The Theory of Tiebreakers

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Which paper tiebreaker do you prefer?

20
47%
Total points
10
23%
Point differential
2
5%
Bonus conversion
4
9%
Another statistical measure (please specify in comments)
1
2%
I don't care
1
2%
It's all arbitrary and doesn't matter
2
5%
This poll doesn't have an option for what I really feel
3
7%

QuizbowlPostmodernist
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The Theory of Tiebreakers

Let us start out by saying that a full round robin is the ideal tournament format, but is usually unpractical. This leads to other tournament formats, usually involving divisional round-robin plus some sort of playoff system.

Occasionally, a tie in win-loss leads to the need in tiebreaking procedures to decide who receives what playoff slot. If there were but packets enough, and time, the ideal tiebreaker would be an additional playoff game, but that is rarely the case, so we must resort to other methods, usually head-to-head or total points. Each has its strong and weak points.

Proponents of head-to-head like it because they feel that directly playing each other is the best test of which team is better.

Proponents of total points (or point differential or bonus conversion) feel that head-to-head overvalues a single game, when superiority over several games is more important.

There exist other arguments for each system. Head-to-head as the first tiebreaker is easier to implement simply because if every point potentially matters (I've seen a matter of 15 points decide who made the top bracket at a tournament), then every protest should matter and be resolved, even if it has no bearing on the winner of the game. I've known of a few players over the years who gained a reputation protesting much more than warranted, and I would hate to encourage them.

If head-to-head and a points-based tiebreaker were equally fair, head-to-head would be the superior tiebreaker. But if something like point differential or bonus conversion was fairer, you would still have to ask if it was sufficiently more fair to compensate for the difficulties I suggest.

Is it possible to determine which tiebreaker method is more fair? Theoretically, yes, if one has enough tournament data.

Assume that the ideal tiebreaker would be a playoff game. Then comparing head-to-head, point differential, total points, bonus conversion, etc. would be a matter of seeing which possible tiebreaker is the best predictor of future victory. Such data does exist. In tournaments where teams played a multiple round-robin, you can take instances where teams were tied for win-loss after the first round-robin (or multiple round robins) and take the game in the next round-robin as the theoretical tie-breaker game that could have been played. Other tournaments may have teams that tied for win-loss in a preliminary round-robin facing each other in a playoff bracket.

Does enough tournament data exist to make a determination? Is it worth the effort? (Probably not on both counts.)

(I'm choosing to ignore mini-games for now. Half- and full-game tiebreakers become time-consuming if you have to break multi-way ties. It wasn't something that I considered when I sketched out these ideas several years ago in an old notebook.)

Matt Weiner
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Re: The Theory of Tiebreakers

QuizbowlPostmodernist wrote:Let us start out by saying that a full round robin is the ideal tournament format, but is usually unpractical. This leads to other tournament formats, usually involving divisional round-robin plus some sort of playoff system.
Almost every tournament besides nationals is in fact small enough for a round robin and operates in that format, so that should color the discussion. Comparing teams who have played the same opponents versus those who have not are horses of a different color.
Proponents of total points (or point differential or bonus conversion) feel that head-to-head overvalues a single game, when superiority over several games is more important.
This is somewhat vague as to why head to head is unfair, so I'd like to elaborate. Every game can, should, and does matter, and there's absolutely nothing wrong with determining anything you like based on a format that comes down to a single game (for example, breaking an exact tie in the standings for 1st and 2nd with a single-game final, which is the format used by both ACF and NAQT nationals and which I doubt anyone objects to). If someone finishes 9-3 and someone else finishes 8-4, and there's only one playoff spot left for the two of them, then the team that's 8-4 has been knocked out by one game's result, and again, I doubt anyone objects to that.

The problem with head to head is not simply that one particular game determines the team's fate, is that you are counting that particular game twice. The team that would come out of a head-to-head tiebreaker as the winner already received credit for that win in order to get into the tie in the first place; there's no sound reason to single out that game and give them an additional win without also double-counting all their other losses, and thus creating the tie all over again.

Really, it just doesn't make any sense on a rational level. If formats were designed from the ground up and no one was trying to emulate the way the NFL does things, I doubt we would have even considered using head to head.

My ideal paper tiebreaker is total points scored, or, in submission tournaments, total points scored in all games not involving either team's packet (to avoid creating incentive for writing an overly hard packet for your bye round and benefitting from the artificial inflation of your own point total should there be a tie).

By the way, there's just no reason not to make sure you have 4 packets available above the number needed for general use: 2 to break all ties by playing them off, and 2 for a weighted finals series. Any tournament can get by with 13 regular packets, and non-submission events with the right field size can make do with 12. Is producing 16 to 17 total packets for a tournament really such a burden, especially considering that almost every tournament these days has four or more people working on it? If you care about question quality, then you should care about tournament format quality, and if you don't care about question quality, then it shouldn't be a lot of work to crank out more crap. You can even re-use your extras for future events if they aren't needed.
In tournaments where teams played a multiple round-robin, you can take instances where teams were tied for win-loss after the first round-robin (or multiple round robins) and take the game in the next round-robin as the theoretical tie-breaker game that could have been played. Other tournaments may have teams that tied for win-loss in a preliminary round-robin facing each other in a playoff bracket.
But we already know which of the two teams is better against each other. If that's all that mattered then of course head to head would be the tiebreaker to use. However, we are trying to determine who is better against the field. In your experiment, the proper thing to examine is how the teams in question did against the whole playoff bracket.

NatusRoma
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Inferior tiebreakers are the result of lazy question writing and offend my sense of quizbowl aesthetics.

alkrav112
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Assuming a timed format, the quickest effective way to break ties (in my opinion) is points per tossup heard. This takes into account slow moderating while still crediting the team that is able to score well both on tossups and on bonuses. To me, it gives credit to the team that plays the game the best. Feel free to disagree, but I felt that the distinction needed to be made from total points because a team playing in a well-moderated room is going to see more point opportunities than another equally skilled team playing in a poorly-moderated room.

That is all.

pblessman
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I agree with Matt, and NAQT: All Tiebreakers are inherently unfair and should be avoided. Ties should be broken through head--to-head play off matches, or half matches, if a nasty circle of death exists. I've run about a dozen tournaments by now and tiebreakers have never taken more than 30 min and 1 packet (2 half packet rounds).

If tiebrekers HAVE to be implemented, because there are not enough packets (poor foresight, in my mind...) then head-to-head should be only used in reverse, if at all. What I mean by that is that if two teams end up tied for first in an eight-team group with a record of 7-1, the team that lost the head-to-head match has the "better loss." They lost to the other 7-1 team, whereas the second team lost to a team with a worse record. It makes NO sense to penalize the team that lost this match. As it's probably silly to use this reverse head-to-head, but it makes more sense than head-to-head, NEVER using head-to-head is probably the right approach.

QuizbowlPostmodernist
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I don't think that not having enough packets for tiebreaking is necessarily lazy. I see people decide that they are capable of producing a tournment set with x packets and their idea of tournament design is to come up with a format that uses x-1 packets to maximize the number of games played, reserving the last packet as a spare in case of major malfunction. Does anyone see value in giving players more games at the expense of decreasing format fairness slightly?

My suggestion is that an extra head-to-head playoff match is superior for breaking ties, but if forced to resort to paper tiebreakers, the best tiebreaker might be the one that has the best predictive value if you could play that extra match. I remain agnostic on whether or not that is head-to-head, total points, bonus conversion, or some other measure.

I am also still concerned about paper tiebreakers involving points requiring the resolution of every protest over even five points. If forced to use such a paper tiebreaker, does anyone disagree with the notion that every protest that could theoretically impact the tiebreaker being used should be resolved (or at least noted and resolved if it matters)?

trphilli
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My two cents is that resolving protests significantly past the end of the match creates significant difficulties for informing teams about the results and their ability to counter any arguements (see recent events at ICT). But at that same time, resolving every protest regardless of match outcome would quickly become burdensome and slow down the tournament as a whole.

In general, my feeling is that failing to advance behind a team we defeated (evil circle of death in 2001 IL State Finals) is a major bummer, so I would vote for head to head.

NotBhan
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QuizbowlPostmodernist wrote: I am also still concerned about paper tiebreakers involving points requiring the resolution of every protest over even five points. If forced to use such a paper tiebreaker, does anyone disagree with the notion that every protest that could theoretically impact the tiebreaker being used should be resolved (or at least noted and resolved if it matters)?
Yes, I disagree. It would be impractical and cumbersome to resolve every such protest, and the unresolved protests tend to even out. A team could theoretically get screwed as a result, but that's a sufficiently infrequent event as to make the resolution of every protest a waste of time, especially since a tournament might have to resolve 40 protests even if there were no eventual ties to be broken! (I don't doubt that more than one player may post examples of suffering said screwery, but I believe that such events are a small minority of tournament outcomes.)

In general, if a tournament has enough good packets (like at the ICT) as to allow for an extra tiebreaker pack, great. But for invitationals whose question quality can be a bit ... hit-or-miss, I'd rather see those schools spend that extra time (which would otherwise be spent writing pack N+1) improving the quality of the existing N packets and use a (clear and pre-announced) paper tiebreaker.

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Phil Castagna
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Tiebreakers

I don't see why points per bonus shouldn't always be used. My biggest pet peeve with tournaments has been sitting around waiting for circles of death to be broken or ties to be decided. More time is lost here than anywhere else in tournaments that run on needlessly. This also eliminates the slow reader problem. The statistical problems with resolving protests and not having to play your own packet are correctable in the second case and unlikely to make a huge difference in the first can be remedied, but are far superior than burning 10/10 or 20/20 on a 2-team playoff while everyone else waits.

Jerry's point about being ahead of Berkeley after one half is misplaced. There is no "perfect" number of tossups/bonuses to differentiate top teams from each other. That is an isolated vagary of questions that happened to skew in Jerry's favor. By any measure of paper tiebreaker, I am sure that they would be ahead of you as a one-person team, and if they are clearly superior, why play to break the tie at all? If you were still ahead after 20 tossups, should that then be the marker?

I just think bonus conversion controls for as many of the variables as possible for the available tiebreakers.

Phil Castagna

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I think the question of tiebreakers comes down to a question of how many questions one believes is required to distinguish two teams. We have arbitrarily set that up as either 20 tossups and associated bonuses or timed rounds (7-9 minutes per half). Ideally, we should be able to distinguish teams based on an infinite number of tossups/bonuses, but that would really mess up a tournament schedule.

Phil brings up a good point on tournament logistics. We don't have infinite time. Head-to-head is used as a convenience to everyone who attends and runs the tournament. This assumes that the "standard game" has properly distinguished a team over another, no matter how close they were in score. Sure, we should do everything we can to be fair, but are people more dissatisfied if the tiebreaker is "unfair" or if the tournament runs an hour late to play a tiebreaker match or minimatch?

I will admit for most tournaments, I don't think we should fret over head-to-head vs other statistical tiebreakers. Each TD should make that decision and everyone should know ahead of time. If someone here wants to write up an FAQ on tiebreakers, make sure we vette it and it's not skewed one way or another. But I agree: breaking the tie should be both fair and expedient. It is the discretion of the TD to make that call.

That said... isn't a variation of bonus conversion the metric of "points per tossup heard"?
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Re: Tiebreakers

Phil Castagna wrote: Jerry's point about being ahead of Berkeley after one half is misplaced. There is no "perfect" number of tossups/bonuses to differentiate top teams from each other. That is an isolated vagary of questions that happened to skew in Jerry's favor. By any measure of paper tiebreaker, I am sure that they would be ahead of you as a one-person team, and if they are clearly superior, why play to break the tie at all? If you were still ahead after 20 tossups, should that then be the marker?
I was just trying to present a situation in which such a tiebreaker would favor the worse team. I think the main argument (or at least the one that convinced me) against head-to-head is the double counting. I'm not sure which paper statistic would have the best predictive value, but I like total points if the two teams played the same field because it seems to me that the total points picked up against the same opponents should correlate rather well with your overall ranking. That holds for ICT, I guess it would hold for other tournaments too. If the teams came from different brackets and you need to break a tie between them, I'd suggest bonus conversion, since that should be independent of who the other teams were.
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Phil Castagna
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Total Points

My problem with total points is when the concept of a clock is in play, this can get skewed. I applaud NAQT's efforts to get experienced and "professional" moderators at tournament sites, but many of them simply cannot get through 28/28 a round, or 14/14 for a 9-minute interval (myself included - I guess I can't go that long without inhaling - like David Blaine - I know - bad joke). Obviously, all moderators are not created equal, and I feel it would be statistically significant depending on the moderator. In a standard untimed 20/20 tournament, I guess there is no problem.

Matt Weiner
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Re: Total Points

Phil Castagna wrote:My problem with total points is when the concept of a clock is in play, this can get skewed.
Doesn't really matter. NAQT is the only timed event in collegiate quizbowl anymore and they always have enough rounds to play off ties. Obviously if someone decided to run an invitational with clocks next year and didn't play off ties, it would have to be points per tossup heard, not points per game.

compucomp
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Re: The Theory of Tiebreakers

Matt Weiner wrote:
This is somewhat vague as to why head to head is unfair, so I'd like to elaborate. Every game can, should, and does matter, and there's absolutely nothing wrong with determining anything you like based on a format that comes down to a single game (for example, breaking an exact tie in the standings for 1st and 2nd with a single-game final, which is the format used by both ACF and NAQT nationals and which I doubt anyone objects to). If someone finishes 9-3 and someone else finishes 8-4, and there's only one playoff spot left for the two of them, then the team that's 8-4 has been knocked out by one game's result, and again, I doubt anyone objects to that.

The problem with head to head is not simply that one particular game determines the team's fate, is that you are counting that particular game twice. The team that would come out of a head-to-head tiebreaker as the winner already received credit for that win in order to get into the tie in the first place; there's no sound reason to single out that game and give them an additional win without also double-counting all their other losses, and thus creating the tie all over again.

Really, it just doesn't make any sense on a rational level. If formats were designed from the ground up and no one was trying to emulate the way the NFL does things, I doubt we would have even considered using head to head.
I disagree. By using statistical tiebreakers the tournaments shifts the focus away from the main objective of every contest in everything, which is to win. The relevant mantra from sports is that the "only stat that really matters is the number of points you scored versus the number of points your opponent scored". Using H2H as the paper tiebreaker guarantees that this principle is preserved. Using other statistical tiebreakers means that the objective isn't to win, it's to prove that you're a good team by putting up good numbers. These goals are not identical. A 20-15 win is a win, as is a 600-15 one. Of course the 600-15 win looks better, but the 20-15 is still a win, and this fact is usually forgotten when statistical tiebreakers are used, because the 20-15 win will make the team look much worse. Besides, the best team doesn't always win, and using statistical tiebreakers is an attempt to help the best team win, which I think is wrong. I think the team that wins should win, and H2H preserves that.

grapesmoker
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Re: The Theory of Tiebreakers

compucomp wrote: I disagree. By using statistical tiebreakers the tournaments shifts the focus away from the main objective of every contest in everything, which is to win. The relevant mantra from sports is that the "only stat that really matters is the number of points you scored versus the number of points your opponent scored". Using H2H as the paper tiebreaker guarantees that this principle is preserved. Using other statistical tiebreakers means that the objective isn't to win, it's to prove that you're a good team by putting up good numbers. These goals are not identical. A 20-15 win is a win, as is a 600-15 one. Of course the 600-15 win looks better, but the 20-15 is still a win, and this fact is usually forgotten when statistical tiebreakers are used, because the 20-15 win will make the team look much worse. Besides, the best team doesn't always win, and using statistical tiebreakers is an attempt to help the best team win, which I think is wrong. I think the team that wins should win, and H2H preserves that.
I think you're missing the double-counting argument. The point is that if two teams have an equal record but a different H2H (i.e. one team has a loss to the other), then that team had to win the game to tie the record anyway. If you then award them the tiebreaker on the basis of that one game, you've effectively given them twice the credit for winning that game, and that's not fair.

I don't think statistical tiebreakers are an attempt to "help" the best team win. I think a statistical measure is going to tell you who that best team is. Remember, it's a tiebreaker, so at least as far as win-loss is concerned they are equal. That doesn't mean that one team isn't better than the other, though, and a statistical tiebreaker shows you that difference.
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yoda4554
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I don't entirely agree with compucomp, but a tournament using a PPG tiebreaker should keep in mind that it will cause a team to try to play aggressively even while winning handily or playing a weak opponent purely for the purpose of racking up points, and this purpose can be antithetical to the purpose of simply trying to win the game. And in response to Phil, the ability to rack up bonus points is not completely correlated with the ability to take tossups early (cf. VCU and Stanford's stats at ICT), the latter of which is certainly as important as the former in determining a team's performance over the day.

Of course, I dislike the head-to-head for the same reasons as have been mentioned, and I agree with Raj that the production of extra packets is detrimental to the production of good core packets. In short, National tournaments and other high-profile tournaments with enough writing staff should have good extra packets, while other tournaments should probably just straw-poll the attendees.
Last edited by yoda4554 on Tue May 09, 2006 6:58 pm, edited 1 time in total.

compucomp
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Re: The Theory of Tiebreakers

grapesmoker wrote:
compucomp wrote:
I think you're missing the double-counting argument. The point is that if two teams have an equal record but a different H2H (i.e. one team has a loss to the other), then that team had to win the game to tie the record anyway. If you then award them the tiebreaker on the basis of that one game, you've effectively given them twice the credit for winning that game, and that's not fair.

I don't think statistical tiebreakers are an attempt to "help" the best team win. I think a statistical measure is going to tell you who that best team is. Remember, it's a tiebreaker, so at least as far as win-loss is concerned they are equal. That doesn't mean that one team isn't better than the other, though, and a statistical tiebreaker shows you that difference.
I don't see double-counting a win as a problem, and it is essentially irrelevant as to which the "best team" is. The team that wins is the winner, not the "best team", which is why I don't think double counting a win is a problem. The best team DOES NOT necessarily win, and artificial measures should not be taken to try to ensure that it happens.

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yoda4554 wrote:I don't entirely agree with compucomp, but a tournament using a PPG tiebreaker should keep in mind that it will cause a team to try to play aggressively even while winning handily or playing a weak opponent purely for the purpose of racking up points, and this purpose can be antithetical to the purpose of simply trying to win the game.
How is attempting to maximize points scored antithetical to trying to win the game?
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yoda4554 wrote:I don't entirely agree with compucomp, but a tournament using a PPG tiebreaker should keep in mind that it will cause a team to try to play aggressively even while winning handily or playing a weak opponent purely for the purpose of racking up points, and this purpose can be antithetical to the purpose of simply trying to win the game.
I don't think I've ever played a single game where I didn't play aggressively or try to rack up points no matter who I was playing against. My objective is to answer the maximum number of questions and earn the maximum number of points that I can. Sometimes, this results in winning the game even.
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yoda4554
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Is this really a difficult concept? Do none of you play differently based on the margin of the score in the game? I certainly do. Examples in which playing to get the most points is antithetical to trying to win--

A. You have a lead of 85 points with 2 questions left in an mACF format (or, for that matter, any lead of slightly over 40n with n questions left). If you were playing purely to win, you would simply not buzz. If you were playing to accumulate points, you would continue to buzz aggressively and potentially neg and open the game up for your opponent.

B. You have any sizable but not insurmountable lead. If you were playing purely to win, you would buzz only when you were sure of the answer, so as to avoid a streak of negs that would hand questions over to the other team and give them an easy path back into contention. If you were playing to accumulate points, you would continue buzzing aggressively to so as to increase that lead.

C. The inverse of B; you are trailing by a sizable but not insurmountable amount. If you were playing purely to win, you would buzz very aggressively (particularly when against a team that frequently knows the answers to tossups early), as that's about your only chance to get back into the game. If you were playing purely for points, you would not buzz more aggressively, so as to avoid a string of negs and potentially pick up a few tossups

D. You're leading by between 10 and 45-50 points in a timed format with 5 seconds left when the last tossup begins. If you were playing purely to win, you'd neg immediately to kill the clock. If you were playing to accumulate points, you'd overlook the small chance the other team would pick up the tossup in such a short time and sit on your buzzer.

E. You're playing in a timed format and you have a small lead with less than a minute left when you answer a tossup. If you're playing to win, you answer the bonus as slowly as possible, so as to lower the amount of time left when the next tossup starts, hoping that it will go dead when time runs out (which would still lower your PPTH). If you're playing for points, you answer the bonus quickly so as to get more time to answer the next tossup yourself.

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Of course there are scenarios like that which make PPG less than ideal. That's why you should always play off ties. But PPG is definitely better than head to head when it comes down to that.

Again, we can avoid this dilemma by caring about the quality of the tournaments we produce and having sufficient packets available to break ties.

QuizbowlPostmodernist
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Matt Weiner wrote:Again, we can avoid this dilemma by caring about the quality of the tournaments we produce and having sufficient packets available to break ties.
Is this a vote for fewer games played to ensure having packets for tiebreakers vs. more games played but having to resort to paper tiebreakers?

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yoda4554 wrote:Is this really a difficult concept? Do none of you play differently based on the margin of the score in the game? I certainly do. Examples in which playing to get the most points is antithetical to trying to win--

A. You have a lead of 85 points with 2 questions left in an mACF format (or, for that matter, any lead of slightly over 40n with n questions left). If you were playing purely to win, you would simply not buzz. If you were playing to accumulate points, you would continue to buzz aggressively and potentially neg and open the game up for your opponent.

B. You have any sizable but not insurmountable lead. If you were playing purely to win, you would buzz only when you were sure of the answer, so as to avoid a streak of negs that would hand questions over to the other team and give them an easy path back into contention. If you were playing to accumulate points, you would continue buzzing aggressively to so as to increase that lead.

C. The inverse of B; you are trailing by a sizable but not insurmountable amount. If you were playing purely to win, you would buzz very aggressively (particularly when against a team that frequently knows the answers to tossups early), as that's about your only chance to get back into the game. If you were playing purely for points, you would not buzz more aggressively, so as to avoid a string of negs and potentially pick up a few tossups

D. You're leading by between 10 and 45-50 points in a timed format with 5 seconds left when the last tossup begins. If you were playing purely to win, you'd neg immediately to kill the clock. If you were playing to accumulate points, you'd overlook the small chance the other team would pick up the tossup in such a short time and sit on your buzzer.

E. You're playing in a timed format and you have a small lead with less than a minute left when you answer a tossup. If you're playing to win, you answer the bonus as slowly as possible, so as to lower the amount of time left when the next tossup starts, hoping that it will go dead when time runs out (which would still lower your PPTH). If you're playing for points, you answer the bonus quickly so as to get more time to answer the next tossup yourself.
Except that negging hurts your statistics. If you are playing to maximize your score, you will not simply buzz in aggressively, you will attempt to avoid negging as well. So that carefullness will still be there.
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yoda4554
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I suppose I used the term "aggressive" a bit too freely. To put it another way (if anyone cares): I assume that most players have worked out a strategy by which they feel a certain level of aggressiveness will result in the best tossup/neg ratio for them on any given question, and thus (in their opinion) maximize their point totals. My point is that if you're playing solely for points, you will not alter this strategy at all during a game. If you're playing to win, you may change that strategy based on the current score of the game, which will however (assuming your strategy does actually maximize your points) lower your expected score. If you're ahead by a lot, particularly against a relatively weak team (i.e. one you expect not to know the answer for certain before you do), buzzing later may cost you a tossup and some points in relation to the neutral strategy, but lowering your probability of negging to nearly 0 nearly eliminates the chance of giving a string of easy points to your opponents and letting them catch up. Likewise, if you're behind a lot against a relatively strong team (i.e., one you expect to know the answer for certain before you), buzzing early will probably result in lots of negs and fewer points, but the chance of going on a run and catching up, which is very low under the neutral strategy, increases a bit.

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Bruce wrote:Except that negging hurts your statistics. If you are playing to maximize your score, you will not simply buzz in aggressively, you will attempt to avoid negging as well. So that carefullness will still be there.
In the scenario given, you're NOT playing to maximize your score, because stats don't matter to you; you just want to win that single game, no matter if it's by 5 or 500. When points matter, the equation changes: the "carefulness" comes in, but that might hurt your team's chances in that game, however marginally.

grapesmoker
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In practice, I find it incredibly hard to gauge how to play against any moderately strong team. I've frequently negged myself out of questions by playing too aggressively against good teams, only to find that I would have still beaten them to those questions; I've also been beaten frequently as a result of sitting on an answer against a team that I didn't think would get it. Although I don't deny that some players might consciously structure their play depending on the circumstances of a game, I can't seem to be disciplined enough to do it. Obviously, scenarios where my team is up or down by some small amount at the end of the game can be straightforward, but in general, I don't think about strategy very much and just try to answer the most questions that I can.
Jerry Vinokurov
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No Rules Westbrook
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Huh, it's interesting that this post has generated so much response.

I'm all for bonus conversion across the board, and I'll explain why. To me the most important purpose of this game should always be to prove that you or your team knows the most stuff (whatever that stuff is defined as - academic, trash, etc.). Teams who are tied are probably going to have roughly equal number of bonus opportunities, and assuming that the bonuses are well written so as not to be wildly variant in difficulty (or assuming that the easy and hard bonuses even out in the end anyway), they really are the best way to figure out which team has more pure knowledge. As a tiebreaker, they solve almost every problem people have brought up with ppg, head-to head, etc. As has been mentioned, head-to-head is really double-counting...and, I'm sure any experienced player has been to tournaments where that one silly match bit them in the ass because it turned out to be the tiebreaker - and, as Weiner said, maybe another brilliant match that resulted in an upset win turns out not to matter so much. I would almost go so far as to say bonus conversion may be better than actually playing off the tie (of course I think you should have to win a playoff to win a tournament).

Now, the only objection I can see people raising to this is that the game is about "winning" or playing well on tossups and bonuses together, not just about racking up bonus points. I don't know, maybe I'm just not that wild about the whole "game" aspect of qb.

Also, I don't think it's laziness or the ultimate solution to just write more packets to play on. To begin with, the focus should be on making existing packets as quality as possible. Even if you can make 4 more quality packets, there's this business of writing questions that noone may ever play on, which I loathe. Of course, you might have a way to reuse them if they're not played on...still, I don't know about anyone else, but I write packets or questions when they're necessary for the purpose at hand - not just as contingencies with options to use later. Even with multiple people, the prospect of crafting extra packets from scratch is not appealing at all. On top of all this, you have the interest of maximizing the number of good packets people play on - so you design a format where as many teams as possible get to play on as many good packets as possible - maybe with 1 in the bank for finals or whatever. Again, maybe I'm just not much for the whole "game" aspect because my feeling is that a tournament that gives teams as many good packets as it can is fine, without thinking about gameplay tiebreak situations, etc.

pblessman
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One more argument against statistical tiebreakers...

Sorry about being a broken record...

I think ALL statistical tiebreakers are anticlimactic, especially when it comes down to the slimmest of margins. I don't mind my team being eliminated because we lost a match by 5 points, but saying that we won't advance because our bonus conversion was 22.4 points to the other team's 22.6? That just seems silly... I think EVERY tournament should be able to have even just a few questions (and minutes) available to play off the spots. If you plan ahead, this shouldn't be aproblem.

grapesmoker
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Re: One more argument against statistical tiebreakers...

pblessman wrote:Sorry about being a broken record...

I think ALL statistical tiebreakers are anticlimactic, especially when it comes down to the slimmest of margins. I don't mind my team being eliminated because we lost a match by 5 points, but saying that we won't advance because our bonus conversion was 22.4 points to the other team's 22.6? That just seems silly... I think EVERY tournament should be able to have even just a few questions (and minutes) available to play off the spots. If you plan ahead, this shouldn't be aproblem.
I think if you look at the actual bonus conversions that you see in good collegiate tournaments, you won't find 22.4 vs. 22.6. Consistently converting more than 20 points per bonus requires an extremely good team; teams like that don't have to worry about tiebreakers because they typically win all their games anyway. What you generally see is that the PPB exhibits a steady decline as one moves down the table, excepting anomalous situations. It's an empirical argument, but I think it's true; PPB has a very high correlation with overall placement, in my experience.

It's important to remember that tiebreakers by definition happen to teams that are on the margin. So the teams in question aren't going to be superlative, converting 20 PPB, nor are they going to be terrible, converting 5. Over the course of 10 matches, even a difference of 3 PPB is a significant statistical measure of the relative quality of two teams.

edit: On the subject of extra packets, while I wholeheartedly aplaud the effort to make extra packets available for resolving ties, I don't think that's very realistic. It's hard to get packets as it is, and if I have 15 packets, I'd much rather every team get to play 15 rounds (or 14 with one remaining for a finals) than hold back two or three packets for tiebreak purposes. This, of course, reflects my own prejudice of preferring to play as many games as possible; if you favor a shorter tournament over a longer one, then you may prefer holding some packets back.
Jerry Vinokurov
ex-LJHS, ex-Berkeley, ex-Brown, sorta-ex-CMU
code ape, loud voice, general nuissance

jonpin
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Re: One more argument against statistical tiebreakers...

grapesmoker wrote:It's important to remember that tiebreakers by definition happen to teams that are on the margin.
Except if you have 3 teams who are X-1 at the end of the day and need to seed them in some way for the final.

My only definite opinion in this debate is that bonus conversion should NOT be used for two reasons: (a) bonuses are only one of the two skills involved in the game, and (b) speaking as a 3-year veteran Stat Boy, it's far too easy to screw up. To use an example from our most recent academic tournament, GIT XI, after the preliminaries, a team that was involved in a tie for 3rd/4th in their pool had 1190 points in 61 bonuses for 19.51/B. If my finger had slipped a little bit and failed to give someone credit for a tossup in the stats program, they would've been listed as 1200 points in 60 bonuses for 20.00/B, a half-point difference.
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Matt Weiner
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Re: One more argument against statistical tiebreakers...

jonpin wrote:Except if you have 3 teams who are X-1 at the end of the day and need to seed them in some way for the final.
Then you seed them by PPG, play 2 and 3 off on a full packet, and play the winner against 1 on the other packet.

You're right though, sometimes excellent teams will be involved in a tie that can't be broken so easily. Perhaps not at average tournaments but at nationals at least.