The Tag Round Robin Schedule by Br~an E, MacTaggart

Introduction Over the past two years in the University of Western

Ontario intramural sports program, a special scheduling problem arose. How do you have all teams play twice on the same night without undue delay between games? This question resulted from the following circumstances. The facility space and time was available for two con- tests per team per week. The participating teams de- sired to play twice per week, but preferred to have both competitions the same night. The sports involved were such that more than one contest could be played on one night without undue physical fatique occurring. Schedul- ing teams to play twice on the same night would have two benefits. First, it would eliminate the need to com- mute to the playing area twice per week. This, in turn, might reduce timetable conflicts and defaults. Second, this schedule would increase the amount of playing time per participant per outing. Both of the above results have been long desired attributes of intramural programs.

One can schedule teams to play twice a night by ad- ding the next round in the round robin to that night's play. Unfortunately, it ended up with one team playing at the beginning of the night and then not again until the end of the night. This was undesirable. One can go through the tedious task of manipulating the numbers until one gets "most" of the teams playing back-to-back and against different opponents for each night's play. However, one will quickly become frustrated doing this for the many different sized round robins one might have. It is impossi- ble to have all teams play twice in the same night back- to-back and against different opponents, unless one has an even number of entries and half that number of play- ing areas. This rarely occurs. In the author's review of related literature, he found no information or existing tournament schedules that would help alleviate this problem. So to assist schedulers who will be or who have been in the same predicament, the Tag Round Robin Schedule was devised. The tournament properties and rotation patterns are outlined and complete Tag Round Robin Schedules are established for up to eight entries. This schedule has been used successfully in volleyball and squash but is also applicable to many other sports (e.g., softball, badminton).

places (as opposed to one in a single round robin). Top seeded entries are always placed in the top two spots because the (1 - 2) pairing allows them to play last.

Tournament Properties N = number of entries

1) Number of games to complete the league schedule (a double round robin): N (N - 1)

2) Number of games for each entry: 2N - 2 3) Number of rounds of play in Tag Round Robin

Leagues: N 4) Number of games in each round: N - 1 5) Percentage of teams that play two games per round:

N - 2

The established rounds provide an equal number of home and away games for each team. However, for any one team, all their home (or away) games are in the first half of the season and their away (or home) games are in the second half. Alternating the home and away games might be desirable (e.g., softball). This can be done by changing the order of the rounds of play. The numbers below represent rounds of play (i.e. round 1, round 2, etc.). The highest number in the series indicates the size of the tournament (number of entries).

By arranging the rounds in this order, the scheduler can alternate the home and away games.

Number of Entries Order of Rounds of Play

3 1, 2, 3 4 1, 3, 2, 4 5 1, 4, 2, 5, 3 6 1, 4, 2, 5, 3, 6 7 1, 5, 2, 6, 3, 7, 4 8 1, 5, 2, 6, 3, 7, 4, 8

Established rounds for more than eight entries will be available from the author if they are needed.

Conclusions A need arose for the Tag Round Robin Schedule at

Rotation Patterns The University of Western Ontario. This type of tourna- Entries are represented by numbers. For all rounds, ment provides for greater playing time per participant

two byes are held fixed as the other numbers are with no additional inconvenience (i.e. making two trips). rotated. Each pairing represents a game. The rotation, The established rounds provide an equal number of here, is conducted counter-clockwise. When rotating, home and away games for each team. This tournament each number in that particular round is rotated two can be used as a method of consolidating one's ports to

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MacTaggart

one night per week leaving other nights free for a dif- ferent activity.

Established Rounds for Tag Round Robin Tournament

ROUND 1 ROUND 2 ROUND 3 ROUND 4 ROUND 5 ROUND 6 ROUND 7 ROUND 8 HOME AWAY H A H A H A H A H A H A H A

Three Teams* bye - 3 b - 2 b - 1 (*With three teams, one may play the two 'bye' teams

1 - 3 3 - 2 2 - 1 (e.g., 3 vs 2) on the same night so that all teams get two 1 - 2 3 - 1 2 - 3 games-and only one of these teams will have to wait b - 2 b - 1 b - 3 (one game).)

Four Teams b - 4 b - 3 b - 2 b - 1 1 - 4 4 - 3 3 - 2 2 - 1 1 - 3 4 - 2 3 - 1 2 - 4 2 - 3 1 - 2 4 - 1 3 - 4 b - 2 b - 1 b - 4 b - 3

Five Teams b - 5 b - 4 b - 3 b - 2 b - 1 1 - 5 5 - 4 4 - 3 3 - 2 2 - 1 1 - 4 5 - 3 4 - 2 3 - 1 2 - 5 2 - 4 1 - 3 5 - 2 4 - 1 3 - 5 2 - 3 1 - 2 5 - 1 4 - 5 3 - 4 b - 3 b - 2 b - 1 b - 5 b - 4

Six Teams b - 6 b - 5 b - 4 b - 3 b - 2 b - 1 1 - 6 6 - 5 5 - 4 4 - 3 3 - 2 2 - 1 1 - 5 6 - 4 5 - 3 4 - 2 3 - 1 2 - 6 2 - 5 1 - 4 6 - 3 5 - 2 4 - 1 3 - 6 2 - 4 1 - 3 6 - 2 5 - 1 4 - 6 3 - 5 3 - 4 2 - 3 1 - 2 6 - 1 5 - 6 4 - 5 b - 3 b - 2 b - 1 b - 6 b - 5 b - 4

Seven Teams b - 7 1 - 7 1 - 6 2 - 6 2 - 5 3 - 5 3 - 4 b - 4

Eight Teams b - 8

4 - % - 1 - ^ 8 1 - 7 2 - 7 2 - 6 3 - 6 3 - 5 4 - 5 b - 4