Circles of Death

[Stained Diviner]

This is related to some of the discussions going on in the College Thread.

For those of you who don't know, a circle of death (I think) is a three-way tie after a round robin. If Team A beats Team B, Team B beats Team C, Team C beats Team A, and they all win the rest of their matches, then you have a three-way tie. In other situations, it is possible that everybody will have at least two losses, which could result in a four-way tie, but three-way ties are more common.

Here in Illinois, where Sectionals and the first part of the State Finals are based on four-team round robins, it is not unusual to have three teams at 2-1. In our conference, which has a 12 team round robin, it would be easy for the top three teams to all finish 10-1.

Does anybody have any bright ideas to break these ties? If you replay all three matches, there is a reasonable chance that you'll end up back where you started, so that idea is flawed. Also, especially with our State Tournament, controlling time and the number of extra questions needed are major factors, so we go by points, counting only the points scored against the teams you are tied with. It's not a great solution, but nobody has proposed a great solution.

What would Chicago Open have done if three teams had ended the round robin with one loss? I'm interested in hearing whatever policies are out there.

[AKKOLADE]

This is related to some of the discussions going on in the College Thread.

For those of you who don't know, a circle of death (I think) is a three-way tie after a round robin. If Team A beats Team B, Team B beats Team C, Team C beats Team A, and they all win the rest of their matches, then you have a three-way tie. In other situations, it is possible that everybody will have at least two losses, which could result in a four-way tie, but three-way ties are more common.

Here in Illinois, where Sectionals and the first part of the State Finals are based on four-team round robins, it is not unusual to have three teams at 2-1. In our conference, which has a 12 team round robin, it would be easy for the top three teams to all finish 10-1.

Does anybody have any bright ideas to break these ties? If you replay all three matches, there is a reasonable chance that you'll end up back where you started, so that idea is flawed. Also, especially with our State Tournament, controlling time and the number of extra questions needed are major factors, so we go by points, counting only the points scored against the teams you are tied with. It's not a great solution, but nobody has proposed a great solution.

What would Chicago Open have done if three teams had ended the round robin with one loss? I'm interested in hearing whatever policies are out there.

Suggestion #1 - play more than three games at sectionals. Doubling or even tripling the number of matches played would likely decrease the likelihood of such a tie (and also give you truer results).

[cdcarter]

I've seen Round Robins of half matches, full RRs between the teams, PPB as the tiebreaker, a match between the top two teams in terms of PPB. You can do a lot.

[Quantum Mushroom Billiard Hat]

At the Chicago SCT, there was a five-way tie for first with one packet left. We ended up in some sort of playoff on 1/3 of a packet per round, but I don't remember the exact details.

[cvdwightw]

In general, I think this is how most of the college circuit views things:

1. Within a bracket that has conducted a full round robin, ties should be broken (or advantages given) based on total points per game. This is the most fair way to do things because every team involved in the tie will have played the exact same opponents with the exception of each other. Therefore this gives a small advantage to the team with the head-to-head total points advantage, while not discounting all the other games the teams played. This assumes that there does not exist some outlier packet that is either much too easy or much too hard (compared to the rest of the tournament) and unfairly skews the data for or against one team.

2. Between brackets, or in an incomplete round robin, the most objective determination of team strength is probably PPB, because it is the most opponent-independent statistic measured (in that your opponent cannot "steal" points away from you when you have a bonus).

Once you have seeded your opponents based on your chosen statistic, any of the following will work:

1. Declare top seed the winner
2. Play a full round robin
3. Play a set of playoff games (or mini-games) as follows:
Three teams: Teams 2 and 3 play, winner plays 1 (2 packets needed, or 2 half packets)
Four teams: Teams 1 and 4 play, 2 and 3 play, winners play for championship (2 packets needed, or 2 half packets)
Five teams: Teams 4 and 5 play, winner plays 1, teams 2 and 3 play, winner plays winner of 1 vs. 4/5 (3 packets needed, or 2 half packets and a full packet, or 3 third-packets)
Six teams: Teams 3 and 6 play, winner plays 2, teams 4 and 5 play, winner plays 1, winners of 1 vs. 4/5 and 2 vs. 3/6 play (3 packets needed, or 2 half packets and a full packet, or 3 third-packets)
Seven/eight teams: Your standard 8-team elimination bracket (if 7 teams than team 1 gets a first round bye) requires 3 packets (or equivalent as in 5 and 6 teams)

Essentially, all of these are variants of the 2^n single-elimination bracket. The important thing is to seed the teams correctly.

[marnold]

http://qbwiki.com/tiki-index.php?page=T ... +in+Urbana

[Captain Sinico]

Probably the best thing to do is to use a statistic of merit (maybe bonus conversion, though that's problematic on IHSA) to seed teams into a single-elimination tournament. That gets you a guaranteed result determined only by actual play in the fewest possible rounds.

MaS

[Ben Dillon]

Ed Cohn then suggested that, instead, a single game involving all three teams should be played. In the subsequent argument, the latter option won out. A three-team game was feasible because one of the buzzer sets at the tournament (owned by the University of Chicago) was capable of handling up to four teams.

Despite trailing to "Chicago" A for most of the game, Chicago B rallied on the last ten questions and won by a final score of 375 to 315 for "Chicago" A and 165 for "Michigan".

Although an amusing idea, some people say that this format is unfair to a more generalist team like Michigan, since they were trapped between the Scylla of a humanities-strong/science-weak team like Chicago A, and the Charybdis of a (relatively) humanities-weak/science-strong team like Chicago B.

This is exactly the kind of situation my summer math class is researching.

Suppose Michigan was the best of the three teams and would have beaten either of the other two head-to-head. (Not knowing the prelims of this tourney, perhaps Michigan in fact had beaten the other two earlier.) If Michigan > Chicago A and Michigan > Chicago B, they would be called a Condorcet winner.

Common sense would dictate that in a three-way matchup, Michigan would prevail (harder to predict who would be second, though). However, this doesn't necessarily happen.

From the information given, let's guess that A > M > B on humanities, B > M > A on science, and M > B > A on generalist stuff. M > A in 2/3 of the categories and M > B in 2/3 of the categories, hence they would win either pairwise comparison. But since only the FIRST correct team gets the points, the category distribution easily could force M to third place.

This is analogous to the three-candidate election. Arrow's Theorem says that no voting system exists that can satisfy all fairness criteria.

In other words, I'm going out on a limb here and saying there is not -- and indeed there can never be -- a fair way to resolve a circle of death.

[Susan]

In the actual, non-theoretical tournament that led up to the "Slamma in Urbana", all three of the teams in the final were 1-1 against each other (the prelims were a double round robin), though Michigan led the other teams in bonus conversion and ppg. Not sure if that changes anyone's analysis.

Also, in the DII SCT pentagon of death, what we did (to resolve a five-way tie for first place with one packet) was to divide the 24-question packet into eight-question minipackets. The teams were seeded 1-5 using (I think) bonus conversion (though it might've been PP20TUH). 4 played 5 on questions 1-8; the winner played 1 on questions 9-16 while 2 played 3; finally, the winners of those two games played each other on the final eight questions, and the winner of that game (WUStL A) was declared the winner (basically, single-elim between the top 4 teams with 4 and 5 having a play-in game for the 4 seed).

[Matt Weiner]

IIRC, the Illinois thing happened because everyone was tired, the tournament was kind of sketchy, and people were more interested in just playing the remaining rounds and moving on to the scheduled singles event than in determining the winner with any degree of reliability. Using a three-team game to determine a title of actual importance is a very poor idea for many reasons, not the least of which is that the structure of quizbowl questions is set up for a two-team game and no one really knows what to do with things such as two players frantically pressing the buzzer while the moderator clears the system from their common opponent's neg.

"It is impossible to do anything if there is a three-way tie" is also a poor response, since just about any possible resolution (including the above severely flawed one) would be more acceptable to most teams than saying "everyone's a winner, let's all have some cake" and ending the tournament without a champion, or whatever it is the "it is impossible to do anything" people would actually do if a three-way tie happened.

Seeding teams on PPG (or PPTH if a timed tournament) and playing off 2 v 3, then winner v 1, seems like the best way, since it rewards actual performance by giving team 1 a slight advantage, but still requires team 1 to actually win in head-to-head play, thus recognizing that they were tied and have not really earned the championship just yet. This format is currently recognized in the rules of the NAQT ICT, ACF Nationals, and PACE NSC, and it's a generally fine principle that when those three tournaments all do the same thing, it's probably correct.

[Ben Dillon]

"It is impossible to do anything if there is a three-way tie" is also a poor response, since just about any possible resolution (including the above severely flawed one) would be more acceptable to most teams than saying "everyone's a winner, let's all have some cake" and ending the tournament without a champion, or whatever it is the "it is impossible to do anything" people would actually do if a three-way tie happened.

I wasn't trying to say that nothing SHOULD be done, just that nothing that IS done will be considered "fair" by everyone. Clearly the tie needs to be broken somehow, given that the tournament outcome depends on it. The best a tournament director can hope for is that at least the teams involved in the circle will consider it to be fair :)

Personally, I liked the solution of the teams holding a three-way match. But the math indicates that there easily could be a team that SHOULD be objecting to the idea as unfair.

[AKKOLADE]

Personally, I liked the solution of the teams holding a three-way match. But the math indicates that there easily could be a team that SHOULD be objecting to the idea as unfair.

This is a bad solution, for the reasons stated in the wiki page on the Slamma in Urbana. Change a two-player game to a three occurs in no competition that tries to determine a legitimate champion. It completely changes the strategy of the game and the reliability of the result. In short, don't do this, it's extremely unfair.

[BGSO]

Suppose Michigan was the best of the three teams and would have beaten either of the other two head-to-head. (Not knowing the prelims of this tourney, perhaps Michigan in fact had beaten the other two earlier.) If Michigan > Chicago A and Michigan > Chicago B, they would be called a Condorcet winner.

IF your going to bring voting mechanism's into this then it should be said that the problem with declaring Michigan the Condorcet winner is that in accordance with normal quizbowl procedure they are the best team, and by instigating a three way match you change the game and therefore is it still really quizbowl? Why not just have the three teams play on a 20/0 math computation packet if your gonna change the game you might as well go big.

I am actually in favor of the IHSA method of breaking it, b/c of the Illinois' bounce back bonuses, bonus conversion is not going to work b/c of the bounce back on all parts, and if I remember correctly the system of taking the score when the teams played each other was put in place so that coaches are able to play subs as they don't have to worry about running the score up against a the weaker 0-3 team.

I guess in terms of Illinois the only possible other way to break a circle of death would be to rate a team on maybe TU per match but then again, depending on the questions that could be severely skewed.

David

P.S. I think that made sense

[Sen. Estes Kefauver (D-TN)]

Why is it that in Illinois bonus percentage conversion couldn't be calculated based on bonus points available to a team?

[Stained Diviner]

With rebounds, it takes a little bit of extra work to calculate it. It could be done--PACE NSC figured it out--especially with the small number of matches.

[Irreligion in Bangladesh]

Why is it that in Illinois bonus percentage conversion couldn't be calculated based on bonus points available to a team?

Because that sort of fancy-pants statistic is only readily available to people who use SQBS (or similar), which is at the moment just us on the boards. That's one of the underrated "things that need to change" - not so important, not so urgent, but it's there nonetheless.

[Mechanical Beasts]

With rebounds, it takes a little bit of extra work to calculate it. It could be done--PACE NSC figured it out--especially with the small number of matches.

I think the actual challenge with PACE format is that the bonuses have different values, so you can either just take a percentage of bonus points available or you can then norm that percentage to being out of 30 for other people's reference (if you want). It's no actual additional challenge to compute BC when you have bouncebacks.

[the return of AHAN]

I am actually in favor of the IHSA method of breaking it, b/c of the Illinois' bounce back bonuses, bonus conversion is not going to work b/c of the bounce back on all parts, and if I remember correctly the system of taking the score when the teams played each other was put in place so that coaches are able to play subs as they don't have to worry about running the score up against a the weaker 3-0 team.

Ahhh... but what if your match is in round 1? Under IHSA tie-breakers, you pretty much have to hammer them mercilessly. And don't talk to me about seeds. In our middle school conference tournament this year, my team, seeded #2, lost in round-robin to the #7 seed, and wound up in a tiebreaker round with #7 and #10. Seriously. In 11 years of coaching, I've had numerous instances of my team clobbering someone early in a round-robin, only to see that team not lose again. And in that conference tournament, it was the #10 seed in our 10 team conference that played like a team posessed the rest of the day.

But what is IESA tiebreakers? Don't know that this will thrill Dr. Reinstein, but we play a mini-match of three toss-ups and accompanying bonus questions, which must all be 5 parts each.