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.) or you can click HERE to get the answers you need!   (Unfortunately you won't have this opportunity on the exam....you'll have to do everything longhand!). 

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.

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.

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:

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:

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:

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