“New” tournament format: “paired prelim brackets”

[Cody]

Two “new” formats were tried at the 2014 incarnation of VCU Winter. Both were devised by Matt Weiner and hold some advantages and disadvantages over a traditional format; here is an explanation of “paired prelim brackets”. 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. A separate thread on “modified double-elim playoffs” will follow later this week, once I’ve had a chance to work out the math for different field sizes.

On “paired prelim brackets”:

The idea here is that you “pair” 2 prelim brackets and play a “crossover” in each “pair”: each team in bracket A plays each team in bracket B, as opposed to each team in bracket A playing all the other teams in bracket A while each team in bracket B plays all the other teams in bracket B. Brackets are the normal size for quizbowl prelims (so, 6 to 8 teams).

You must have an even number of prelim brackets to do this format. If you do not have an even number, you should use a different prelim format or change your prelim bracket size so that there are an even number of brackets.

Brackets are paired such that the bracket with the overall #1 seed plays the bracket with the worst 1 seed (overall #4 if there are 4 brackets, overall #N for N brackets), and so on. As for a traditional round-robin prelim, brackets are created by “snake” seeding teams; then the brackets are “snake” seeded by #1 seeds for pairing.

Advantages:

• Creates more comparable records out of the prelims. In a normal round-robin, you can only rank teams within each bracket; in a paired system, A and B records are commensurable because they were generated by playing each other, while records within A can also be compared since all A teams played the same schedule.
• Reduces or eliminates the need for byes for certain field sizes. 7-team brackets play all 7 rounds instead of having a bye. Systems with some brackets of 7 and some of 6 can play with only one bye on the schedule (one per group of 7 team) as opposed to three (one per group of 7 and two per group of 6) as you would have to do in a round-robin. In particular, this covers the problematic 25-28 teams very well.
• Ensures more prelim rounds without rigamarole – paired brackets for 24 teams means every team gets 6 games in the prelims instead of 5, opening up some shorter / different playoff formats while still guaranteeing 9 games.
• In many field sizes, reduces the necessary length of a crossover playoff by 1 round. Every playoff team from tier X has already played M other playoff teams in tier X, where M is the number of playoff teams taken from each bracket to tier X. In a traditional round-robin, every playoff team from tier X has played M-1 teams from tier X because they only play teams from their own prelim group in the prelims and do not “play themselves”. This saves a round if there are an odd number of teams in prelim brackets (it does not save a round for even prelim brackets since prelims then take 1 extra round).
• Can require the same number of rooms as a bracketed round-robin prelims; for example, 26 teams with 7/6, 7/6 paired brackets requires 12 rooms.

Disadvantages:

• Seeding is much more important because you can have an unlimited number of 0 or 1 loss teams in a bracket. This is very different from a round-robin, where you have a maximum of 1 undefeated team, and a maximum of three 1-loss teams (and the only way to have multiple 1-loss teams is for them to all be tied for first). Any playoff format that is sensitive to this should remember that the mathematical maximums on 0 and 1 loss teams from round-robins do not apply here! This should not matter if your seeding is even a little bit careful – after all, most formats that start with round-robins also do not want to place multiple tournament-winning contenders in the same bracket because they also have to break a limited number of teams out of each prelim group. If you end up with the fifth-place team in a bracket standing at 1 loss because they beat teams 2-5 in their pair bracket, then you did your seeding very poorly or you had bad information about rosters; but, poor seeding and bad roster info do happen, so just like in any format, build in in safeguard making sure no team is needlessly screwed by it. The upshot of this is: take at least THREE teams from every bracket to the playoffs (whatever the playoff format might be) and not just two, especially if you are doing paper tiebreakers.
• If you have an odd number of teams in every bracket, extra rooms are required (and thus extra readers and extra etc.) – +1 room per pair of brackets. For example, 28 teams with 7/7, 7/7 paired brackets requires 14 rooms instead of 12. If you are hurting for staff, this is not the format for you.

[tabstop]

One thing I had thought of (but still haven't sat down and worked out all the consequences of) is to change "three from each pool" to "six from each pool pair" (since in a sense the pair of pools is the smallest self-contained unit) and allow yourself some asymmetry -- if you end up with five 5-1 teams in bracket A, then this can allow you to make the split 4/2 or 5/1 instead of requiring 3/3. I suspect, though, this will have a bigger impact in deciding which bubble team barely makes it in. (In this case, looking at the results on the day, this would have put Western Branch (who finished 2nd in the middle tier) in the top playoff tier and Nandua A (who finished last in the top tier) in the middle.)

I think this might also alleviate some of the weirdness that can result from treating (say) B1 as necessarily above A2, when A2 can be undefeated and B1 not. (In fact, there can only be one pool in each pair that has an undefeated team; ranking by pair-of-pool means that all the undefeated teams will go on top.) OTOH, I know rewarding people for winning their pool is a good thing, so that might come out to be a wash.

[btressler]

Swarthmore tried a variation on this many years ago at a QOTC. I think there were 18 teams and you played all the teams in the other two groups of 6.

Do you put teams from the same school in the same bracket or different ones? As I recall, Swarthmore put them all in the same bracket. That meant that after two rounds, my team was 2-0, but in 4th place out of 6 in our group behind Maryland A, B, and C. (We lost a bunch after that, but I do agree that seeding is important.)

[Cody]

Swarthmore tried a variation on this many years ago at a QOTC. I think there were 18 teams and you played all the teams in the other two groups of 6.

Do you put teams from the same school in the same bracket or different ones? As I recall, Swarthmore put them all in the same bracket. That meant that after two rounds, my team was 2-0, but in 4th place out of 6 in our group behind Maryland A, B, and C. (We lost a bunch after that, but I do agree that seeding is important.)

Seeding is the most important thing, so you should of course disregard different teams from schools until the end when you can make switches up and down a place to avoid some schools playing each other. (Fairness trumps aesthetics). The prelim brackets @ VCU Winter, for instance, turned out quite nice just by happenstance and I didn't wind up doing any switching -- a couple of schools playing their B or C team isn't a big deal.

[Fado Alexandrino]

This format seems interesting and makes awkward numbers work. However, would a record-based playoff be more efficient than a standing-in-bracket playoff to adjust for possible imperfections in the seedings? So something like the top twelve teams by WL/PPB make the playoffs with all undefeatedsandr X-1s coming in with winner bracket benefits.

[Northern Central Railway]

This format seems interesting. One thing I wonder though is whether or not having a hybrid preliminary structure, i.e. some morning pools be typical round robins and others be paired brackets would be fair to teams.

If you have a field size of 34, there would be the possibility of having 4 pools of 6 doing a round robin, and then 2 pools of 5 doing a paired prelim (each team would get 5 prelim games). One possible downside would be bracketing for the afternoon, but I think this could be solved for 12 teams making playoffs in the following way:

For the 4 pools that are round robin, the 1st and 4th place PPBs of teams that finished first in their morning pool would be in the same afternoon bracket as the 2nd and 3rd place PPBs among teams that finished second in their morning pool, and have the other four teams that finished in the top two in their morning pool in the other playoff bracket. For the 2 pools that are paired prelim pools, teams that finish 1st and 2nd in one pool would go to one playoff bracket and the top two from the other paired prelim pool would go to the either, since they wouldn't have played each other in the morning.

Does this sound like a workable solution or an absolute mess?