36-team ICT

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36-team ICT

Post by setht » Thu Mar 07, 2013 4:05 pm

What schedule would you use for a 36-team field at ICT? Let's assume the tournament runs in one day, but that the number of packets needed isn't a restriction.

The clear options to me are 6x6 into 3x12, 12x12 into 6x6, and 6x6 3 times over. Of those, I think my favorite is 6x6 into 3x12--6 prelim brackets of 6, then 3 playoff brackets of 12--but perhaps I'm not thinking of some drawback, or some appealing feature of one of the other options. In particular, I think 6x6 into 3x12 compares favorably with the current system: it's a bit easier to make it into the top bracket, and we take a larger fraction of the field into the top bracket (I guess those are the same thing, but whatever). I suppose the downside is that there's a bit more of a skill range in each bracket, so there are more one-sided games/fewer games against opponents of similar strength, compared with the current system (4x8 into 4x8). Also every team plays two more games and the tournament ends a bit later compared with the current system; I regard the former as a plus for teams, and the latter as a small minus (definitely outweighed by the former).

Thoughts?

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Re: 36-team ICT

Post by grapesmoker » Thu Mar 07, 2013 4:19 pm

Why is 9x4 not an option?

edit: I mean, I realize this induces a bye, but that might not be such a horrible thing.

edit: but if people don't like that, 6x6 into 3x12 seems perfectly reasonable.
Last edited by grapesmoker on Thu Mar 07, 2013 4:23 pm, edited 2 times in total.
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Re: 36-team ICT

Post by Auroni » Thu Mar 07, 2013 4:20 pm

i'm in favor of 6 brackets of 6, top 2 from each advance, then 3 brackets of 12
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Re: 36-team ICT

Post by AKKOLADE » Thu Mar 07, 2013 4:27 pm

You could do 6x6 -> 6x6 with the top two brackets doing crossover games (though for an event like ICT, 3x12 would be superior).
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Re: 36-team ICT

Post by Important Bird Area » Thu Mar 07, 2013 4:56 pm

grapesmoker wrote:Why is 9x4 not an option?

edit: I mean, I realize this induces a bye, but that might not be such a horrible thing.

edit: but if people don't like that, 6x6 into 3x12 seems perfectly reasonable.
9x4 adds the bye, which lengthens everyone's day and requires the production of more questions without offering anyone more actual quizbowl.

6x6 into 3x12, by contrast, works perfectly with the existing 18-packet ICT.

Edit: not quite: it would require a 19th and 20th packet to break ties.
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Re: 36-team ICT

Post by vcuEvan » Thu Mar 07, 2013 6:10 pm

I really like the 6x6 into 3x12. The prospect of a full round robin between the top 12 teams in the country is really exciting.
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Re: 36-team ICT

Post by Adventure Temple Trail » Thu Mar 07, 2013 6:21 pm

While 6x6 into 3x12 would be exhilarating for the top 12 for the reasons Evan suggests, I worry that it's hard to fairly determine which teams should advance with only five games plus potential half-packet tiebreakers, and it's a pretty big bummer for a team on the cusp (think last year's Georgia Tech, Michigan, or Penn) to lose two close games, go 3-2, and spend two-thirds of the day playing games that don't matter. Perhaps the increased number of brackets makes it less likely that you'll get stacked brackets such as the ones we had at 2012 ICT, but someone's still liable to get pretty screwed. For this reason I'm more sympathetic to a 9x4 schedule, rebracketed into 4x8 and a bottom bracket of 4, for six crossover games. There would be a bye and the need for two additional rounds to be written (9 game prelims + 1 game tiebreaker + 6 rounds playoffs + 1 round tiebreaker + 2 finals + emergency = 20 packets), but eight games is a much more robust sample size to determine the best teams for playoff advancement than five.
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Re: 36-team ICT

Post by AKKOLADE » Thu Mar 07, 2013 6:28 pm

Why not 3x12 -> 6x6 then?
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Re: 36-team ICT

Post by touchpack » Thu Mar 07, 2013 6:51 pm

Fred wrote:Why not 3x12 -> 6x6 then?
3x12 into 6x6 would be worse when it comes to getting the best teams in the playoffs, mainly because the top bracket is now very small. While 6x6 into 3x12 gives you a smaller sample size (5 games vs 7), the competition is going to be weaker. Last years ICT had brackets containing these teams:

Illinois
Minnesota
Michigan

Penn
Yale
Brown

UCSD
Virginia
Harvard

Maryland
Chicago

Michigan and Penn, two very excellent teams that ended up finishing 3rd and 4th at ACF Nats, ended up out of the top bracket because there were two other national contenders in their prelim bracket. With 12 teams advancing to the top bracket, it's much easier to spread these good teams out, making the brackets less stacked. I have much less sympathy for the hypothetical team that takes an upset loss to a team like OSU or MIT and is eliminated from the top bracket than I do for 2012 Michigan, who took losses to Illinois A and Minnesota A and were eliminated. Anyway, you still have to lose TWICE to get eliminated, so I don't really think 6x6 into 3x12 is problematic.
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Re: 36-team ICT

Post by Pilgrim » Thu Mar 07, 2013 7:05 pm

Fred wrote:Why not 3x12 -> 6x6 then?
If the prelim bracket is simply a round robin, increasing the size doesn't really improve the robustness - if only two teams advance, it's likely that the only games that really "matter" for advancement are between the top three teams.
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Re: 36-team ICT

Post by Tees-Exe Line » Thu Mar 07, 2013 7:09 pm

the 36-team ICT should happen this year.
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Re: 36-team ICT

Post by Important Bird Area » Thu Mar 07, 2013 7:18 pm

Tees-Exe Line wrote:the 36-team ICT should happen this year.
The 2013 ICT will remain at its originally announced size (because we already have a signed contract with the hotel for a set number of rooms). Potential field expansion would happen, at the earliest, in 2014, and is subject to constraints of team, staff, and room availability.
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Re: 36-team ICT

Post by Auks Ran Ova » Thu Mar 07, 2013 7:22 pm

I also support the 6x6 => 3x12 format. The increased number of prelim pools, with the same number of teams qualifying from each one, eases the burden on teams trying to get into the top bracket; Billy has clearly outlined the reasons why.
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Re: 36-team ICT

Post by theMoMA » Thu Mar 07, 2013 7:36 pm

Ukonvasara wrote:I also support the 6x6 => 3x12 format. The increased number of prelim pools, with the same number of teams qualifying from each one, eases the burden on teams trying to get into the top bracket; Billy has clearly outlined the reasons why.
I'll echo this. The more prelim pools, the better the focusing power of the tournament.
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Re: 36-team ICT

Post by Sima Guang Hater » Thu Mar 07, 2013 7:47 pm

theMoMA wrote:
Ukonvasara wrote:I also support the 6x6 => 3x12 format. The increased number of prelim pools, with the same number of teams qualifying from each one, eases the burden on teams trying to get into the top bracket; Billy has clearly outlined the reasons why.
I'll echo this. The more prelim pools, the better the focusing power of the tournament.
Agreed wholeheartedly.
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Re: 36-team ICT

Post by Sun Devil Student » Thu Mar 07, 2013 8:03 pm

How about 3 prelim brackets of 12, followed by 4 playoff brackets of 10, 10, 8, and 8 teams? This is 20 rounds (which would mean 22 or 23 packets to account for tiebreakers - I guess you could shave two packets by double-counting the prelim games), but poor seeding (e.g. teams changing lineups from SCT to ICT, or dramatically improving by studying) wouldn't be as much of a problem, and you still have a large, exciting top bracket. If I were on a top team (which sadly I'm not) I would definitely be willing to play more rounds in exchange for a more rigorous ranking - this seems like the best of both worlds to me.

Or how about this: 3 prelim brackets of 12, followed by 6 crossover matches (the top 3 teams of each prelim bracket play the other 6 teams they haven't played before) - this fits into 20 packets including tiebreakers/finals, and effectively makes a 4x9 playoff bracket without actually playing all 9 games.

As another variant, I'd also love to see a 3x12 prelims followed by 3x12 playoff brackets with prelim games carried over (effectively 8 crossover matches, which means 19 rounds + tiebreakers = 22 packets). Play 7 rounds, lunch/tiebreaker, 9 more rounds, dinner, 3 more rounds, up to 2 rounds of finals as needed. Or go for 2 days like ACF Nationals (I'd rather play until 9pm if that keeps History Bowl on Sunday, though. But that's just me).

Comments?
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Re: 36-team ICT

Post by setht » Thu Mar 07, 2013 8:09 pm

RyuAqua wrote:While 6x6 into 3x12 would be exhilarating for the top 12 for the reasons Evan suggests, I worry that it's hard to fairly determine which teams should advance with only five games plus potential half-packet tiebreakers, and it's a pretty big bummer for a team on the cusp (think last year's Georgia Tech, Michigan, or Penn) to lose two close games, go 3-2, and spend two-thirds of the day playing games that don't matter. Perhaps the increased number of brackets makes it less likely that you'll get stacked brackets such as the ones we had at 2012 ICT, but someone's still liable to get pretty screwed. For this reason I'm more sympathetic to a 9x4 schedule, rebracketed into 4x8 and a bottom bracket of 4, for six crossover games. There would be a bye and the need for two additional rounds to be written (9 game prelims + 1 game tiebreaker + 6 rounds playoffs + 1 round tiebreaker + 2 finals + emergency = 20 packets), but eight games is a much more robust sample size to determine the best teams for playoff advancement than five.
It looks like several people already beat me to this, but I want to say it anyway: in the current system, a team is eliminated from title contention if it comes in 3rd out of 8 teams. In the 6x6 into 3x12 system, a team is eliminated from title contention if it comes in 3rd out of 6 teams. Also the smaller bracket size should mean that each bracket is less deeply stacked.

It is true that 5 games is a smaller sample size than 7, but I think it makes sense to assume that what really decides (almost always) who gets into the top bracket and who doesn't quite make it is the games between the top 3 teams in each prelim bracket. In other words, most of the prelim sample doesn't really matter, and in both formats what really matters is the same sample of 3 games (1-3, 2-3, 1-2). With that assumption, 6x6 prelims actually seems more robust than 4x8.

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Re: 36-team ICT

Post by setht » Thu Mar 07, 2013 8:31 pm

Sun Devil Student wrote:How about 3 prelim brackets of 12, followed by 4 playoff brackets of 10, 10, 8, and 8 teams? This is 20 rounds (which would mean 22 or 23 packets to account for tiebreakers - I guess you could shave two packets by double-counting the prelim games), but poor seeding (e.g. teams changing lineups from SCT to ICT, or dramatically improving by studying) wouldn't be as much of a problem, and you still have a large, exciting top bracket. If I were on a top team (which sadly I'm not) I would definitely be willing to play more rounds in exchange for a more rigorous ranking - this seems like the best of both worlds to me.

Or how about this: 3 prelim brackets of 12, followed by 6 crossover matches (the top 3 teams of each prelim bracket play the other 6 teams they haven't played before) - this fits into 20 packets including tiebreakers/finals, and effectively makes a 4x9 playoff bracket without actually playing all 9 games.

As another variant, I'd also love to see a 3x12 prelims followed by 3x12 playoff brackets with prelim games carried over (effectively 8 crossover matches, which means 19 rounds + tiebreakers = 22 packets). Play 7 rounds, lunch/tiebreaker, 9 more rounds, dinner, 3 more rounds, up to 2 rounds of finals as needed. Or go for 2 days like ACF Nationals (I'd rather play until 9pm if that keeps History Bowl on Sunday, though. But that's just me).

Comments?
Okay, I'll bite. I'm not sure your first scheme is actually more robust against seeding mistakes--you've just shifted the cutoff point from 3rd among 6 teams to 4th among 12. If anything, I'd guess that this is less robust than 6x6. Second, you're proposing 20 rounds of play, not including tiebreakers and finals; there is no way this can happen in one day, and I'm not sure there's 36 teams interested in doing a 2-day tournament--maybe there is, I don't know. Third, you'd actually need 25 packets: 20 for prelims and playoffs, 2 more for tiebreakers (1 after prelims, 1 after playoffs), 2 more for finals, and 1 more as an insurance policy against screw-ups. The current ICT format calls for 18 packets, so this is a 7 packet increase. Over here I gave a breakdown of where the questions in last year's ICT and SCT sets came from. At the moment, there are about 100 "questions from circuit people who have not historically kicked in bunches of ICT questions" in this year's ICT set--in other words, about 2 packets' worth, once again (hopefully that number will go up). I just don't think it's feasible to produce 7 more packets without a very large chunk of the additional questions coming from circuit people who haven't already been kicking in lots of questions for years. Shaving rounds and packets by carrying over prelim games would be nice, but I don't think you can do it in this format: because of the bracket sizes, the top bracket of 10 teams has 3, 3, and 4 teams from the prelim brackets, which means that some teams have effectively played 2 playoff matches during prelims while others have played 3. Maybe there's a way to make that work, but I suspect not.

Your second proposal (3x12, 6 crossover matches) is 17 rounds of play plus tiebreakers and finals, which is stretching it for a one-day tournament. Actually, this is probably beyond "stretching it" and into "this can't happen in one day" territory. This format requires 22 packets (17 for prelims + playoffs, 2 for tiebreakers, 2 for finals, 1 for insurance), which is better than 24 but probably not doable--I certainly wouldn't want to set up a format requiring 22 packets without having good reason to think a lot more people would be shouldering the writing load (and by "good reason" I pretty much mean that I'd need to see an increase in such contributions for a year or two before I'd consider this kind of format).

Your third proposal is 19 rounds of play plus tiebreakers and finals. Can't be done in a day (much less "by 9 pm"), requires 24 packets.

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Re: 36-team ICT

Post by AKKOLADE » Thu Mar 07, 2013 8:47 pm

touchpack wrote:
Fred wrote:Why not 3x12 -> 6x6 then?
3x12 into 6x6 would be worse when it comes to getting the best teams in the playoffs, mainly because the top bracket is now very small. While 6x6 into 3x12 gives you a smaller sample size (5 games vs 7), the competition is going to be weaker. Last years ICT had brackets containing these teams:

Illinois
Minnesota
Michigan

Penn
Yale
Brown

UCSD
Virginia
Harvard

Maryland
Chicago

Michigan and Penn, two very excellent teams that ended up finishing 3rd and 4th at ACF Nats, ended up out of the top bracket because there were two other national contenders in their prelim bracket. With 12 teams advancing to the top bracket, it's much easier to spread these good teams out, making the brackets less stacked. I have much less sympathy for the hypothetical team that takes an upset loss to a team like OSU or MIT and is eliminated from the top bracket than I do for 2012 Michigan, who took losses to Illinois A and Minnesota A and were eliminated. Anyway, you still have to lose TWICE to get eliminated, so I don't really think 6x6 into 3x12 is problematic.
I just don't see how being eliminated after 5 games is superior to being eliminated after 11 games. If you don't finish in the top 2 after an 11 game round robin, I really don't have a problem with that team not being in the top 6. Teams have to be eliminated at some point and I don't see how it's fundamentally unfair to do it here.
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Re: 36-team ICT

Post by Sun Devil Student » Thu Mar 07, 2013 8:58 pm

setht wrote:the top bracket of 10 teams has 3, 3, and 4 teams from the prelim brackets,
Oh, crap, sorry! Thanks for catching that - I don't know why I thought 3 teams from each of 3 brackets would add up to 10 teams... so yes, with 10 teams you wouldn't be able to carry over prelim games. I was trying to avoid the 4x9 playoffs because it would require byes.
setht wrote:19 rounds of play plus tiebreakers and finals. Can't be done in a day (much less "by 9 pm"), requires 24 packets.
HSNCT does 15 rounds before dinner, a round every half hour. Why not another 6 rounds (4 + tiebreak/final) during the 3 hours from 7-10pm? (Actually, good point, "by 9pm" really needs to be "by 10pm". I was excited and in a hurry when I wrote this, my math was fuzzy. Still, though, could we run the whole tournament from 8am to 10pm?)
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Re: 36-team ICT

Post by setht » Thu Mar 07, 2013 9:02 pm

Fred wrote:I just don't see how being eliminated after 5 games is superior to being eliminated after 11 games. If you don't finish in the top 2 after an 11 game round robin, I really don't have a problem with that team not being in the top 6. Teams have to be eliminated at some point and I don't see how it's fundamentally unfair to do it here.
I think the idea (which I subscribe to) is that almost always, the way a team is eliminated is by losing games to teams of similar or superior strength. Obviously there are occasional upsets, but if you're team number 2 in your bracket and you take an unexpected loss you're in trouble regardless of whether your bracket size is 6 or 12. One difference between a 6-team and a 12-team bracket at that point is that a 12-team bracket gives team number 3 more opportunities to take its own unexpected loss and restore "the natural order"; this would suggest that a 12-team bracket is more stable against upsets. Another difference is that in a 12-team prelim bracket, team number 4 is the equivalent of a team number 2 in a 6-team prelim bracket, and team number 3 in a 6-team bracket is equivalent to a team number 6 in a 12-team bracket. In other words, an upset* in a 6-team bracket is the equivalent of team 6 (or lower) in a 12-team bracket beating team 4 or higher. This would suggest that a 6-team bracket is more stable against upsets, and I suspect that this feature is more important than the previous "more rounds to get a second, balancing upset" feature.

* Note that I'm not counting stuff like "3 beats 1" or "3 beats 2" as an upset in a 6-team bracket, because if that happens in a 6-team bracket it would have happened in a 12-team bracket--after all, the 12-team bracket has more strong teams than the 6-team bracket.

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Re: 36-team ICT

Post by Auks Ran Ova » Thu Mar 07, 2013 9:02 pm

Humans enjoy eating dinner and do not enjoy writing six extra packets of questions.
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Re: 36-team ICT

Post by setht » Thu Mar 07, 2013 9:06 pm

Sun Devil Student wrote:
setht wrote:19 rounds of play plus tiebreakers and finals. Can't be done in a day (much less "by 9 pm"), requires 24 packets.
HSNCT does 15 rounds before dinner, a round every half hour. Why not another 6 rounds (4 + tiebreak/final) during the 3 hours from 7-10pm? (Actually, good point, "by 9pm" really needs to be "by 10pm". I was excited and in a hurry when I wrote this, my math was fuzzy. Still, though, could we run the whole tournament from 8am to 10pm?)
19 rounds of play plus tiebreakers (up to 2 rounds) and finals (up to 2 rounds) means up to 23 rounds, so if you do 15 rounds before dinner you've still got as many as 8 more rounds left to go. Assuming a pace of a round every half hour, I guess you could run the whole tournament from 8 am to 11 pm, but I can't imagine very many people actually want to do that.

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Re: 36-team ICT

Post by AKKOLADE » Thu Mar 07, 2013 9:36 pm

setht wrote:
Fred wrote:I just don't see how being eliminated after 5 games is superior to being eliminated after 11 games. If you don't finish in the top 2 after an 11 game round robin, I really don't have a problem with that team not being in the top 6. Teams have to be eliminated at some point and I don't see how it's fundamentally unfair to do it here.
I think the idea (which I subscribe to) is that almost always, the way a team is eliminated is by losing games to teams of similar or superior strength. Obviously there are occasional upsets, but if you're team number 2 in your bracket and you take an unexpected loss you're in trouble regardless of whether your bracket size is 6 or 12. One difference between a 6-team and a 12-team bracket at that point is that a 12-team bracket gives team number 3 more opportunities to take its own unexpected loss and restore "the natural order"; this would suggest that a 12-team bracket is more stable against upsets.
The point of a tournament is to determine the winner, and at some point, you've got to eliminate people from contention. 11 games gives you a larger sample size for determining who the best teams are; if you're supposed to be the 2 seed and you lose to the 6 seed, that's on you.

Look: to win a tournament, you have to win games. If you lose too many games in the prelims, you don't make the top playoff brackets. No schedule is going to force you to lose games. If you're going to throw out a format because it gives a team too many chances to be upset, then you're basically saying people should get into the championship bracket by reputation and not actual performance. If that's the case, then just put those 6 or 8 or whatever teams on the pedestal right away and tell everyone to screw off because their name brand isn't good enough.
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Re: 36-team ICT

Post by Auks Ran Ova » Thu Mar 07, 2013 9:44 pm

Fred wrote:The point of a tournament is to determine the winner, and at some point, you've got to eliminate people from contention. 11 games gives you a larger sample size for determining who the best teams are; if you're supposed to be the 2 seed and you lose to the 6 seed, that's on you.
This is true. However, I (and presumably most people) would rather eliminate obviously good teams as late as possible, and would rather that a majority of the deciding games be against teams of a similar skill level. More, smaller prelim brackets make it much easier for the group of teams good enough to contend for the title to actually remain in contention for that title.
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Re: 36-team ICT

Post by AKKOLADE » Thu Mar 07, 2013 9:56 pm

Ukonvasara wrote:
Fred wrote:The point of a tournament is to determine the winner, and at some point, you've got to eliminate people from contention. 11 games gives you a larger sample size for determining who the best teams are; if you're supposed to be the 2 seed and you lose to the 6 seed, that's on you.
This is true. However, I (and presumably most people) would rather eliminate obviously good teams as late as possible, and would rather that a majority of the deciding games be against teams of a similar skill level. More, smaller prelim brackets make it much easier for the group of teams good enough to contend for the title to actually remain in contention for that title.
32 team double round robin, just to be sure no one gets eliminated too soon.
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Re: 36-team ICT

Post by theMoMA » Thu Mar 07, 2013 10:59 pm

setht wrote:Another difference is that in a 12-team prelim bracket, team number 4 is the equivalent of a team number 2 in a 6-team prelim bracket, and team number 3 in a 6-team bracket is equivalent to a team number 6 in a 12-team bracket. In other words, an upset* in a 6-team bracket is the equivalent of team 6 (or lower) in a 12-team bracket beating team 4 or higher. This would suggest that a 6-team bracket is more stable against upsets, and I suspect that this feature is more important than the previous "more rounds to get a second, balancing upset" feature.
This is the main advantage of the six-team prelim pools as opposed to the twelve-team pools.

Also, it's not entirely accurate say that teams are eliminated "after 5 rounds" in the 6x6 format, but are eliminated "after 11 rounds" in the 12-team pools. Teams are eliminated when they lose the number of games that ensures that they cannot make the top bracket. The very worst team in each bracket is probably going to be eliminated after two or three games, regardless of the format. Plenty of mid-tier teams would eliminated after five rounds regardless of how many teams are in each prelim pool.

I guess what I'm getting at is that I see no particular benefit to keeping teams "alive" for 11 rounds versus five rounds. It's much more important to focus on the quality of games needed to escape a particular prelim pool for the better teams. The more prelim pools there are, the fewer must-win prelim games come against opponents of similar quality, and the clearer the paths to the top bracket for the true contending teams. That seems to me to be a thing worth considering.
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Re: 36-team ICT

Post by evilmonkey » Fri Mar 08, 2013 3:30 am

I decided to empirically test whether the 3x12 to 6x6 or the 6x6 to 3x12 would provide more stability. I assigned 36 teams random strengths on a (0,1) scale, and then bracketed teams in such a way that teams 1-3, 4-6, ..., 34-36 would be placed into separate brackets in the first scenario, and 1-6, 7-12, ..., 31-36 in the second. Then, using some awesome random number generation, I simulated every game of the the prelims for both tournaments, and determined which teams would advance. For my preliminary simulation, I ran 5000 simulations; I am now in the process of running 50,000.

In every case, the strongest team made the playoffs. Percentage of times advancing by seed is as follows:

Code: Select all

Seed:	1		 2		  3	   4     5		   6		7		 8		9		10		11		12		
3X12:	100%	99.7%	94.6%	77.6%	75.1%	64.1%   NA		NA		NA		NA		NA		NA
6X6:	100%	99.9%	99.0%	97.3%	96.3%	93.8%	81.0%	78.8%	73.6%	72.9%	60.2%	57.5%
In the first case, 78% missed 0 or 1 of the top 6; in the second case, 71% missed 0-2 of the top 12. I know those numbers aren't really comparing the
same thing - in this upcoming simulation, I'm looking at how often case two misses 1 or 2 of the top 6.
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Re: 36-team ICT

Post by setht » Fri Mar 08, 2013 10:06 am

evilmonkey wrote:I decided to empirically test whether the 3x12 to 6x6 or the 6x6 to 3x12 would provide more stability. I assigned 36 teams random strengths on a (0,1) scale, and then bracketed teams in such a way that teams 1-3, 4-6, ..., 34-36 would be placed into separate brackets in the first scenario, and 1-6, 7-12, ..., 31-36 in the second. Then, using some awesome random number generation, I simulated every game of the the prelims for both tournaments, and determined which teams would advance. For my preliminary simulation, I ran 5000 simulations; I am now in the process of running 50,000.

In every case, the strongest team made the playoffs. Percentage of times advancing by seed is as follows:

Code: Select all

Seed:	1		 2		  3	   4     5		   6		7		 8		9		10		11		12		
3X12:	100%	99.7%	94.6%	77.6%	75.1%	64.1%   NA		NA		NA		NA		NA		NA
6X6:	100%	99.9%	99.0%	97.3%	96.3%	93.8%	81.0%	78.8%	73.6%	72.9%	60.2%	57.5%
In the first case, 78% missed 0 or 1 of the top 6; in the second case, 71% missed 0-2 of the top 12. I know those numbers aren't really comparing the
same thing - in this upcoming simulation, I'm looking at how often case two misses 1 or 2 of the top 6.
This looks cool, but I want to make sure I understand what this says: this is saying that the team ranked number 6 out of 36 has a 64.1% chance of making the top bracket (of 6 teams) out of a 3x12 prelims, right? And, in particular, teams 4, 5, and 6 are way more likely to make the top bracket out of a 6x6 prelims then they are out of a 3x12 prelims, right?

Of course all of these results depend entirely on your algorithm for deciding the outcome of games. Maybe it would be worth tweaking the algorithm to make upsets a bit more likely and see what things look like then--is 6x6 still more robust throughout, or does that change?

It might also be interesting to continue the simulations to see what happens in the top bracket each time: how often does each team from number 1 to number 36 wind up in the finals match? Or tied for a spot in the finals, I guess--I assume it's a bit of a hassle to deal with stuff like tiebreaker matches, finals that might be advantaged, etc., and I don't think adding those wrinkles would make the results that much more interesting.

Finally, it might be interesting to try simulating imperfect seeding--you may already have imperfect seeding to some extent if you allow a bracket of 1/4/7/10/etc. and a bracket of 3/6/9/12 in the 3x12 scenario, but maybe try some slightly more jumbled brackets. So, instead of balancing brackets so that you separate triplets or sextuplets by rank and have equal summed ranks in each bracket (not sure if you have that second restriction currently or not), try some brackets that relax one or both of those restrictions (equal summed ranks, separating triplets/sextuplets). I guess ideally you'd relax one or both restrictions "a little bit"--I wouldn't do completely random brackets, for instance.

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Re: 36-team ICT

Post by setht » Fri Mar 08, 2013 10:45 am

setht wrote:Maybe it would be worth tweaking the algorithm to make upsets a bit more likely and see what things look like then--is 6x6 still more robust throughout, or does that change?
Actually, what is your algorithm for deciding the outcome of games? I'm imagining something very simple like: draw two random numbers uniformly distributed in (0,1), add them to the team strengths, whichever one has the higher total wins. With that algorithm, a simple way to increase the likelihood of an upset is to draw two random numbers in (0,2) and add them to team strengths (equivalently, assign every team a strength value in (0,1/2), then add a random number in (0,1) in each game). This would make upsets exactly twice as likely in every match. That might be interesting, but I also think it might be interesting to change the form of the function mapping team strengths to outcome probabilities: maybe something like draw two random numbers from a normal distribution instead of a uniform distribution (or, having just reminded myself what the difference of identical normal distributions is, draw one random number from a normal distribution with mean 0 and whatever variance, and add it to one of the teams--say, always add it to the underdog, for consistency). That way the distribution of the difference in the strength added is normal rather than triangular.

Now that I'm thinking about this more, I guess you can always just draw one number representing the "difference in strengths added" as long as you use a distribution with mean zero, so a quick way to mess around with what kinds of upsets are likely to happen would be to try different distributions for the difference in strengths added--normal, triangular, uniform, whatever (all with mean zero, and always added to the underdog [or the favored team--doesn't matter as long as you're consistent]).

Apologies for piling up a bunch of suggestions, this is more interesting than what I should be doing.
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Re: 36-team ICT

Post by grapesmoker » Fri Mar 08, 2013 1:41 pm

I would like to suggest that the cutoff point for where the a team would/would not make the top bracket is not really a good criterion to use. As Fred has pointed out, at some point you gotta win the games. You seed the initial brackets according to the expected performance and you go from there. If the last ICT did a bad job of this, then it did a bad job of seeding, and this has nothing to do with the size of the brackets themselves. If anything, spreading out the top seeds across 6 rather than 3 brackets ought to, theoretically, give those top seeds a better shot at winning/coming in second; most of the time, the really better teams win out, and worrying about the teams on the cusp is not a great idea because someone will always be on the cusp. That's just life.
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Re: 36-team ICT

Post by evilmonkey » Fri Mar 08, 2013 3:22 pm

setht wrote: This looks cool, but I want to make sure I understand what this says: this is saying that the team ranked number 6 out of 36 has a 64.1% chance of making the top bracket (of 6 teams) out of a 3x12 prelims, right? And, in particular, teams 4, 5, and 6 are way more likely to make the top bracket out of a 6x6 prelims then they are out of a 3x12 prelims, right?
Correct. I would imagine that what Jerry just posted is the reason that that occurs.
Of course all of these results depend entirely on your algorithm for deciding the outcome of games. Maybe it would be worth tweaking the algorithm to make upsets a bit more likely and see what things look like then--is 6x6 still more robust throughout, or does that change?
For each team, I simulated a random "true winning percentage" number in the range (0-1) [I might want to limit the range to (0.5-1), since theoretically the worst quizbowl team at ICT is better than the average quizbowl team]. For each game, I used Bill James' log5 to calculate the probability that a team would win, and then simulate a number from a U(0,1) distribution. If the probability of winning was greater than that random number, team 1 wins; if the probability of winning was less, then team 2 wins.

In the last simulation I ran, the top 2 teams had virtually no chance of losing to the bottom team; team 1 had a 0.005 chance of losing to the 20th best team, while team 2 had a 2.5% chance. I'm inclined to believe that this is a particularly high level of upsets - for example, last year I'm not sure I would have taken Carleton or Carnegie Mellon in a single game out of 100 against Illinois/Yale.
It might also be interesting to continue the simulations to see what happens in the top bracket each time: how often does each team from number 1 to number 36 wind up in the finals match? Or tied for a spot in the finals, I guess--I assume it's a bit of a hassle to deal with stuff like tiebreaker matches, finals that might be advantaged, etc., and I don't think adding those wrinkles would make the results that much more interesting.
I suppose that would be interesting - in Fred's suggested model, the top teams do have fewer games they could lose. In this simulation, for ties in the standings, I used a fairly lame tiebreaker to stand in for PPG/PPB; for each game, the winning team received abs(Random Number - Win Chance), the losing team received -abs(Random Number-Win Chance), and all ties in the standings were broken on the basis of this "margin" statistic.
So, instead of balancing brackets so that you separate triplets or sextuplets by rank and have equal summed ranks in each bracket (not sure if you have that second restriction currently or not).
I do not have the second restriction. I already question the validity of being able to separate "top 3" from "second 3" in general, even though that appears to be the case this year. Instead, for each simulation I re-randomized the brackets, subject to the first constraint; in this way, even if one simulation sees a team in a particularly difficult bracket, that bracket will only last for one round.

I do wonder whether I should get new team strengths every simulation.
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Re: 36-team ICT

Post by evilmonkey » Fri Mar 08, 2013 3:46 pm

A quick simulation that I just did: this is the probability that a given seed makes the top bracket. In this case, we should remember that the left hand column will sum to 6, and the right hand column will add to 12. I ran this with both resampling during every simulation, and keeping teams constant over all simulations. The fixed-strength simulation happened to choose teams where there was a dropoff in quality after teams 1-6 - reminding me why I should be changing team strengths in each simulation. Below are the results of the variable-strength simulations.

Code: Select all

       3x12   6X6
 [1,] 0.9761 0.9935
 [2,] 0.9350 0.9805
 [3,] 0.8773 0.9665
 [4,] 0.7354 0.9433
 [5,] 0.6441 0.9189
 [6,] 0.5527 0.8884
 [7,] 0.3239 0.7930
 [8,] 0.2608 0.7478
 [9,] 0.2032 0.7133
[10,] 0.1265 0.6700
[11,] 0.1048 0.6240
[12,] 0.0766 0.5690
[13,] 0.0538 0.3577
[14,] 0.0396 0.3105
[15,] 0.0293 0.2859
[16,] 0.0189 0.2438
[17,] 0.0136 0.2148
[18,] 0.0091 0.1854
[19,] 0.0066 0.1240
[20,] 0.0052 0.1022
[21,] 0.0031 0.0864
[22,] 0.0020 0.0722
[23,] 0.0011 0.0597
[24,] 0.0008 0.0474
[25,] 0.0001 0.0261
[26,] 0.0003 0.0236
[27,] 0.0001 0.0174
[28,] 0.0000 0.0134
[29,] 0.0000 0.0088
[30,] 0.0000 0.0058
[31,] 0.0000 0.0030
[32,] 0.0000 0.0012
[33,] 0.0000 0.0014
[34,] 0.0000 0.0009
[35,] 0.0000 0.0002
[36,] 0.0000 0.0000
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Re: 36-team ICT

Post by Sima Guang Hater » Fri Mar 08, 2013 3:58 pm

Bryce, can you integrate the probability over the size of the top bracket? i.e. can you find the probability that the top n teams get into a top bracket of size n?
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Re: 36-team ICT

Post by Adventure Temple Trail » Fri Mar 08, 2013 4:59 pm

I'm convinced at this point that a 6x6-into-3x12 format would be better at alleviating the problems I posed than a 9x4-into-something format.
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Re: 36-team ICT

Post by evilmonkey » Fri Mar 08, 2013 10:34 pm

Eric, can you explain further what you would like for me to do?

Seth - here is a chart of the proportion of times each seed made the finals; as you can see, in the end it doesn't appear that there is a very big difference between the two formats in determining an overall champion. The proportion of finals matchups including only the the top 4 seeds was .8485 vs. .8648.

Code: Select all

     Seed   3x12   6x6
 [1,]    1 0.8566 0.8760
 [2,]    2 0.5831 0.5993
 [3,]    3 0.2724 0.2632
 [4,]    4 0.1325 0.1238
 [5,]    5 0.0725 0.0641
 [6,]    6 0.0390 0.0344
 [7,]    7 0.0165 0.0183
 [8,]    8 0.0118 0.0090
 [9,]    9 0.0065 0.0050
[10,]   10 0.0036 0.0038
[11,]   11 0.0028 0.0016
[12,]   12 0.0013 0.0005
[13,]   13 0.0006 0.0005
[14,]   14 0.0003 0.0001
[15,]   15 0.0002 0.0002
[16,]   16 0.0001 0.0001
[17,]   17 0.0002 0.0001

On a non-empirical note: As I was riding up to Dallas, I had time to reflect upon Fred's idea that 11 games is a lot for teams that have already been knocked out of contention. I think I can appreciate the sentiment he is reflecting; I remember last year at ICT, becoming somewhat less enthused about upcoming games as chances at top bracket, then 2nd bracket slipped away; in every case, there was a renewed vigor by the thought of "well, we can still make [next lower bracket]", and then the final 6 games brought the idea "we can win the bottom bracket", which was quickly dashed. I think even after rebracketing, there was still the motivation of improving our final positioning.
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Re: 36-team ICT

Post by touchpack » Fri Mar 08, 2013 11:23 pm

I THINK what Eric is asking for is to find the probability that the #1 team makes the top bracket, that BOTH the #1 and #2 teams make the top bracket, that all three of the #1, #2, and #3 teams make the top bracket, all the way up to the top 6.
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Re: 36-team ICT

Post by Sima Guang Hater » Fri Mar 08, 2013 11:32 pm

Billy wrote:I THINK what Eric is asking for is to find the probability that the #1 team makes the top bracket, that BOTH the #1 and #2 teams make the top bracket, that all three of the #1, #2, and #3 teams make the top bracket, all the way up to the top 6.
That. Although that information would be most useful if we could take into account bad seeding (I don't know how to do that). I was just interested in seeing the probability that the best teams actually make the top bracket in each situation.
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Re: 36-team ICT

Post by evilmonkey » Sat Mar 09, 2013 1:14 am

Proportion of times that ALL of the top n teams made the top bracket:

Code: Select all

	3x12		6x6
1	.9796	.9940
2	.9162	.9778
3	.8059	.9441
4	.5846	.8926
5	.3858	.8221
6	.2177	.7316
I'm not quite sure how to simulate the scenario where we have bad seeding (other than complete randomization of brackets).
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Re: 36-team ICT

Post by Excelsior (smack) » Sat Mar 09, 2013 1:31 am

I'm not quite sure how to simulate the scenario where we have bad seeding (other than complete randomization of brackets).
Just to be clear, the bracketing procedure you're currently using is:
I assigned 36 teams random strengths on a (0,1) scale, and then bracketed teams in such a way that teams 1-3, 4-6, ..., 34-36 would be placed into separate brackets in the first scenario, and 1-6, 7-12, ..., 31-36 in the second
...right?

Given this bracketing scheme, you might have brackets like:
A: {1, 11, ...}
B: {2, 7, ...}
C: {3, 9, ...}
D: {4, 12, ...}
E: {5, 8, ...}
F: {6, 10, ...}

Then, to simulate bad seeding, perform k swaps in which a random pair of teams which are <=n seeds apart are interchanged. So, for k=2 and n=2, you might swap 6<->7 (differ by 1) and 4<->2 (differ by 2), to yield:
A: {1, 11, ...}
B: {4, 6, ...}
C: {3, 9, ...}
D: {2, 12, ...}
E: {5, 8, ...}
F: {7, 10, ...}

This seems to imitate the ways in which seeding actually goes wrong (basically, misunderestimation of a team's strength relative to some other team), and could produce interesting results. What remains, then, is to make a good choice of k and n. I think n=2~3 should suffice (larger seeding errors seem unlikely in the top sextets, and though there are probably larger seeding errors in the bottom sextets, I doubt they propagate to the top sextets in any meaningful way). As for k, I dunno - try some values and see how it turns out, maybe? Keeping in mind, of course, that some swaps will be "meaningless" e.g. the swap 4<->2 mentioned above, because it swaps teams that are within the same sextet (and the proportion of meaningless swaps increases as n decreases).
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Re: 36-team ICT

Post by Cody » Sat Mar 09, 2013 1:45 am

Excelsior (smack) wrote:Given this bracketing scheme, you might have brackets like:
A: {1, 11, ...}
B: {2, 7, ...}
C: {3, 9, ...}
D: {4, 12, ...}
E: {5, 8, ...}
F: {6, 10, ...}
If this is truly the case and the teams were not snake seeded, you have already done a large part in simulating bad seeding.
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Re: 36-team ICT

Post by evilmonkey » Sat Mar 09, 2013 2:07 am

SirT wrote:
Excelsior (smack) wrote:Given this bracketing scheme, you might have brackets like:
A: {1, 11, ...}
B: {2, 7, ...}
C: {3, 9, ...}
D: {4, 12, ...}
E: {5, 8, ...}
F: {6, 10, ...}
If this is truly the case and the teams were not snake seeded, you have already done a large part in simulating bad seeding.
That is the case - I guess I started from the assumption that, when bringing together so many teams that don't usually play each other, there is going to be some error in the seeding; I was tried to introduce some variability in that. I suppose I could have snake-seeded and used Ashvin's adjustments, but I'm guessing that with adjustments made to minimize teams from the same region (or school), as well as errors in estimating seed, what I did is likely indistinguishable from that procedure.
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Re: 36-team ICT

Post by Sima Guang Hater » Sat Mar 09, 2013 12:45 pm

This seems pretty convincing to me that 6x6 into 3x12 is superior; there's a greater chance of the best teams making it into the top bracket (if only because the bracket is larger). Considering in any given year there's usually 6-7 teams, maximum, that have a reasonable shot at the title, so picking the scheme that allows those teams the highest chance at playing against each other makes sense.
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Re: 36-team ICT

Post by Sen. Estes Kefauver (D-TN) » Mon Mar 11, 2013 6:53 pm

So, I think the reason Fred's taking the position he's taking is that, for a high school national, where teams are eliminated after round 5, you run a big risk of having a lot of teams consider leaving, or getting frustrated at playing games that don't matter. When PACE did that in 2011 I correctly predicted it would be a poorly received mess. However, in college, teams should be way more used to playing a lot of games after they are out of contention, at least at the D1 ICT level, so I don't think the problem is the same. I will admit it still feels strange to me to have a college event where 5 rounds is all you have for prelims, because at regular tournaments you usually have at least 7 and sometimes up to like 10 games before the playoffs, but Fred, I don't think that the inherent problems are quite the same for ICT as they were with PACE.
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Re: 36-team ICT

Post by AKKOLADE » Mon Mar 11, 2013 7:42 pm

That wasn't part of my thinking on this issue.
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Re: 36-team ICT

Post by jonpin » Wed Mar 13, 2013 4:26 am

evilmonkey wrote:Proportion of times that ALL of the top n teams made the top bracket:

Code: Select all

	3x12		6x6
1	.9796	.9940
2	.9162	.9778
3	.8059	.9441
4	.5846	.8926
5	.3858	.8221
6	.2177	.7316
I'm not quite sure how to simulate the scenario where we have bad seeding (other than complete randomization of brackets).
The problem with making conclusions off of these numbers is that of course the right-hand column is bigger: On the left, you're measuring the probability that the top N teams make the 6-team championship bracket; on the right, you're measuring the probably that the top N make the 12-team bracket.
That said, I think the 6x6 is superior, because the 12-team playoff brackets will make it likelier that each team winds up at an appropriate final rank. With 3x12 prelims, seeding errors in the middle and unbalanced prelim pools can leave a team one or even two tiers lower than their performance would deserve. And it means that most teams will play more games where the outcome is basically fait accompli. Let's (arbitrarily) say that a team will play a great game against a team within 4 ranks of them and an interesting game against a team within 10 ranks of them. Assuming perfect snake bracketing, under 3x12->6x6, the #15 team will play one great game (#16) and four interesting games (#9, #10, #21, #22) out of 11 prelims, plus get beat down twice and administer four beat downs, before playing four great games in the playoffs (total 5, 4, 6). Under 6x6->3x12, their prelims are a little more boring, playing two interesting games (#9, #22) and three likely blowouts, but they're shorter and they get to a playoff team where six great games and four interesting games await (total 6, 6, 3).
The 6x6->3x12 system gives the top-third and bottom-third more games against themselves and fewer games against each other, allowing a more accurate final standings.
Sun Devil Student wrote:
setht wrote:19 rounds of play plus tiebreakers and finals. Can't be done in a day (much less "by 9 pm"), requires 24 packets.
HSNCT does 15 rounds before dinner, a round every half hour. Why not another 6 rounds (4 + tiebreak/final) during the 3 hours from 7-10pm? (Actually, good point, "by 9pm" really needs to be "by 10pm". I was excited and in a hurry when I wrote this, my math was fuzzy. Still, though, could we run the whole tournament from 8am to 10pm?)
HSNCT has games of 2x9:00 (IIRC 8:00 until recently?), ICT is 2x10:00. HSNCT's "15 rounds" are 10 rounds + 5 byes for the teams, ICT doesn't have byes. Playing at 30-minutes per round, you'd be going straight through from 8:00 to 1:30, then a lunch break, tiebreakers at 2:30, playoffs from 3:00 to 7:00, then out of complete necessity a dinner break before tiebreakers and finals. It would be fucking exhausting. On top of, y'know, 19 natural rounds instead of 13, which means 6 more packets to write.
Jon Pinyan
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evilmonkey
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Re: 36-team ICT

Post by evilmonkey » Thu Mar 14, 2013 9:42 pm

jonpin wrote:
evilmonkey wrote:Proportion of times that ALL of the top n teams made the top bracket:

Code: Select all

	3x12		6x6
1	.9796	.9940
2	.9162	.9778
3	.8059	.9441
4	.5846	.8926
5	.3858	.8221
6	.2177	.7316
I'm not quite sure how to simulate the scenario where we have bad seeding (other than complete randomization of brackets).
The problem with making conclusions off of these numbers is that of course the right-hand column is bigger: On the left, you're measuring the probability that the top N teams make the 6-team championship bracket; on the right, you're measuring the probably that the top N make the 12-team bracket.
I don't think that invalidates the conclusion; I think that it instead explains the conclusion.
Bryce Durgin
Culver Academies '07
University of Notre Dame '11
Texas A&M '15

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Mewto55555
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Re: 36-team ICT

Post by Mewto55555 » Thu Mar 14, 2013 9:49 pm

Wouldn't it make more sense (so the numbers were actually comparable) to figure out each team's probability of making the top 4 in their bracket? Obviously, the chances of the top 6 teams all making the top bracket increase dramatically when that bracket has 12 teams in it instead of 6.
Max
formerly of Ladue, Chicago

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sephirothrr
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Re: 36-team ICT

Post by sephirothrr » Tue Mar 19, 2013 2:39 am

Mewto55555 wrote:Obviously, the chances of the top 6 teams all making the top bracket increase dramatically when that bracket has 12 teams in it instead of 6.
I think that's the point they are using to state that the 12-team playoff bracket is superior.
Ramapriya Rangaraju
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AKKOLADE
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Re: 36-team ICT

Post by AKKOLADE » Tue Apr 09, 2013 6:12 pm

Horned Screamer wrote:So, I think the reason Fred's taking the position he's taking is that, for a high school national, where teams are eliminated after round 5, you run a big risk of having a lot of teams consider leaving, or getting frustrated at playing games that don't matter. When PACE did that in 2011 I correctly predicted it would be a poorly received mess. However, in college, teams should be way more used to playing a lot of games after they are out of contention, at least at the D1 ICT level, so I don't think the problem is the same. I will admit it still feels strange to me to have a college event where 5 rounds is all you have for prelims, because at regular tournaments you usually have at least 7 and sometimes up to like 10 games before the playoffs, but Fred, I don't think that the inherent problems are quite the same for ICT as they were with PACE.
This isn't accurate.

Also, I don't see how Bryce's argument is actually meaningful. "If you take more teams to the playoffs, you get more teams there!"
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