/rd
= _____ games/round
______ leagues x ______games/rd =
games/rd
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Total number of games per round = (Odd) + (Even) = _____ total games per round
If our calculation of the number of games per day (Step 4) is less than the total number of games per
round, teams will not play more than once per day.
Answer: A minimum of _____ games must be available per day in order to complete the tournament.
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Unit 2 Notes:
Round Robin Scheduling
Facility Availability
One of the FIRST items of concern for a recreational sports programmer is to get an idea of the availability of
your potential playing site. Each setting and each organization will have different ways of reserving facility
space. In some organizations, you will have unlimited access to facilities for your programs' use. In other
settings, you will have to request to use certain facilities and you better have a good idea of what you will
need, because if you do not utilize the facilities which have been reserved for you, you will undoubtedly be
impacting the ability of others to run other programs. For example, if you are programming an intramural
soccer league and you reserve 4 soccer fields for play at 5:00 p.m., 6:00 p.m., 7:00 p.m. and 8:00 p.m., but
you only end up playing games at 5:00 p.m. and 6:00 p.m., you will be wasting the game times available to
you at 7:00 p.m. and 8:00 p.m. The next time you decide to run a soccer league, you can bet that the facility
coordinator will remember that you didn't maximize the use of your facility! Count on getting less facility
availability the next time around!
Example:
Lets go back to our example of the intramural tennis league that we are going to program. The first thing that
you should do is reserve your tennis facility. Lets say that our facility coordinator has allowed you to play
matches Monday through Friday, on 4 courts, between the hours of 4:00 p.m. and 7:00 p.m. during a 1 week
period of time. Now you have a decision to make. Because you only have limited use of your tennis courts,
you must consider putting a time limit on each of the matches that will be played. How long are your tennis
matches going to last? Are you going to play matches on the hour? If so, you have to modify your tennis
rules so that your matches will be complete in one hour. The decision that you make will have an impact on
the number of teams that you will be able to allow to enter into your league. This is your decision, and is
based on a number of factors, including the philosophy of your program, the number of participants you want
to allow play, the number of matches you want to give each participant, etc.
Okay, lets say you've decided to play matches consisting of one set. The winner of the set will win the
match, and you feel confident that participants should be able to play a set in approximately 45 minutes.
Allowing time for injuries, check-in and other possible delays, you decide to schedule matches every 1 hour.
Your next step is to develop a Master Facility Schedule showing the times you have available to play.
Develop your Master Schedule for every day that the league is going to operate.
Monday:
Time/Field
1
2
3
4
4:00 p.m.
5:00 p.m.
6:00 p.m.
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Tuesday
Time/Field
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
4:00 p.m.
5:00 p.m.
6:00 p.m.
Wednesday:
Time/Field
4:00 p.m.
5:00 p.m.
6:00 p.m.
Thursday:
Time/Field
4:00 p.m.
5:00 p.m.
6:00 p.m.
Friday
Time/Field
4:00 p.m.
5:00 p.m.
6:00 p.m.
Now that you have your Master Facility Schedule drawn, you can figure out how many total matches are
possibly available to you. In this case, you see that you are able to play 12 matches in a day. This would
allow you to play 60 matches in one week. Since you have only have 1 week reserved, you can play a total
of 60 possible matches. This information is the starting point to help you begin creating your round robin
schedule!
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Unit 2 Notes:
Scheduling the Tournament
Who Plays Who?
Now that you know what your facility availability looks like and now that you know the total number of matches
you POSSIBLY could play, it is time to start the scheduling process. Lets go back to the example we have
been using. Lets say that we have 30 participants signed up to play in our tennis tournament. After we
develop our tournament Master Schedule, we need to make a decision on league and tournament format.
How many leagues are we going to offer? How many participants are going to be in each league? Now is
the time to start playing with possible team/league combinations, and plugging numbers into the formulas we
learned to see how many games it is going to take us to play our tournament. You can go ahead and try
various combinations that add up to your total of 30 participants (one league of 30, two leagues of 15, etc.)
Upon reviewing your choices, which combination of leagues and teams makes the most sense? Remember,
we only have 60 possible matches available to us. Knowing this, we can forget about one big 30 participant
league (takes 435 matches), two leagues of 15 participants (takes 210 matches), three leagues of 10
participants (takes 135 matches), or five leagues of 6 participants (takes 75 matches). So what's left? It
looks like we could choose, 1) six leagues of 5 participants (60 matches) or, 2) ten leagues of 3 participants
(30 matches). In this case, we want to maximize the use of our facility and waste as few matches as
possible. If we go with choice #1, we will not waste any matches...we will use every available match time (60
minus 60). If we choose choice #2, we would be wasting 34 matches (64 minus 30). So lets go with choice
#1.
So how is our schedule going to look? Who plays who? In some settings, your work is practically done. Now
that you made the tough decisions, you may have the luxury of plugging all of this information into a computer
scheduling program and the computer will do all of the scheduling work for you. Other settings aren't so
fortunate, though, and you will be stuck doing schedules the old way. Since we chose to go with six leagues
of 5 participants, we should come up with a basic scheduling template.
Scheduling Template
The first step to accomplish is to figure out how many rounds are going to be played in your tournament. A
round is just one completed set of games played in the entire round robin tournament. To figure out how
many rounds make up your tournament, you can use these formulas:
where "n" = the number of teams in the league:
For even number entries: n - 1
For odd number entries: n
In our case, we have six leagues of 5 teams. Since "5" is an odd number, it will take 5 rounds to complete
one of our 5 team leagues.
Rounds
1
2
3
4
5
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The second step to accomplish is to figure out how many games (or matches) are going to be played in each
round. You can accomplish this by using these formulas:
where "n" = the number of teams in the league
For even number entries: n/2
For odd number entries: n-1/2
In our case, we are going to play 2 games per round. This is because 5 is an odd number; so we use the
formula n-1/2 to yield our number of games. Since n-1 = 4, and 4/2 = 2, we will play 2 games per round.
Games/Rounds
1
2
3
4
5
Bye
1
2
You can see that in our example, we placed the word "Bye" in the top slot. Whenever you have an odd
number of entries in a league, you will always have one team that will not be able to play during that round.
The "bye" rotates, so that every team eventually will sit out for one round. Even though we don't consider the
"bye" slot to be a game, we still account for it because it makes our scheduling process easier.
In order to figure out who plays who in each round (for odd number entries), begin in the first round. Always
place a "B" in the upper left had corner, followed by a sequence of numbers starting with "1" for each game in
the round. When you hit the last game listed, come back up the column, beginning from the bottom to the
top. The "v" between the numbers stands for "versus". For example:
Rounds
1
Bye
B-5
1
1v4
2
2v3
2
3
4
5
For subsequent rounds, again begin with the "B" in the upper left hand corner. The other numbers will rotate
counterclockwise, beginning with the "bye" team. The "B" always remains constant. Do this for all
subsequent rounds. For example:
Rounds
1
2
3
4
5
Bye
B-5
B-4
B-3
B-2
B-1
1
1v4
5v3
4v2
3v1
2v5
2
2v3
1v2
5v1
4v5
3v4
You now have a scheduling template for a 5 team league. Notice that by the end of 5 rounds, every team has
played every other team, and each team has taken a turn as the "bye" team.
To create a scheduling template for a league with an even number of teams, use the same principle, except
the number "1" will be your constant. Place the "1" in the upper left-hand corner and rotate all other numbers
around the 1 in a counterclockwise pattern. For example, lets look at a 4 team league:
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Number of rounds: use n - 1; we have 4 -1 = 3 rounds
Number of games per round: use n/2; we have 4/2 = 2 games per round
Games/Rounds
1
2
3
1
1v4
1v3
1v2
2
2v3
4v2
3v4
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Unit 2 Notes:
Creating the Schedule
Lets recap...we have been working on putting together a round robin schedule for a tennis tournament
consisting of 30 teams. In order to accomplish this feat, we have gone through the following steps:





Created a Master Facility Schedule based on facility availability
Determined the total number of possible games available to us to play
Figured out how many leagues we would offer and how many teams would be in each league
Determined the number of rounds and number of games played in each round for each of our
leagues
Created a scheduling template for each league, determining the opponents for each round of the
tournament
Now its time to place our participants in their appropriate leagues and schedule our tournament.
Determining which participants are placed in which leagues is totally at the discretion of the programmer.
This is your chance to place participants into leagues based on skill level, time preferences, gender, housing
units or other units of participation. You can obtain this information from your participants when they register
for your tournament. Have the participants note on their registration form the information that you would want
in order to place them in a league. Lets keep our example simple....in our tournament, we have 30 total
participants. We have 15 men and 15 women. Of the 15 men, 5 are considered "advanced" and 10 are
considered "intermediate". Of the women, 5 are considered "advanced", 5 are considered "intermediate" and
5 are considered "beginners". We will assume that all participants will be available to play at the times we
schedule them...we will not have any participant time conflicts.
Our participants are:
Arnold, Alice, Bob, Barbara, Chuck, Candy, Doug, Darla, Ed, Emily, Frank, Feona, Greg, Glenda, Harry,
Helen, Jerry, Jackie, Kurt, Karla, Larry, Laura, Mike, Millie, Nick, Nora, Pete, Paula, Rich, Rachael
Remember, we decided to program six leagues of 5 participants each.
Men's
Men's
Intermediate Intermediate
1
2
League/Participant
Men's
Advanced
1
Arnold
Frank
2
Bob
3
Women's
Advanced
Women's
Intermediate
Women's
Beginner
Larry
Alice
Feona
Laura
Greg
Mike
Barbara
Glenda
Millie
Chuck
Harry
Nick
Candy
Helen
Nora
4
Doug
Jerry
Pete
Darla
Jackie
Paula
5
Ed
Kurt
Rich
Emily
Karla
Rachael
We now need to place our league matches on our Master Facility Schedule. Lets go ahead and begin with
the first round of our tournament. There are several rules of thumb that we want to use when we are
determining our league schedules. Remember, we want to be fair to everyone. When possible, try to follow
these basic rules:
1. Try to keep participants' match/game times consistent
2. Try not to schedule participants to play more than once in a given day
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3. If you have to play more than once per day, try not to schedule back-to-back matches/games
4. If you have to schedule back-to-back matches, try to schedule the same for everyone
Lets go ahead and start. We need to first determine how many match slots one of our leagues will occupy in
order to complete one round. We can get this information by looking at the number of games that we will play
in each round. Remember, we can use the formula n-1/2 to figure this out. In this case, we are playing in 5
team leagues. Therefore, 5-1 = 4 and 4/2 = 2. So each league will require us to play 2 matches to complete
one round. This means that each league will require the use of 2 courts to play their first round matches.
Lets use the following abbreviations for our leagues:
Men's Advanced = MA
Men's Intermediate 1 = MI-1
Men's Intermediate 2 = MI-2
Women's Advanced = WA
Women's Intermediate = WI
Women's Beginner = WB
Begin plugging in leagues into available time slots, making sure you use 2 courts for each league. Where you
place the leagues on the schedule is up to you!
Monday:
Time/Field
1
2
3
4
4:00 p.m.
MA
MA
MI-1
MI-1
5:00 p.m.
WA
WA
MI-2
MI-2
6:00 p.m.
WI
WI
WB
WB
Remember our scheduling template? This is going to decide the schedule for Monday's matchups. In a 5team league, we determined that our first round would be:
Bye - 5
1v4
2v3
So our first round matchups in the Men's Advanced League will be:
Court 1 at 4:00 p.m. Arnold v. Doug
Court 2 at 4:00 p.m. Bob v. Chuck
(Ed has the Bye!)
Go ahead and repeat this scheduling process for all of your leagues, and you have scheduled the first round
of your tournament!
In order to schedule the subsequent rounds of your tournament, repeat this process. Remember to try and
keep match times consistent, when possible. If the Men's Advanced league is playing at 4:00 p.m. on
Mondays, try to have them play at 4:00 p.m. on Tuesdays as well. Lets try this again:
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Tuesday:
Time/Field
1
2
3
4
4:00 p.m.
MA
MA
MI-1
MI-1
5:00 p.m.
WA
WA
MI-2
MI-2
6:00 p.m.
WI
WI
WB
WB
Notice that our league times are able to stay the same. The only thing that will change, here, is going to be
our scheduling matchups. For example, you will now use the scheduling template for round 2 of a 5 team
round robin to determine Tuesday's matches.
Our second round template shows that:
Bye - 4
5v3
1v2
So our second round matchups in the Men's Advanced league will be:
Court 1 at 4:00 p.m. Ed vs. Chuck
Court 2 at 4:00 p.m. Arnold vs. Bob
(Doug now has the Bye!)
Again, go ahead and repeat this process for all of your leagues, and you will have scheduled the second
round of your tournament! You can also go and repeat all of these steps to finish scheduling your tournament
for Wednesday, Thursday, and Friday!
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Round Robin Scheduling
In-Class Problem #1
Problem Type III: Number of Entries
Under the conditions stated below, find the MAXIMUM NUMBER OF ENTRIES that can be scheduled in a
round robin tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Sunday. Two
days are set aside at the end of league play to cover the possibility of league
ties.
Two weeks are available and 5 games can be played per day.
Step 1. Determine the actual number of days that are available for play. This includes days set aside for
league ties, rainouts, etc.
Total days available = Days available - (League ties, rainouts, etc.)
= (___ weeks X ___ days per week) - (___ days set aside)
= ___ - ___
= ____total days available
Step 2. Determine the total number of league games possible.
Total league games
= Total days available X Number of games available per day
= ___ X ___
= ___ total league games possible
Step 3. Determine the number of games required to complete a 3-team round robin.
n(n - 1)
2
= ___ games per league
Step 4. Determine the number of leagues possible by dividing the number of games required per league (___)
into the total number of league games possible (___).
= ___ leagues
Step 5. Determine the total number of teams that can be scheduled. This is calculated by multiplying the
number of leagues (___) times the number of entries in each league (___).
___ leagues X ___ teams per league = ___ total teams
ANSWER: ___ total teams can be accommodated in the tournament.
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Round Robin Scheduling
In-Class Problem #2
Problem Type III: Number of Entries
Under the conditions stated below, find the MAXIMUM NUMBER OF ENTRIES that can be scheduled in a
round robin tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday.
Postponed games can be completed on weekends. Two days are set aside
at the end of league play to cover the possibility of league ties.
Ten weeks are available and 3 games can be played per day.
Step 1. Determine the actual number of days that are available for play. This includes days set aside for
league ties, rainouts, etc.
Step 2. Determine the total number of league games possible.
Step 3. Determine the number of games required to complete a 3-team round robin.
Step 4. Determine the number of leagues possible by dividing the number of games required per league
(___) into the total number of league games possible (___).
Step 5. Determine the total number of teams that can be scheduled. This is calculated by multiplying the
number of leagues (___) times the number of entries in each league (___).
ANSWER: ___ total teams can be accommodated in the tournament.
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Round Robin Scheduling
In-Class Problem #3
Problem Type III: Number of Entries
Under the conditions stated below, find the MAXIMUM NUMBER OF ENTRIES that can be scheduled in a
round robin tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday.
Postponed games can be completed on weekends. Two days are set aside
at the end of league play to cover the possibility of league ties.
Four weeks are available and 5 games can be played per day.
ANSWER: ____ total teams can be accommodated in the tournament.
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Round Robin Scheduling Homework Assignment #4
(See Worksheet Provided for Help)
(Use additional paper if more space is needed)
Problem Type III: Number of Entries
Homework Assignments (Collected at the beginning of every class). Please make a copy of your
completed homework assignment before class if you wish to review your homework as we go over the
assignment in class.
Please answer the following questions regarding round robin tournament scheduling and show all of your
work and staple your pages together!
Under the conditions stated below, find the MAXIMUM NUMBER OF ENTRIES that can be scheduled in a
round robin tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. Postponed
games can be completed on weekends. Two days are set aside at the end of league
play to cover the possibility of league ties.
A.
Seven weeks are available and 4 games can be played per day.
B.
Nine weeks are available and 8 games can be played per day.
C.
Five weeks are available and 8 games can be played per day.
D.
Five weeks are available and 5 games can be played per day.
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Worksheet for Homework Assignment #4
(Worksheet for Problem Type III: Number of Entries)
Homework Assignments (Collected at the beginning of every class). Please make a copy of your
completed homework assignment before class if you wish to review your homework as we go over the
assignment in class.
Please answer the following questions regarding round robin tournament scheduling and show all of your
work and staple your pages together!
Use this worksheet as a guide in determining the MAXIMUM NUMBER OF ENTRIES that can be
accommodated in a round robin tournament.
Step 1. Determine the actual number of days that are available for play. This includes days set aside for
league ties, rainouts, etc.
Total days available
= Days available - (League ties, rainouts, etc.)
Step 2. Determine the total number of league games possible.
Total league games
= Total days available X Number of games available per day
Step 3. Determine the number of games required to complete a 3-team round robin.
n(n - 1) =
2
_____ games per league
Step 4. Determine the number of leagues possible by dividing the number of games required per league
(___) into the total number of league games possible (___). (Always round down)
Step 5. Determine the total number of teams that can be scheduled. This is calculated by multiplying the
number of leagues (___) times the number of entries in each league (___).
___ leagues X ___ teams per league = ___ total teams
ANSWER: ___ total teams can be accommodated in the tournament.
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Round Robin Scheduling Homework Assignment #5
(Use additional paper if needed)
Please answer the following questions regarding round robin tournaments scheduling and show all your work!
1. As the sports coordinator for your corporation, you are responsible for programming a flag football
tournament for your corporation’s recreational sport program. Available to you for this single round robin
tournament are 3 fields for 2 nights per week (Monday and Tuesday) and 4 fields for 3 nights per week
(Wednesday, Thursday and Friday). On all fields and on all nights the tournament will be played from 5pm
until 9pm. For each of the 280 teams entered in the tournament, games will take one hour to play with no
team playing more than 1 game on any given day/ You have reserved the facility for 12 weeks, and remember
you must plan on 2 days for league ties.
A. How many games can be played in one week?
________games per week
B. How many leagues can be accommodated and how large is each league? (What combinations make
sense?)
________leagues of ________ teams
C. How many total games will be played in the tournament? (Here you work out each combination from #
B and pick the best combination that will use the maximum space given, but allow time to finish the
tournament).
________games for the entire tournament
D. If you begin play on Tuesday of the first week, when will the round robin be
Completed?
________ day of the _______ week
2.
You have 107 entries in your wallyball tournament which have already been placed into 10 leagues of 8
teams and 3 leagues of 9 teams. You have reserved the courts for 5 weeks and will be able to play 4
days (M, T, W, R) per week. In order to finish this tournament in the allotted time (plan on 2 days for
league ties), how many games must be played per day?
3.
At the tennis club of which you are the program director, you want to host a round robin tournament. You
have 9 weeks available for this tournament and are able to accommodate 8 games a day. How many
entries can you accept for this tournament? Assumptions: Regularly scheduled games are played
Monday through Thursday. Postponed games can be completed on weekends. Two days are set aside
at the end of league play to cover the possibility of league ties, rainouts, etc. determine # of games
required to complete a 3-team round robin when applicable.
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39 of 68
Round Robin Scheduling Homework Assignment #6
(Use additional paper if needed)
Please answer the following questions regarding round robin tournament scheduling. Use the Teams
Schedule and Master Schedule forms to complete this assignment. Staple all of your worksheets to this page!
Problem: You are responsible for scheduling a recreational sports volleyball tournament. You have access
to four volleyball courts on Monday, Wednesday, and Thursday nights for a period of two weeks. Nine teams
have entered the tournament.
Women’s League A
Men’s League A
Safe Sets
Bumps-n-Bruises
Supreme Court
Bump-Set-Spike
Kimbas
License to Kill
Spikers
VB Six Pack
Purple Helmets
th
Dates for the tournament begin on Monday, October 13 . Teams in Women’s League are unable to play on
th
Wednesday, October 15 and the teams in the Men’s League are unable to play on Thursday, October 16th
and Monday, October 20th.
Games are one hour in length.
There will be two officials per game receiving $10.00 per game each.
There will be one supervisor per night receiving $12.00 per hour.
The courts are only available from 6:00p.m.-10p.m.
A team should only play one game per night.
Assignment:
Based on the information given above, complete the following tasks:
1. Prepare team schedules using the attached forms.
2. Develop a master schedule using the attached forms.
3. Determine personnel costs for:
A. Officials
B. Supervisors
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P/R324 Recreational Sports Programming
Round Robin Scheduling
SPORT: ________________________________
LEAGUE: _______________________________
DIVISION: _____________________________
Team # vs
Team #
Date
Time
Field
Team # vs
Team #
Date
Time
Field
LEAGUE TEAMS
Team #
1.
2.
3.
4.
SPORT: ________________________________
LEAGUE: _______________________________
DIVISION: _____________________________
LEAGUE TEAMS
Team #
1.
2.
3.
4.
5.
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Round Robin Scheduling Extra Study Problems
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. Postponed
games can be completed on weekends. Two days are set aside at the end of league
play to cover the possibility of league ties.
Under the conditions stated above, find the NUMBER OF WEKS AND THE DAY OF THE WEEK in which a
round robin tournament should end.
A. N = 42 teams. There are three leagues of 4 teams and six leagues of 5 teams. The first day of play
rd
is Monday, and the number of games played per day is 10. Answer: Tuesday of 3 calendar week.
B. N = 90. There are 15 leagues of 6 teams. The first day of play is Wednesday and 60 games can be
played per day. Answer: Thursday of the 2nd calendar week.
C. N = 64 teams. There are eight leagues of 5 teams and six leagues of 4 teams. The first day of play
is Tuesday, and the number of games played per day is 8. Answer: Tuesday of the 5th calendar
week.
D. N = 30. There are six leagues of 5 teams. The first day of play is Monday and 5 games can be
played per day. Answer: Tuesday of the 4th calendar week.
Under the conditions stated above, find the MINIMUM NUMBER OF GAMES that must be available for each
day to complete a round robin tournament.
A. N = 45 teams. There are nine leagues of 5 teams. Eight weeks are available for play. Answer: 3
games per day.
B. N = 17. There are three leagues of 4 teams and one league of 5 teams. Five weeks are available for
play. Answer: 2 games per day.
C. N = 75 teams. There are 15 leagues of 5 teams. Five weeks are available for play. Answer: 9
games per day
D. N = 220. There are 40 leagues of 5 teams and five leagues of 4 teams. Six weeks are available for
play. Answer: 20 games per day.
Under the conditions stated above, find the MAXIMIMUM NUMBER OF ENTRIES that can be accommodated
in a round robin tournament.
A.
B.
C.
D.
Three weeks are available and 16 games can be played per day. Answer: 159 total teams.
Four weeks are available and 40 games can be played per day. Answer: 558 total teams
Five weeks are available and 10 games can be played per day. Answer: 180 total teams.
Two weeks are available and 10 games can be played per day. Answer: 60 total teams.
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43 of 68
Unit 2 Notes:
Single Elimination Tournament Introduction
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
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




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
to equal or exceed "N"
Number of first round games = N- (next lowest power of 2)
2x2x2x2 = 4 rounds
13-8 = 5 first round games
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Unit 2 Notes:
Forecasting Single Elimination Tournament - Determining Number of Days
There are basically three variables that a sports programmer needs to know in order to schedule a single
elimination tournament. They are the number of entries in the tournament (n), the number of days
needed to conduct the tournament, and the number of games needed to play each day of the
tournament. By knowing any of these two variables, the programmer can figure out the third. The first step
for the programmer, therefore, is to figure out which piece of information they need to figure out.
For forecasting days, the programmer will know the number of teams in the tournament and the number of
games that are played each day of the tournament. The programmer is trying to determine how many days
the tournament will take, if teams are ONLY PLAYING ONE GAME PER DAY.
Here's how it works....
Lets say that the following information is applicable for our tournament:
N= 27 teams
Number of games that can be played each day = 5
Step 1: Determine the number of first round games
You can determine this by subtracting the NEXT LOWEST POWER OF 2 from the number of teams in your
tournament. In this case, 27 - 16 = 11 first round games.
Step 2: Establish the number of rounds for the tournament.
You can determine this by determining the number of times 2 must be multiplied to equal or exceed N. For
example:
2 x 2 x 2 x 2 x 2 =32. We multiplied 2 FIVE times...therefore, we will have 5 rounds in our tournament.
Step 3: After the number of rounds have been determined, the next step is to enter the number of first round
games (Step 1) under round 1 and always enter 1 game in the last round.
Round 1
2
Games 11
3
4
5
1
Step 4: Once the number of first and last round games has been listed, list the number of games in each
round starting with the next to last round (in this case, the 4th round) and work our way back to the first
round. The number of games per round is always a multiple of 2.
Round 1
Games 11
2
8
3
4
4
2
5
1 = 26 games
Always check your answer by using the formula of N-1 for the total number of games. In our case, 27-1 = 26
games.
Step 5: After the number of games per round has been established, we can determine how many days are
required to play the number of games in each round. We do this by determining the number of games that
can be played on a round by round basis (no team plays more than once per day). Start with the last round
and work backwards. For rounds which only take one day to complete, when the number of games available
per day is greater than or equal to the number of games listed in the round, place a 1 in that column.
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Round 1
Games 11
Days
2
8
3
4
1
4
2
1
5
1
1
When the number of games is greater than the number available per day, STOP!
Step 6: Once we have reached the point where the number of games needed per day per round is greater
than the number of games available per day, we go back to the first round and determine the number of days
required to play each round. We subtract the difference in games from the NEXT round in order to eliminate
wasted games early in the tournament.
Round 1
Games 11
Days 3
2
3
8 (4) 4
1
1
4
2
1
5
1
1 = 7 days
Notice it will take 3 days to play 11 games if we can play 5 games per day. Given that information, we will
have 4 days left over (3 x 5 =15 games....we only need to play 11 games in the first round, so 15-11 = 4
games left over). We subtract 4 from the 8 games in the second round, leaving us with 4 games to play. If
we can play 5 games per day, it will only take us 1 day to play the 4 games in the second round.
The total number of days needed to complete the tournament is determined by adding the number of days for
each round.
47 of 68
Single Elimination Scheduling
In-Class Problem #1
Problem Type I: Forecasting Days
Under the conditions stated below, find the MINIMUM NUMBER OF DAYS needed to conduct a single
elimination tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. No team should
play more than one game per day.
N = 14 entries
Number of game times available each day = 6
Step 1. The first step in solving the problem is to determine the number of first round games that will be
played.
First round games
= (N) - the next lower power of two
= (___) - ___ (Remember, 2, 4, 8, 16, 32......)
= ___ first round games
Step 2. Establish the number of rounds for the entire tournament.
The number of rounds is always the power to which 2 must be raised to equal or exceed N.
Power of two =
N = ___
2
2 = (2 x 2) = 4
Round
Step 3. After the number of rounds has been determined, the next step is to enter the number of first round
games (Step 1) under Round 1.
Round
Games
Step 4. Once the number of first round games has been listed, list the number of games in each round
starting with the last round and working your way back to the first round. The number of games per round is
always a multiple of two (1, 2, 4, 8, 16, 32, 64, 128, etc.)
Round
Games
= ___ games
48 of 68
Always check you answer by using the formula of (N - 1) for the total number of games. In this case, N=___
or ___ games which is what we determined in the previous step.
Step 5. After the number of games per round has been established, we can determine how many days are
required to play the number of games in each round. We do this by determining the number of games that
can be played on a round by round basis (no team plays more than once per day). Start with the last round
and work backwards. For rounds which only take one day to complete (when the number of games available
per day is greater than or equal to the number of games listed in the round), place a 1 in that column.
Round
Games
Days
= ___ days
Since six games are available per day, we can play each round in one day.
The total number of days needed to complete the tournament is determined by adding the number of days for
each round (___ + ___+ ___ + ___) which totals ___.
Answer: It will take ____ days to complete the tournament.
49 of 68
Single Elimination Scheduling
In-Class Problem #2
Problem Type I: Forecasting Days
Under the conditions stated below, find the MINIMUM NUMBER OF DAYS needed to conduct a single
elimination tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. No team should
play more than one game per day.
N = 17 entries
Number of game times available each day = 9
Step 1. The first step in solving the problem is to determine the number of first round games that will be
played.
Step 2. Establish the number of rounds for the entire tournament.
Step 3. After the number of rounds has been determined, the next step is to enter the number of first round
games (Step 1) under Round 1.
Step 4. Once the number of first round games has been listed, list the number of games in each round
starting with the last round and working your way back to the first round. The number of games per round is
always a multiple of two (1, 2, 4, 8, 16, 32, 64, 128, etc.)
Always check you answer by using the formula of (N - 1) for the total number of games. In this case, N= ___
or ___ games which is what we determined in the previous step.
50 of 68
Step 5. After the number of games per round has been established, we can determine how many days are
required to play the number of games in each round. We do this by determining the number of games that
can be played on a round by round basis (no team plays more than once per day). Start with the last round
and work backwards. For rounds which only take one day to complete (when the number of games available
per day is greater than or equal to the number of games listed in the round), place a 1 in that column.
Round
Games
Days
Answer: It will take ___ days to complete the tournament.
51 of 68
Single Elimination Scheduling Homework Assignment #1
Problem Type I: Forecasting Days
Homework Assignments (Collected at the beginning of every class). Please make a copy of your
completed homework assignment before class if you wish to review your homework as we go over the
assignment in class.
Please answer the following questions regarding round robin tournament scheduling and show all of your
work and staple your pages together!
Under the conditions stated below, find the MINIMUM NUMBER OF DAYS needed to conduct a single
elimination tournament.
ASSUMPTIONS:Regularly scheduled games are played Monday through Thursday. No team should play
more than one game per day.
A) N = 45
Number of games that can be played each day = 3
B) N = 87
Number of games that can be played each day = 9
C) N = 27
Number of games that can be played each day = 5
D) N = 36
Number of games that can be played each day = 6
52 of 68
Worksheet for Homework Assignment #1
Worksheet for Problem Type I: Forecasting Days
Homework Assignments (Collected at the beginning of every class). Please make a copy of your
completed homework assignment before class if you wish to review your homework as we go over the
assignment in class.
Please answer the following questions regarding round robin tournament scheduling and show all of your
work and staple your pages together!
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. No team should
play more than one game per day.
N = ___ entries
Number of game times available each day = ___
Step 1. The first step in solving the problem is to determine the number of first round games that will be
played.
Number of first round games (N) - next lower power of two
Step 2. Establish the number of rounds for the entire tournament.
The number of rounds is always the power to which 2 must be raised to equal or exceed N.
N = ___
Power of two =
Round
Step 3. After the number of rounds have been determined, the next step is to enter the number of first round
games (Step 1) under Round 1.
Round
Games
Step 4. Once the number of first round games has been listed, list the number of games in each round
starting with the last round and working your way back to the first round. The number of games per round is
always a multiple of two (1, 2, 4, 8, 16, 32, 64, 128, etc.)
Round
Games
= ___ games
Always check you answer by using the formula of (N - 1) for the total number of games.
53 of 68
Step 5. After the number of games per round has been established, we can determine how many days are
required to play the number of games in each round. We do this by determining the number of games that
can be played on a round by round basis (no team plays more than once per day). Start with the last round
and work backwards. For rounds which only take one day to complete (when the number of games available
per day is greater than or equal to the number of games listed in the round), place a 1 in that column.
Round
Games
Days
When the number of games is great than the number available per day, we must STOP!
Step 6. Once we have reached the point where the number of games needed per day per round is greater
than the number of games available per day, we go back to the first round and determine the number of days
required to play each round.
Round
Games
Days
The total number of days needed to complete the tournament is determined by adding the number of days for
each round.
Answer:
54 of 68
Single Elimination Scheduling
In-Class Problem #1
Problem Type II: Number of Games--Index Numbers
Under the conditions stated below, find the MINIMUM NUMBER OF GAMES needed to conduct a single
elimination tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. No team should
play more than one game per day.
N = 39 entries
Number of days that are available = 6
Number of total games (N-1) = 38
Step 1. The first step in solving the problem is to determine the number of first round games that will be
played.
Step 2. Establish the number of rounds for the entire tournament.
Round
Step 3. After the number of rounds has been determined, the next step is to enter the number of first round
games (Step 1) under Round 1.
Step 4. Once the number of first round games has been listed, list the number of games in each round
starting with the last round and working your way back to the first round. The number of games per round is
always a multiple of two (1, 2, 4, 8, 16, 32, 64, 128, etc.)
55 of 68
Always check your answer by using the formula of (N - 1) for the total number of games.
Step 5. After the number of games per round has been established, determine the number of days that
must be available. First, divide the number of games in the tournament (___) by the number of days we
have available (___). This results in our first index number which is ___ or ___ (always round up).
Start with the last round and work backwards. For rounds whose number of games is less than our first
index number (___), place a 1 in that column.
Round
Games
= ___ games
Days
Once we have reached the point where the number of games needed per day per round is greater than
our first index number (8 games in Round 3), we must STOP!
Step 6. The last three rounds of seven total games required three days to complete. Now, we divide the
remaining number of days (___) (___days available - ___ days used) into the remaining number of
games left to be played (___) (___ original games - ___ games played). This results in our second
index number which is ___ or (___). Always round up. Working backwards from Round ___, we
recognize the rounds whose number of games is less than the second index number of ___. The index
number of ___ is greater than the ___ games in Round ___ so place a ___ under Round ___. Since ___
games in Round ___ is greater than our index number of ___, we must ________!
Round
Games
= ___ games
Days
Step 7. Divide the remaining number of days in the tournament (___) (___ days available - ___ days
used) into the remaining number of games left to be played (__) (___ original games - ___ games
played). This results in our third index number which is ___ or (___). Since this number is smaller than
the number of games in Round ___, which is ___, the index becomes the answer to the problem.
Answer: _____ games must be available per day to complete the tournament.
Double-Check:
Round
Games
___
Days
= ___ days
Page 56 of 68
Single Elimination Scheduling
In-Class Problem #2
Problem Type II: Number of Games--Index Numbers
Under the conditions stated below, find the MINIMUM NUMBER OF GAMES needed to conduct a single
elimination tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. No team
should play more than one game per day.
N = 32 entries
Number of days that are available = 7
Number of total games (N-1) = 31
Answer: ___ games must be available per day to complete the tournament.
Page 57 of 68
Double-Check:
Page 58 of 68
Single Elimination Scheduling Homework Assignment #2
(See worksheet for help)
Problem Type II: Number of Games
Homework Assignments (Collected at the beginning of every class). Please make a copy of your
completed homework assignment before class if you wish to review your homework as we go over the
assignment in class.
Please answer the following questions regarding round robin tournament scheduling and show all of
your work and staple your pages together!
Under the conditions stated below, find the MINIMUM NUMBER OF GAMES needed to conduct a single
elimination tournament.
ASSUMPTIONS:Regularly scheduled games are played Monday through Thursday. No team should play
more than one game per day.
E) N = 48
Number of days that are available = 10
F) N = 37
Number of days that are available = 13
G) N = 24
Number of days that are available = 5
H) N = 20
Number of days that are available = 4
Page 59 of 68
Worksheet for Homework Assignment #2
Worksheet for Problem Type II: Number of Games
Homework Assignments (Collected at the beginning of every class). Please make a copy of your
completed homework assignment before class if you wish to review your homework as we go over the
assignment in class.
Please answer the following questions regarding round robin tournament scheduling and show all of
your work and staple your pages together!
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. No team
should play more than one game per day.
N = ___
Number of days that are available = ___
Number of total games (N-1) = ___
Step 1. The first step in solving the problem is to determine the number of first round games that will be
played.
First round games = (N) - next lower power of two
Step 2. Establish the number of rounds for the entire tournament.
The number of rounds is always the power to which 2 must be raised to equal or exceed N.
N = ___
Power of two =
Round
Step 3. After the number of rounds have been determined, the next step is to enter the number of first
round games (Step 1) under Round 1.
Round
Games
Step 4. Once the number of first round games has been listed, list the number of games in each round
starting with the last round and working your way back to the first round. The number of games per round
is always a multiple of two (1, 2, 4, 8, 16, 32, 64, 128, etc.)
Round
Games
= ___ games
Always check you answer by using the formula of (N - 1) for the total number of games.
Step 5. After the number of games per round has been established, determine the number of days that
must be available. First, divide the number of games in the tournament (___) by the number of days we
have available (___). This results in our first index number of (___) (always round up). Start with the
Page 60 of 68
last round and work backwards. For rounds whose number of games is less than our first index number,
place a 1 in that column.
Round
Games
Days
Once we have reached the point where the number of games needed per day per round is greater than
our first index number, we must STOP!
Step 6. Now, we divided the remaining number of days (___) (___days available -___days used) into the
remaining number of games left to be played (___) (___ original games - ___games played). This results
in our second index number which is (___) always round up. Working backwards from the last round
completed, 3, we recognize the rounds whose number of games is less than the second index number.
Round
Games
Days
Continue to work backwards using the same procedure found in Step 6. When the index number is
smaller than or equal to the number of games in the round, that index number becomes the answer to the
problem.
Answer: _____ games must be available per day to complete the tournament.
Double-Check:
Round
Games
Days
= ___ games
Page 61 of 68
Unit 2 Notes:
Wasted Games - Determining Number of Entries
There are basically three variables that a sports programmer needs to know in order to schedule a single
elimination tournament. They are the number of entries in the tournament (n), the number of days
needed to conduct the tournament, and the number of games needed to play each day of the
tournament. By knowing any of these two variables, the programmer can figure out the third. The first
step for the programmer, therefore, is to figure out which piece of information they need to figure out.
For determining number of entries, the programmer will know how many games are available per day and
how many days he/she has to play the tournament. This is a fairly common scenario...most of the time,
we receive a facility reservation, and we must determine how many teams we can accommodate in our
tournament. In this case, we are assuming that teams will not play more than one game per day....
Here's how it works....
Lets say that the following information is applicable for our tournament:
Number of games that can be played each day = 5
Number of days that are available = 7
Step 1: The first step in solving the problem is to determine the number of total possible games that can
be scheduled in a single elimination tournament. Do this by multiplying the number of days that are
available (7) by the number of games that can be played each day (5). The answer will be the TOTAL
POSSIBLE number of games that can played in the tournament (35).
Remember, in single elimination tournaments, you will never use all of the possible games
available to you...you will always end up wasting games. For example, if we have 5 games available
to play each day, during our final round, we will only use 1 of these games. That means in the final
round, we will be wasting 4 games. We must figure out how many TOTAL games we will waste
throughout the tournament, and subtract that number from the TOTAL POSSIBLE number of games that
can be played (35).
Step 2: Begin with the last round of the tournament.....how many games will always be played in the last
round? That’s right, the answer is 1. We know that if we can play 5 games in a day, and we only are
playing 1 game in the last round, we will be wasting 4 games.
How about the other rounds? Work backwards from the last round and determine the number of games
that will be played....remember, we use powers of 2 to figure this out. Continue to figure out the number
of wasted games by subtracting the number of games in the round from the number of games that can be
played each day (5). In the next to last round, you will play 2 games. If you can play 5 games in one day,
you will be wasting 3 games. Continue working backwards until you hit a point where you will not be
wasting any games....in this case, when you hit 8 games in a round, you won't be wasting any of the
games you will play in one day. You will use all 5 games. At this point, you STOP, and add the number
of wasted games.
Round R
Games 16
Wasted 0
R
8
0
R
4
1
R
2
3
Last
1
4 = 8 wasted games
Page 62 of 68
Step 3: Subtract the total wasted games (8) from the total number of possible games (35). Your answer
will be 27. This represents the ACTUAL number of games that can be played in your tournament.
Step 4: The total number of entries that can be accommodated in the tournament is determined using the
following formula:
Number of games = N - 1
27 = N - 1
28 = N
Therefore, in your tournament, you could accommodate a MAXIMUM of 28 teams. Once you receive 28
entries, you must close your registration and it would be advisable to start a waiting list!
Page 63 of 68
Single Elimination Scheduling
In-Class Problem #1
Problem Type III: Number of Entries--Wasted Games
Under the conditions stated below, find the MAXIMUM NUMBER OF ENTRIES that could be scheduled
in a single elimination tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. No team
should play more than one game per day.
Number of games that can be played each day = 3
Number of days that are available = 8
Step 1. The first step in solving the problem is to determine the number of total possible games that can
be scheduled in the tournament.
Number of available days X the number of games that can be played each day.
___ days available X ___ games per day
___ possible game times are available in the tournament
Step 2. Establish the number of rounds for the entire tournament.
The number of rounds is always equal to number of days available.
Number of days available = ___
Number of rounds = ___
Round
Step 3. After the number of rounds has been determined, the next step is to enter the number of games
in each round. List the number of games in each round starting with the last round and working your way
back to the first round. The number of games per round is always a multiple of two (1, 2, 4, 8, 16, 32, 64,
128, etc.)
Round
Maximum Games
Step 4. Working backwards from the last round, determine the number of wasted games in each round
by subtracting the maximum number of games per round (Step 3) from the number of games that can be
played each day (___).
Round
Maximum Games
Wasted Games
= ___ wasted
games
Step 5. Subtract the total wasted games (___) from the total number of possible games (___)
determined in Step 1.
This number represents the maximum number of games that can actually be played in the
tournament.
Page 64 of 68
Step 6. The total number of entries that can be accommodated in the tournament is determined by using
the following formula:
Number of games
___
___ + ___
___
=
=
=
=
N-1
N-1
N
N
Answer: ___ entries can be accommodated in the tournament without having any team play more
than once per day.
Page 65 of 68
Single Elimination Scheduling
In-Class Problem #2
Problem Type III: Number of Entries--Wasted Games
Under the conditions stated below, find the MAXIMUM NUMBER OF ENTRIES that could be scheduled
in a single elimination tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. No team
should play more than one game per day.
Number of games that can be played each day = 9
Number of days that are available = 5
Answer: ____ entries can be accommodated in the tournament without having any team play
more than once per day.
Page 66 of 68
Single Elimination Scheduling Homework Assignment #3
Problem Type III: Number of Entries--Wasted Games
Under the conditions stated below, find the MAXIMUM NUMBER OF ENTRIES that could be scheduled
in a single elimination tournament.
ASSUMPTIONS:
Regularly scheduled games are played Monday through Thursday. No team
should play more than one game per day.
1 . Number of games that can be played each day = 4
Number of days that are available = 8
2. Number of games that can be played each day = 10
Number of days that are available = 10
3. Number of games that can be played each day = 7
Number of days that are available = 7
4. Number of games that can be played each day = 5
Number of days that are available = 16
Page 67 of 68
Unit 2 Notes:
Drawing Single Elimination Tournament Brackets
When drawing tournament brackets, it is important to FIRST have all of the teams or participants
registered in your tournament. It is difficult to place teams in the tournament draw after you have already
scheduled your tournament, so you should make sure that all team entries have been received before
scheduling your tournament. Remember, single elimination tournaments are based on powers of 2, so
your tournament bracket should be balanced in such a way that from the second round through the final
round, the same number of teams will be in the upper half of the bracket as will be in the lower half of the
bracket. This may not be true for the first round, due to the possible presence of bye games in the first
round.
When you are ready to draw your tournament bracket, you may choose to draw and "implied bye"
bracket or an "explicit bye" bracket. Implied bye games are not indicated on the tournament
bracket....rather, blank spaces replace first round bye games and only second round games appear.
Explicit bye brackets show all bye games by placing the word "bye" or drawing an "x" through the bye
game. For the purposes of this course, it is easier to draw explicit bye brackets, to more easily
accommodate seeding and placing of bye games. We will focus on this type of bracket from here on out.
How to draw/choose the tournament bracket:
Begin by taking the number of teams you have in your tournament....lets say 7. Always use the bracket
format for the NEXT HIGHEST power of two...in our case here, you would use an 8 team bracket. If
you had 12 teams in your tournament, you would use a 16 team bracket, if you had 23 teams in your
tournament, you would use a 32 team bracket, etc. You can see examples of different sized brackets on
this web-file www.mtsu.edu/~hjgray/4110/RSMch6 p. 141-145!
After you choose your bracket, you must determine your tournament SEEDS. Remember, the easiest
way to determine seeds is to look at past performance or team's ability. If you do not know this
information, random seeding is possible. STOP, make sure you review the example of how to seed a
single elimination tournament bracket by referring to this web-file www.mtsu.edu/~hjgray/4110/RSMch6
on p. 108 - 111!
After drawing the bracket and determining your seeds, you must place your BYE games. The number
of BYE games is equal to the number of teams in your tournament subtracted from the next
highest power of 2 (or in this case, the size of the bracket you initially drew). In our example, we have 7
teams in our tournament. The next highest power of 2 is 8, so 8-7 =1, giving us 1 bye game. Go down
your tournament bracket and draw a line through every game that is represented by a seed higher than
7. In our example, you would draw a line through the game matchup 1 vs. 8, because we only have 7
teams in the tournament.
Once you have completed placing your bye games, you are ready to schedule your tournament games!
Page 68 of 68
16 team bracket: Brackets are determined by the next highest power of 2 to = or exceed N. Ex: N=14, use a 16 team bracket
Magic # 17
1
* Place seeds 1 and 2 and work backwards from final round by using magic #'s
Magic # is max number of games possible in a round + 1
Ex: Here max number of games possible in round 1 is 16 +1 = magic # is 17
Magic # 9
Remember, assume top seed always wins!
1
Magic # 5
You can double check round 1 is correct by using your seeding below
1
Note: this bracket is not complete…only partial info is provided for demonstration purposes!
(5-1=4)
Magic # 3
1
4
4
(magic # - top seed = team to be played)
(3-1=2)
1
4
up
down
down
up
up
down
down
up
Top
Bottom
Top
Bottom
Top
Bottom
Top
Bottom
1
2
3
4
5
6
7
8
Seeding
vs
vs
vs
vs
vs
vs
vs
vs
16
15
14
13
12
11
10
9
bye
bye
3
3
(9-3=6)
6
3
2
(5-2=3)
2
2
2
*Seeding = Power of 2 to = or exceed N, then divide by 2
Ex: 14 teams: 16/2= 8
number 1 through 8 down, then start bottom to top on other side
9 through 16
*since only 14 teams, 15 and 16 become byes!
*Top = top of game bracket
*Bottom = bottom of game bracket
****Up/Down applies only to the first round****
*Up means above middle of the bracket (green line)
** Down means below the middle of the bracket (green line)
69
16 team bracket: Brackets are determined by the next highest power of 2 to = or exceed N. Ex: N=14, use a 16 team bracket
Magic # 17
1
16 or bye
9
8
5
12
13
4
3
14
11
6
* Place seeds 1 and 2 and work backwards from final round by using magic #'s
Magic # is max number of games possible in a round + 1
Ex: Here max number of games possible in round 1 is 16 +1 = magic # is 17
Magic # 9
Remember, assume top seed always wins!
1
Magic # 5
You can double check round 1 is correct by using your seeding below
1
NOTE: This IS a completed bracket!!!
(9-1=8)
8
Magic # 3
Seeding
(5-1=4)
1
up
Top
1
vs
down
Bottom
2
vs
down
Top
3
vs
5
4
up
Bottom
4
vs
(9-4=5)
up
Top
5
vs
4
(magic # - top seed = team to be played)
down
Bottom
6
vs
(3-1=2)
1
down
Top
7
vs
up
p
Bottom
8
vs
3
(9-3=6)
6
3
2
(5-2=3)
7
10
7
(9-2=7)
(9-2
7)
2
16
15
14
13
12
11
10
9
bye
bye
*Seeding = Power of 2 to = or exceed N, then divide by 2
Ex: 14 teams: 16/2= 8
number 1 through 8 down, then start bottom to top on other side
9 through
h
h 16
*since only 14 teams, 15 and 16 become byes!
2
*Top = top of game bracket
*Bottom
Bottom = bottom of game bracket
15 or bye
****Up/Down applies only to the first round****
2
*Up means above middle of the bracket (green line)
** Down means below the middle of the bracket (green line)
Note: once you get to round 1, you can look at the seeding to see who plays who (or you can use the formula: magic #-top seed = team to be played)
70
32 team bracket (one side)
Magic # = 33
1
Magic # = 17
1
Magic # = 9
32
(17-1=16
16
1
16
(9-1=9)
Magic # is max number of games possible in a round + 1
* Place seeds 1 and 2 and work backwards from final round by using magic #'s
Remember, assume top seed always wins!
You can double check round 1 is correct by using your seeding below
*Seeding = Power of 2 to = or exceed N, then divide by 2
Ex: 26 teams: Next highest power of 2 to = or exceed 26 is 32. 32/2 = 16
number 1 through 8 down, then start bottom to top on other side, 9 through 16
Magic # = 5
*** seeds 27 through 32 become byes because N=26!!!!!
1
8
8
Magic # = 3
Use to double check Round 1 is correct
8
1
(5-1=4)
4
4
(Magic # - top seed = team to be played)
4
4
(3-1=2)
1
Seeding
vs 32
vs 31
Top
Bottom
1
2
Top
Bottom
Top
3
4
5
vs
vs
vs
30
29
28
Bottom
Top
Bottom
6
7
8
vs
vs
vs
27
26
25
Top
Bottom
Top
9
10
11
vs
vs
vs
24
23
22
Bottom
B
tt
Top
Bottom
12
13
14
vs
vs
vs
21
20
19
Top
Bottom
15
16
vs
vs
18
17
3
2
7
26
(5-2=3)
7
7
2
15
18
(9-2=7)
15
(17-2=15)
2
2
2
71
32 team bracket (left/right)
Magic # are the same as 32 bracket on one side: We are just moving the bottom brackets over to the right
Start with 1 & 2 seeds and work backward from the final round using the magic number for each
Magic # 33
Use the patterns: Left, Right, Right, Left and Top/Bottom to help guide you
Magic # 33
1
Magic # 17
Assume top seed always wins
Magic # 17
3
1
Magic # 9
Magic # 9
3
32
1
3
30
Magic # 5
Magic # 5
(9-1=8)
1
3
8
25
8
8
(9-3=6)
6
Champion
(5-1=4)
(5 1 4)
1
1
2
(5-2=3)
(5
2 3)
6
(magic # - top seed = team to be played)
27
6
Final Round
7
7
5
7
4
13
4
2
(9-4=5)
(9
4 5)
(9-2=7)
(9
2 7)
4
2
4
2
31
2
****see next page for seeding
72
Top
Bottom
Top
Bottom
Top
Bottom
Top
Bottom
Top
Bottom
Top
B tt
Bottom
Top
Bottom
Top
Bottom
Left
Right
Right
Left
Left
Right
Right
Left
Left
Right
Right
L ft
Left
Left
Right
Right
Left
Seeding
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
vs
vs
vs
vs
vs
vs
vs
vs
vs
vs
vs
vs
vs
vs
vs
vs
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
*Top = top of game bracket
*Bottom = bottom of game bracket
** Left = left side brackets
**Right
g = right
g side brackets
73
Blank Single Elimination Brackets 74
* Place seeds 1 and 2 and work backwards from final round by using magic #'s
Remember, assume top seed always wins!
You can double check round 1 is correct by using your seeding below
Magic #
Magic #
Magic #
Seeding
1
vs
Magic #
1
75
Magic # = ?
Magic # = ?
Magic # = ?
Magic # = ?
Magic # = ?
76
* Place seeds 1 and 2 and work backwards from final round by using magic #'s
Remember, assume top seed always wins!
You can double check round 1 is correct by using your seeding below
Use to double check Round 1 is correct
1
Seeding
vs
77
Magic # are the same as 32 bracket on one side: We are just moving the bottom portion over to the right
Start with 1 & 2 seeds and work backward from the final round using the magic number for each
Use the patterns: Left, Right, Right, Left and Top/Bottom to help guide you
Assume top seed always wins
Champion
Final Round
78
Top/Bottom Left/Right
1
Seeding
vs
vs
vs
vs
vs
79
RlP324 In-Class Single Elimination Tournament Problem
Forecasting and Scheduling
You are in charge of programming a tennis tournament for a military base. The base operates
three indoor courts that you may use a maximum of six hours on Saturday and seven hours on
Sunday. You are allowing one hour for each match scheduled. Twenty-nine participants have
entered the tournament and all will play in the same division.
1. Draw the single elimination bracket for these entrants.
2. Seed all players by indicating their position with the number 1, 2, 3, and 4.
3. Position byes appropriately.
4. Schedule matches so that each player has at least one hour of rest between matches.
5. Determine how much money will be spent for officials if you provide one per court per
match until the semi-finals and provide two linesman plus the official for the semi-finals
and final match. All officials and linesman will be paid $5.00 per game.
80
Forecasting and Scheduling
You are in charge of scheduling an indoor soccer post-season playoff tournament as part of the
new World Professional Indoor Soccer League. The teams in the playoff are the national
champions from the countries that are participating in this new league. Your goal is to detennine
an overall "World Champion." You have decided to program a single elimination, winner-take­
all tournament. Games will be played at the United Center in Chicago on one field. Games are
being played at 5:00 p.m., 7:00 p.m., and 9:00 p.m. You are playing games beginning Tuesday,
December 2 for as many days as it takes you to finish the tournament. Your job is to figure out
how many days it is going to take you to play this event in order to schedule your tournament and
to obtain television coverage for the event. Make sure that teams will only play once per day.
You have 13 teams in your tournament and all of them are men's teams. All teams are going to
be around the same skill level, so all will play against each other in one skill division. The teams
entered in your tournament, ranked in order ofperfonnance in the regular season, are:
1. England, 2. Kenya, 3. United States, 4. Mexico, 5. Russia, 6. France, 7. Germany,
8. Austria, 9. Egypt,10. Israel, 11. Ireland,12. Dominica,13. Australia
Please complete the following:
1. 2. 3. 4. Draw a tournament bracket for 13 teams, designating the appropriate number ofbyes.
Seed the tournament, according to regular season rankings, and detennine the position of
the seeded games on the tournament bracket.
Forecast how many days it will take to complete the tournament.
Complete the tournament schedule, including designating opponents (in the first round
and placing "bye" teams in appropriate placed), days, dates, and times for each round of
the tournament.
81