In order to make the schedule work, I devised a new type of round-robin schedule for an even numbers of teams that gives each team 1 bye; I call it a “limited single-bye” round-robin (in that there is 1 bye per team, but the way byes are distributed is limited). This thread is a resource for information about the format, can be used to ask questions, and will be updated with a FAQ as appropriate.
On “limited single-bye” prelims:
A “limited single-bye” schedule is in contrast to a “double-bye” schedule (see Berkeley’s Scheduling Guide). To briefly expound on the theory: a “double-bye” schedule takes n + 1 rounds, where n is the number of (even) teams for which you are doing a round-robin, and (as suggested by its name) gives every team 2 byes. It is generated by taking the schedule for n + 1 (odd) teams and making the last team a bye. (Example: an 8-team double-bye schedule is generated from a 9-team single-bye schedule by designating the 9th team as a bye and condensing the schedule.)
A “limited single-bye” schedule takes n rounds, where n is the number of (even) teams for which you are doing a round-robin, and (as suggested by its name) gives every team 1 bye. The manner in which a limited single-bye schedule is generated is very different, and there is no universal scheduling theory; every schedule can be different. So, how do you generate a limited single-bye schedule?
You start with the schedule for an even team round-robin; we’ll use 10 teams since that’s an example I’ve already generated. A 10-team round robin takes 9 rounds. You generate byes by moving some games from rounds 1 thru 9 into a new “round 10” (4 games to be precise; for an even team round-robin of n teams, you move n – 1 games). Assuming you move games from the different rounds, you create 1 bye for 2 teams in each round, for a total of 5 rounds with 2 teams on bye (4 rooms) and 5 rounds with no teams on bye (5 rooms). Note that “round 10” is in quotes for a reason—remember, you can order the rounds however you like! An example is in order:
Code: Select all
Round Room 1 Room 2 Room 3 Room 4 Room 5 BYE 1 5 v 9 4 v 10 6 v 7 2 v 3 1 v 8 2 3 v 10 6 v 9 1 v 4 2 v 7 5, 8 3 2 v 4 5 v 7 8 v 9 1 v 10 3, 6 4 6 v 8 1 v 3 7 v 9 4 v 5 2, 10 5 2 v 8 3 v 5 4 v 6 9 v 10 1, 7 6 3 v 4 5 v 10 7 v 8 1 v 9 2 v 6 7 5 v 6 3 v 9 1 v 2 7 v 10 4 v 8 8 8 v 10 1 v 6 4 v 9 2 v 5 3 v 7 9 2 v 9 4 v 7 6 v 10 3 v 8 1 v 5 10 1 v 7 2 v 10 5 v 8 3 v 6 4, 9
The properties of a limited single-bye schedule are a hybrid of the (odd team) single-bye and (even team) double-bye schedules, with its own unique disadvantages:
- Takes n rounds, where n is the (even) number of teams for which you are doing a round-robin (single-bye).
- Can handle packets with 1 packet author in a bracket (single-bye) or 2 packet authors in a bracket (double-bye); the latter is an ideal case since you immediately know which match to move to your “new” round.
- Only generates byes for half the rounds, and so can only be used if a bracket contain teams who've written at most n / 2 different packets.
When Should You Use It?
This schedule works very well in some situations and not so well in others; here are two examples:
- A 12-team ACF Regionals field where you need to use at most 6 submitted packets.
- A bracketed prelim with brackets of n – 1 odd teams and n even teams.
The reason it works for n – 1 odd teams is that the same principles of the “limited single-bye” schedule for n teams can be used to extend an n – 1 round odd team schedule to an n round odd team schedule, creating an odd team “limited double-bye” schedule. (This schedule has (n – 2)/2 rounds with 3 byes and the rest of the rounds with 1 bye.) (I use n – 2 in order to have n consistently refer to the number of even teams for which you are doing the round-robin; it is n – 1 if you are referencing the number of odd teams for which you are doing a round-robin.) An odd team double-bye schedule has the same advantages as an even team double-bye schedule in that it can handle 2 authors of the same packet in a single bracket, but is “limited” because the rounds with 3 byes only occur for less than half the rounds.
Obviously, due to point #1, this schedule would not work for a 16-team CO field where you need to use 16 submitted packets.
Hopefully this is a clear explanation of the format; again, this thread is intended to serve as a resource about the format, so drop any questions below.