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Round Robin Scheduling

Round Robin Scheduling. Round Robin. Each entry plays all other entries in their league at least ONCE Wins and losses do not affect participation Winner determined from win-loss percentage. Terminology.

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Round Robin Scheduling

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  1. Round Robin Scheduling

  2. Round Robin • Each entry plays all other entries in their league at least ONCE • Wins and losses do not affect participation • Winner determined from win-loss percentage

  3. Terminology • Tournament:We will use the word "tournament" when we are referring to the overall event.   • For example, we might program an intramural basketball tournament for 100 teams.  • We will always use the word "tournament" when we are referring to the largest unit which we are programming. • League (aka - division, pool): We will use the word "league" when we are referring to the different "groups" that we put our entries into.  • For example, if we are programming an intramural basketball tournament for 100 teams, we might choose to break down our tournament into 20 leagues with 5 teams in each league.  • This means that not all 100 teams will play each other.  • Teams will only play other teams within their particular league.

  4. Round Robin Basics -- Total Number of Games • For example, if you are programming an intramural singles tennis tournament in round robin format and you have 30 people entered, you need to place these people into different leagues.  • You have several choices that you can make: • You could offer one big league of 30 teams and have every tennis player play everyone else.   • You could offer ten small leagues with 3 teams in each league, where teams will only play the other teams in their particular league. 

  5. How do you choose?  • What is the difference between one BIG 30 team league and ten small leagues of 3 teams?   • You still have the same number of TOTAL teams, you are just formatting them differently.  • Major differences lie in: • the number of games that EACH TEAM will play • depending on the number of teamsin their league • and the number of games that it will take to complete EACH LEAGUE • depending on the number of teams in their league. 

  6. 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

  7. 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

  8. Ex. 2:  Three leagues of 7 teams each and ten leagues of 6 teams eachHint:  when you have leagues with unequal numbers of teams, treat these as separate problems.  • number of games per team:  7 - 1 = 6 • each team will play 6 games in these leaguenumber of games per league:  7(7-1)/2 = 21 gamesnumber 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!

  9. 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 gamesREMEMBER:  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!

  10. Lets go back to our tennis tournament that we are programming from above! If you were to use the formulas, you would find the following information regarding some different scheduling combinations involving 30 total teams: • Go to overheads

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