Scheduling a 25 team, 14 packet tournament

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AKKOLADE
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Scheduling a 25 team, 14 packet tournament

Post by AKKOLADE »

What's the best schedule for a tournament with a field of 25 teams and 14 packets, where preferably two rounds are saved for emergency and tiebreaker use?
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Re: Scheduling a 25 team, 14 packet tournament

Post by Ye Unfeeling Romeo »

Not an expert in TDing or anything, but I'll give this a shot. The best I can come up with is this:

Prelims: 5 pools of 5 teams each. 5 rounds where every team plays 4 games.
Playoffs: Upper and middle pools of 10 teams each (top 2 / 3rd and 4th teams from each prelim pool), resulting in 8 matches for a round robin where one prelim match carries over. Lower pool of 5 teams. I initially thought of the lower pool having a double round robin, but that would take up 10 more packets, so the best idea is probably just having the lower pool play a 5-round round robin in the same way as the prelims – unideal, since they don't play the same amount of games as the top and middle pools, but I can't think of anything better.

That leaves 13 packets used, which is the best I can think of. I look forward to seeing what other people come up with.
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Re: Scheduling a 25 team, 14 packet tournament

Post by Silverman »

You can use the following pretty unique format, which I saw used at SAGACITY IX at Pitt (beware, a few games are missing from those stats):

Arrange the teams in a 5x5 grid, labeled as a spreadsheet is (columns A-E, rows 1-5). Each team plays 8 prelim games: one game against each team in its row and column. You can do it over 9 rounds, which 1 bye team in each of the first 5 rounds and 5 bye teams in each of the last 4.

For rebracketing, rank the teams first by W-L and then by points (or PPB if you want to control for not having common opponents). The top 8 play a 3-round single-elim championship bracket, the next 8 play a 3-round single-elim consolation bracket, and the teams ranked 17-19, 20-22, and 23-25 play 3-team RRs for 2 games in 3 rounds.

Every team gets at least 10 games in 12 rounds, and the top 16 teams get 11 games. That saves 2 packets (or you can use one to break ties for the break between first and second bracket).

(This was all shamelessly reverse-engineered from the bracket that Dwight Kidder put together for that SAGACITY.)

Example schedule (with redundant games; also attached as a .xlsx):

Code: Select all

A1-A2	B2-B1	C3-B3	D4-D5	(BYE)	A3-E3	E5-E4	E1-E2	A5-A4	C4-C5	D2-D1	B4-B5	C5-C4	C1-C2	E3-A3	B5-B4	A2-A1	C2-C1	B1-B2	D1-D2	D5-D4	E4-E5	B3-C3	A4-A5	E2-E1
A1-A4	B2-E2	C3-C5	D4-D1	D3-D5	A3-A5	E5-E3	E1-E4	A5-A3	C4-C1	D2-C2	B4-B1	C5-C3	C1-C4	E3-E5	B5-B3	(BYE)	C2-D2	B1-B4	D1-D4	D5-D3	E4-E1	B3-B5	A4-A1	E2-B2
A1-A3	B2-B4	C3-C1	D4-D2	D3-D1	A3-A1	E5-D5	E1-E3	A5-B5	C4-C2	D2-D4	B4-B2	(BYE)	C1-C3	E3-E1	B5-A5	A2-A4	C2-C4	B1-B3	D1-D3	D5-E5	E4-E2	B3-B1	A4-A2	E2-E4
A1-A5	B2-B3	C3-C2	D4-A4	D3-D2	A3-A2	E5-E1	E1-E5	A5-A1	C4-E4	D2-D3	(BYE)	C5-C1	C1-C5	E3-E2	B5-B1	A2-A3	C2-C3	B1-B5	D1-D5	D5-D1	E4-C4	B3-B2	A4-D4	E2-E3
A1-C1	B2-B5	C3-C4	D4-D3	D3-D4	A3-A4	E5-E2	(BYE)	A5-A2	C4-C3	D2-D5	B4-B3	C5-C2	C1-A1	E3-E4	B5-B2	A2-A5	C2-C5	B1-D1	D1-B1	D5-D2	E4-E3	B3-B4	A4-A3	E2-E5
A1-B1	B2-A2	(BYE)	D4-E4	D3-E3	A3-B3	E5-C5	E1-D1	A5-D5	(BYE)	D2-E2	B4-A4	C5-E5	(BYE)	E3-D3	(BYE)	A2-B2	(BYE)	B1-A1	D1-E1	D5-A5	E4-D4	B3-A3	A4-B4	E2-D2
A1-D1	(BYE)	C3-E3	D4-B4	D3-A3	A3-D3	(BYE)	E1-C1	A5-C5	C4-A4	D2-A2	B4-D4	C5-A5	C1-E1	E3-C3	B5-D5	A2-D2	C2-E2	(BYE)	D1-A1	D5-B5	(BYE)	(BYE)	A4-C4	E2-C2
A1-E1	B2-D2	C3-A3	(BYE)	D3-B3	A3-C3	E5-A5	E1-A1	A5-E5	C4-B4	D2-B2	B4-C4	C5-B5	C1-B1	(BYE)	B5-C5	A2-C2	C2-A2	B1-C1	(BYE)	(BYE)	E4-A4	B3-D3	A4-E4	(BYE)
(BYE)	B2-C2	C3-D3	D4-C4	D3-C3	(BYE)	E5-B5	E1-B1	(BYE)	C4-D4	(BYE)	B4-E4	C5-D5	C1-D1	E3-B3	B5-E5	A2-E2	C2-B2	B1-E1	D1-C1	D5-C5	E4-B4	B3-E3	(BYE)	E2-A2
Attachments
5x5 grid schedule.xlsx
(9.37 KiB) Downloaded 114 times
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Re: Scheduling a 25 team, 14 packet tournament

Post by Cody »

Despite having only 4 prelim games and taking 5 rounds, a 5x5 prelim structure is probably the best. This leaves 6-7 packets for the playoffs (6 if you want to do a packet tiebreaker for ties into the finals, 7 if you're comfortable with a paper tiebreaker of playoffs PPG).

You can then use wildcards (PPB) to bring extra 2 seeds into the playoffs so that you aren't stuck with a crossover by 1s (meaning one loss eliminates you from championship contention) or 2s (which requires 8 packets and leaves only 1 packet for finals). With 7 packets, you can do playoff brackets of 7/6/6/6 (straight round robins, no carryover). (The 6 brackets can be run straight through and finish early, which requires some buzzer planning, or you could do double-byes or limited single-byes.) I think a sample size of 6 games is sufficient to break ties into the finals on PPG, and letting lower bracket teams out after (potentially only) 10 rounds is a plus.

6 playoff packets is trickier, requiring a setup with 6 teams in the top bracket and weird slices elsewhere. I don't think it is possible to give every team 9 games in this scenario without using 3 brackets of 6 and one lower bracket of 7, which takes two more rounds than the 6 brackets (unless you use limited single-byes to make the 6 brackets take 6 rounds.)

Uneven prelim brackets (6/6/6/7, for example) probably won't work very well because you're limited to a maximum of 5 packets in the (top bracket) playoffs and 25 teams does not break down well – it would be difficult to get 4 more games for all teams without having a top bracket of 6 and one lower bracket of 7. (Same problems as the previous paragraph, except you don't have enough packets to do limited single-bye in the upper bracket so some number of teams there are pretty much guaranteed to finish 2 rounds early.) You also reduce the number of playoff games pretty significantly, and can't reserve a packet for finals tiebreakers in any scenario.
Last edited by Cody on Thu Oct 11, 2018 7:19 am, edited 1 time in total.
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Re: Scheduling a 25 team, 14 packet tournament

Post by Cody »

Silverman wrote: Thu Oct 11, 2018 12:23 am You can use the following pretty unique format, which I saw used at SAGACITY IX at Pitt (beware, a few games are missing from those stats):

Arrange the teams in a 5x5 grid, labeled as a spreadsheet is (columns A-E, rows 1-5). Each team plays 8 prelim games: one game against each team in its row and column. You can do it over 9 rounds, which 1 bye team in each of the first 5 rounds and 5 bye teams in each of the last 4.

For rebracketing, rank the teams first by W-L and then by points (or PPB if you want to control for not having common opponents). The top 8 play a 3-round single-elim championship bracket, the next 8 play a 3-round single-elim consolation bracket, and the teams ranked 17-19, 20-22, and 23-25 play 3-team RRs for 2 games in 3 rounds.
I would implore anyone thinking about scheduling for a 25 team tournament (or any other tournament) to avoid this type of schedule, which horrifies me. For any given team, 4 of their 9 prelim games are against non-common opponents, so the strength of the schedule that teams within a bracket played is entirely variable. This means that neither W-L record nor PPG have any significance for seeding the playoffs, and you are – by design – unfairly eliminating some teams.

Even if you constructed the schedule to spread out the seeds in-bracket (i.e. A bracket has its 1 seed as A1, B bracket has its 2 seed as B1, C bracket has its 3 seed as C1, etc.), these seeds are not comparable in any way and the games against teams in other brackets only total 4, which necessarily means that a schedule cannot be constructed in which all teams within a bracket play the same set of in-bracket seeds from other brackets. (Barring more rounds being added.)

The fairness of single elimination is a separate issue in its entirety; suffice it to say that I think it has no place determining the champion of a quizbowl tournament, especially when the scheduling and physical constraints necessitating single-elimination in other sports do not apply.
Cody Voight (he/him), VCU ‘14. I wrote lots of science and am an electrical engineer.
VCU Tournament Director ‘13-‘17. HSAPQ President ‘15-‘16. ACF Treasurer ‘19-‘20. ACF Nats ‘21 TD.
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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