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 page 113 of the text...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
• 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:

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.

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.