New tournament format: “limited single-bye” (for packet sub)

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Cody
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New tournament format: “limited single-bye” (for packet sub)

Post by Cody » Wed Apr 26, 2017 11:58 am

After some drops, ACF Nationals 2017 was going to run with 40 teams across 20 packets (including 2 tiebreaker and 2 finals packets). A traditional schedule would’ve been 5 brackets of 8 with double byes and then a crossover by 2s, but that would’ve taken 21 packets (9 prelims, 1 tiebreaker, 8 playoff, 1 tiebreaker, 2 finals).

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.

(Sidenote: while the idea for this schedule struck me in a fit of inspiration and I’ve never heard about it before, I’m sure someone must’ve thought of it before me. Is anyone aware of historical uses of this type of schedule?) See the bottom of Berkeley’s Scheduling Guide for an example of this format; it was also definitely used at ACF Nationals 2015.

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
Unlike other round-robin schedules with byes, you do not eliminate 1 room per bracket (odd team single-bye schedule) or 1 room per bracket for n of n + 1 rounds (even team double-bye schedule for n teams); instead, you eliminate one room per two “paired” brackets, in the case where all the byes for each “paired” bracket are in different rounds. (This case does not occur, for example, if you have 2 brackets and a packet with 2 authors that are in different brackets, as you obviously must have a round where there is a bye for both brackets.)

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:

Properties:
  • 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.
Disadvantages:
  • 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.
Obviously, for a tournament with no “brackets”, the schedule can be considered to consist of a single “bracket”. Do note that some care must be taken when constructing such a schedule; it’s possible to make some REALLY dumb errors the scheduling is done manually. I encourage the use of the COUNTUNIQUE function to ensure you have the expected number of matches. Example:

Image

When Should You Use It?

This schedule works very well in some situations and not so well in others; here are two examples:
  1. A 12-team ACF Regionals field where you need to use at most 6 submitted packets.
  2. A bracketed prelim with brackets of n – 1 odd teams and n even teams.
With respect to #2, this schedule does not work well for brackets of n even teams and n + 1 odd teams because you would have some brackets taking n rounds and some brackets taking n + 1 rounds.

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.
Last edited by Cody on Thu Apr 27, 2017 10:03 am, edited 1 time in total.
Cody Voight, VCU ‘14. I write lots of science and am an electrical engineer.
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Re: New tournament format: “limited single-bye” (for packet

Post by jonpin » Wed Apr 26, 2017 12:20 pm

Just to check, is this a new twist on the "Two-Bracket Packet-Submission Even-Team Round Robin" listed on Berkeley's scheduling page?
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Cody
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Re: New tournament format: “limited single-bye” (for packet

Post by Cody » Wed Apr 26, 2017 12:54 pm

jonpin wrote:Just to check, is this a new twist on the "Two-Bracket Packet-Submission Even-Team Round Robin" listed on Berkeley's scheduling page?
A-ha, there's the historical use; I guess I've never scrolled down that far! I would say it's a trivial generalization of that concept. The difference is that there's no need to consider multiple (even numbers of) brackets to make the schedule work; it can be done for any number of brackets, including a single round-robin. Additionally, there is no requirement to structure the byes to eliminate a room (as that's impossible when a packet has two authors not in the same bracket).
Cody Voight, VCU ‘14. I write lots of science and am an electrical engineer.
VCU Tournament Director ‘13-‘17. HSAPQ President ‘15-16.
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Re: New tournament format: “limited single-bye” (for packet

Post by Benin Rebirth Party » Thu Apr 27, 2017 9:37 am

I'm pretty sure this format was used for ACF Nationals 2015 and CO 2016. Two brackets shared a common room and the round order was adjusted (since it doesn't really matter what order you play the other teams) so that every round, two teams from one bracket had byes and two teams from the other played in the shared room. CO 2016 round report isn't up for me to confirm this.

In this situation, packets would have to be combined within the bracket (or in the case of ACF Nationals 2015, each round could have a combination of up to 4 packets, 2 each from 2 different brackets).

I like this situation for something like the 12 team ACF Regionals. An added perk is that you need less staff as the reader in the room with n/2 games can double up on doing stats or something, or can be someone who can only come for half the tournament.
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Re: New tournament format: “limited single-bye” (for packet

Post by Cody » Thu Apr 27, 2017 12:39 pm

Aaron Manby (ironmaster) wrote:I'm pretty sure this format was used for ACF Nationals 2015 and CO 2016. Two brackets shared a common room and the round order was adjusted (since it doesn't really matter what order you play the other teams) so that every round, two teams from one bracket had byes and two teams from the other played in the shared room. CO 2016 round report isn't up for me to confirm this.

In this situation, packets would have to be combined within the bracket (or in the case of ACF Nationals 2015, each round could have a combination of up to 4 packets, 2 each from 2 different brackets).

I like this situation for something like the 12 team ACF Regionals. An added perk is that you need less staff as the reader in the room with n/2 games can double up on doing stats or something, or can be someone who can only come for half the tournament.
I just checked the TD documents for ACF Nationals 2015 and you're totally correct. Matt Jackson even referenced the Berkeley site that apparently, I need to actually read!

One of the advantages of the Berkeley method (in thinking about the format in terms of pairs of brackets) is that you eliminate rooms for the whole schedule, but I think that creates a fundamental weakness as opposed to thinking of the format in terms of individual brackets. Eliminating entire rooms is good, but it's rare that you strictly need to do so. By thinking about it in terms of individual brackets, you can create byes for as many packet authors as you like (as long as no more than n / 2 teams in a bracket have authored distinct packets).
Cody Voight, VCU ‘14. I write lots of science and am an electrical engineer.
VCU Tournament Director ‘13-‘17. HSAPQ President ‘15-16.
Hero of Socialist Quizbowl Labor (NSC ‘14). “esteemed colleague” of Snap Wexley, ca. 2016. Stats Hero (Nats ‘16).
Quizbowl at VCU

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