On the Clock, and how to play with it

[Great Bustard]

As usual, I had a great time reading at HSNCT, and one of the major reasons for that is the clock. From my understanding, the primary reason NAQT uses timed rounds at Nationals is to ensure that rounds all stay on a largely equal footing, and that a somewhat slower reader does not hold up the tournament. However, the clock itself introduces all sorts of dimensions of strategy, and from what I saw, the majority of teams did not adjust their game accordingly nearly as well as they should. Interestingly, this also seemed to hold for many of the top teams that I watched during the playoffs on Sunday. So, forthwith, here are my tips on how to play the clock:

Madden's Clock Theory
So, here's a controversial notion, but one that I think has some statistical validity to it. I posit that not only towards the end of the game, but at any point, where a team takes a lead, they should then kill the clock as much as possible on bonuses (and if possible, even by drawing out the extra second at the end of a tossup). For example, if team A answers the first tossup correctly, they should stall on the bonus. Why? Well, statistically speaking, if a team is up, it's going to on average be to their benefit to have fewer tossups for the other team to mount a comeback. This principle becomes relatively clear enough late in the game, but I would hold that it's the percentage play even in the early stages. Of course this would mean less quizbowl overall gets played (and it would put a damper on those moderators who judge their self worth by how many tossups per game they average), but it would help teams win, which is the whole point of a competition.

Exceptions to the above
1. If a team knows they are significantly better than the other team, and has a lead over them, they may wish to delay their initiation of stalling until their lead is at least 100 points or so. To reference the central limit theorem, if say, the game had 1000 tossups, the better team would always win. So the more tossups heard, the greater the likelihood that things even out. Or, to take an example from this past weekend, in the LASA A / LASA B game, with LASA B up by 5 at half, but LASA A getting the first tossup of the second half, if I had been on LASA A on that particular tossup, I would have wanted not to stall, but to get through the bonus as quickly as possible. LASA B's overall chances of winning decrease with each additional tossup heard (on average), so in this case, LASA A probably shouldn't stall until they built a lead of at least 70 points or so.

2. Quizbowl is undoubtedly a game of momentum at some level (if anyone wants an idea for a project for a Stat AP class, calculate the increased chances that a team gets the next tossup correct if they had answered the prior tossup correct. This could be extended to include what happens if the prior question is powered, negged, or the prior bonus is 30ed or 0ed too). If a team has some momentum, they may wish to forget the clock (esp. early in the game) and just keep motoring through if they're in the zone.

3. New teams should focus primarily on the questions; the clock is less of an issue. But still, it's not that complicated to figure out good clock management. So perhaps some new teams should avoid trying to get too clock obsessed.

4. If a team is soundly beating another, they should probably refrain from stalling late in the match, since this is basically just gamesmanship. Still, if there's a .01% chance that it might matter, a team should still go ahead and use this tactic.

The corollary to this of course is that teams who are trailing should try and answer bonuses as quickly as possible (unless, perhaps, it's the reverse of situation #1 above - namely, an underdog is trailing by just a bit, and they're better off trying to take the number of tossups down).

Some other clock thoughts:
-Teams should practice timed rounds before HSNCT. I'm sure some do; I'm sure many don't.
-Tournaments meant to be tuneups for HSNCT should strongly consider using timed rounds. If you don't have enough good moderators to do this, at least perhaps do it for however many playoff tiers you can.
-Aside from not obsessing over the # of questions they get through in a round (note: if you're reading for teams in the middle part of the draw, {i.e. those who are not powering most questions, nor those who are missing many tossups, and thereby not doing the bonuses} and are finishing the packet in most games, you are definitely reading too fast), moderators should also avoid the temptation to speed up/slow down their reading towards the end of a match since this is certain to benefit one team over another.
-Teams who need to make up time should get away from the reflex to hear the entire question if the first team has negged. If you need time, and you know the answer, then go for it - there's no point in giving up 5-10 seconds per question if you're 100% sure of what the answer is.
-In timed rounds, I personally never give score checks unless teams call time out and ask for it (this is their responsibility, not yours as a reader), and I try and cut down as much as possible on any extraneous words. For example, don't say "your answer please" when "answer" is fine on bonuses. Likewise, try and wherever possible be efficient about turning pages. The best time to turn pages is when teams are conferring on bonuses.
-Similarly, I really don't understand why NAQT (and most other set authors) doesn't just list the bonus under the question. This would avoid the need to separate tossups and bonuses, and make it easier for moderators. Is there a reason for this that's not coming to me?
-If teams are in a position where stalling is to their advantage, they should say as full an answer as possible. Don't say "USA" - (articulation time about .8 seconds) when "The United States of America" could eat up another 1.5 seconds or so. Don't get too cute here (e.g. "Why of course this would be the United States of America") since any moderator should cut you off if you're going over the limits, but this could be another way to clock manage.
-I think there's a temptation for moderators to allow more than 5 seconds on math bonuses. This wasn't as much of an issue at HSNCT as at MSNCT, but I still think that if math comp is going to be in bonuses, then more questions should be 10 seconds. Still, if 5 seconds is the rule, moderators need to stick with that. I saw many moderators going over this at times.
-Time outs should be called with timing in mind. For students focused on getting questions right, it might be better for the coach to be the one primarily focusing on the score, and what the appropriate stalling/clock strategy should be during the endgame portion.

Those are all my thoughts for now, but I'm certainly interested to hear what everyone thinks of these things, especially my theory about stalling early in the game if you're in the lead. Congrats to NAQT for a great event and to LASA for winning the triple crown of Nationals this year!

[Frater Taciturnus]

Bonuses aren't listed under the tossup because bonuses are read sequentially, rather than tied to a specific tossup.

[aescandell]

There are situations when a team is behind and it's in their interest to kill the clock. For example, let's say you just answered a tossup to close the gap to 35ish with around one minute to go. Assuming you know any portion of the bonus at all it's in your interest to kill. Hearing two more tossups in that situation can actually significantly dampen your chance to win. . . you only want to hear one more. Similarly if you are behind in a close game to a team that you know is superior to you, it's probably in your interest to limit the total number of tossups heard.

That being said I don't train my students in these situations or have them use any special clock strategies. In my experience, the best teams play at a quick, but still careful, pace almost all of the time. Moreover, changing your pace while playing quizbowl is much more challenging than its made out to be. It's very distracting and puts your mind on something other than clues and answers. So I specifically tell students to ignore the clock and play at their normal (fast) pace focusing on one question at a time. If there's a very specific endgame situation that requires discussion, that's what my timeout is for. I imagine many coaches share the same philosophy.

[fett0001]

Bonuses are separated because they are not linked to the tossup, currently.

[vinteuil]

It's always possible for the other team to make a comeback, so, as many good players have learned, stalling can just as easily hurt your your team.

[Cheynem]

Just as a note, for timed rounds, this is the strategy that I apply as a moderator:

1. Maintain the same pace even if it is at the end of games and a team is trying to slow down or speed up. Do not allow a team's strategy to dictate the pace of the game. Obviously, if they're directing answers at you hurriedly, take them and move on.

2. When I read, I say usually some variant of "answer?" when seeking an answer (sometime's it's "anything?" or "answer please?"). I typically "neg" or "neg five" on tossups, but sometimes "no." On bonuses, I typically say "30" or "20" or whatever to indicate quickly what a team has scored and to help out my scorekeeper.

3. I never give score checks except at the half or if a team has called timeout. I had to specifically tell a team I cannot give a score check at one point.

4. Stop the clock if an answer requires some deliberation or if you are having trouble turning the pages on sheets.

I disagree with Dave's strategy because I think you should never do it too early as it kills momentum and if you have a small enough lead, you could very well want another question at the end as well. I agree with Dave that in a timed format, you should play more deliberately and within reason "stall" on bonuses at the very end of games (I find the better teams simply "stall" by waiting until the end of the question and not interrupting rather than using up all five seconds in silence, but some do as well). For example, if you are nursing a 20 point lead and get a tossup, and there is only 20 seconds to go, obviously don't rush through the bonus. Ways to stall also can include if a tossup is going dead, buzzing in with a guess to restart the time.

For the record, I think a clock is necessary at very large tournaments, but the clock-gamery is something that I don't enjoy as a player or reader. It's smart play and I'm not denouncing anyone for it, but it's very unsatisfying when teams win by basically running out the clock rather than getting to have a tossup 20 for all the marbles.

[jonah]

It's always possible for the other team to make a comeback, so, as many good players have learned, stalling can just as easily hurt your your team.

It's not always possible for the losing team to make a comeback. The point of stalling is to make there be not enough time to read the number of questions that a comeback would require.

[vinteuil]

It's always possible for the other team to make a comeback, so, as many good players have learned, stalling can just as easily hurt your your team.

It's not always possible for the losing team to make a comeback. The point of stalling is to make there be not enough time to read the number of questions that a comeback would require.

I agree with this, but David's strategy of stalling no matter when doesn't seem to reflect this kind of thinking.

[tiwonge]

\2. When I read, I say usually some variant of "answer?" when seeking an answer (sometime's it's "anything?" or "answer please?"). I typically "neg" or "neg five" on tossups, but sometimes "no." On bonuses, I typically say "30" or "20" or whatever to indicate quickly what a team has scored and to help out my scorekeeper.

This actually caused confusion for me in one round. The third part of a question asked for a certain highway, and the team answered US 1 and got it correct. Since it was the last part of the bonus, I said "20," indicating that they got 20 points on the answer, but both of the teams thought I was saying that was the correct answer. (My scorekeeper understood me correctly, so the official score was different than their scores.) In the future, if the third part of an answer is a number, I'm going to try to be more clear on the difference between the answer and the points. "Yes. 20 points." would have been better than just "20" in that one case (and possibly on math computation questions). Lesson learned.

[Charles Martel]

David's point is that even though stalling could hurt your team if you have a lead, it's more likely to hurt the opposing team, and thus increase your chance of winning.

[tiwonge]

Bonuses are separated because they are not linked to the tossup, currently.

Right. I think what Dave is saying is that since the bonuses are essentially arbitrary, there's no reason why they can't be listed under each tossup (not tied to the tossup, and still randomly ordered) instead of at the end. I guess if it's done that way, it's possible that the distribution of the bonuses might get messed up.

It's possible, for example, that all science bonuses are listed with tossups that don't get converted, so no science bonuses are heard, whereas if they're read sequentially, you have a little more control over the distribution of the bonuses. I guess this is the reason why bonuses are done the way they are.

[Great Bustard]

David's point is that even though stalling could hurt your team if you have a lead, it's more likely to hurt the opposing team, and thus increase your chance of winning.

Exactly. It's all about playing the averages.

As for bonuses, I see the point about the distribution. I doubt there are that many instances where this would really come into play, but that makes sense as to why it's done the way it is.

[Cody]

Bonuses not being under tossups is not a problem and doing such would cause all sorts of problems with dead tossups that one wouldn't be able to predict.

Instead, the moderator should be separating the tossup and bonus sections of a packet and reading them separately. There should be no "flipping pages" involved.

As to "always stalling if up", it's totally wrong. The time to stall is if your team is worse than the other team - reducing the number of tossups heard means you have a greater chance of the packet falling in your favor / something wacky happening and winning. You generally want to stall when you're worse even when you're down. If you're looking at two top-tier teams (say, UVA and Yale for an example), each one stalling when up is insane: they're very evenly matched, so they could very well screw themselves pretty hard by stalling when up (one could say this happened to Yale in the ICT final this year, in fact - the protest probably would've had to be ruled upon if there'd been enough time for the final tossup [music] to be read). Certainly, stalling when up can help a lot - but not if you're doing it the whole game. Playing to averages sounds good, but there aren't 162 games in the tournament here - much less that many where it truly matters. Stalling is only going to hurt your team if you're applying it blindly.

[jonpin]

To further Cody's point, this strategy assumes the only variable is to maximize the probability of winning the present game. Since NAQT seeds their playoffs by wins and then PPTH, this is not at all the only variable worth considering on HSNCT Saturday. If I've got a playoff caliber team and they're up against LASA, mathematically it's in my interest to make the game as few tossups as possible so that the thrashing I take will not hurt my team's PPTH as much.

[Great Bustard]

To further Cody's point, this strategy assumes the only variable is to maximize the probability of winning the present game. Since NAQT seeds their playoffs by wins and then PPTH, this is not at all the only variable worth considering on HSNCT Saturday. If I've got a playoff caliber team and they're up against LASA, mathematically it's in my interest to make the game as few tossups as possible so that the thrashing I take will not hurt my team's PPTH as much.

Okay, that's a valid point, I wasn't aware of that. Though wouldn't PPB be a better stat to seed teams off of, since PPTH is so dependent on how the card system plays out? As for Cody's point, yes, I agree that teams who are the underdog should stall to keep the game within reach (I mentioned this in the original post, even). But if you're talking about two teams who are otherwise evenly matched, it does seem to hold. If two teams are otherwise evenly matched (and after awhile, most teams who play in HSNCT matches are quite close to each other in difficulty), then even a short lead (say 50 points) is worth defending through stalling. It provides a minor advantage early in the game, to be sure, but why throw away even a small edge?

[Cody]

But if you're talking about two teams who are otherwise evenly matched, it does seem to hold. If two teams are otherwise evenly matched (and after awhile, most teams who play in HSNCT matches are quite close to each other in difficulty), then even a short lead (say 50 points) is worth defending through stalling. It provides a minor advantage early in the game, to be sure, but why throw away even a small edge?

Because "evenly matched" doesn't mean equal chance of getting every question. It's not a minor advantage at all because it has the potential to screw you, hard - consider if a run of questions goes to Team B (formerly down 50) and Team A (formerly up 50) now finds itself down by 70 [say, 2/1/0 20,30,30 on three questions] - they've hurt their chance of winning (according to your analysis, anyway) by stalling. I'm sure you can find some cases where a team who was up stalled and won - at the end of a game. But stalling all game when you don't know how the questions will turn out is a recipe for disaster. How many first-half runs have you seen that dissolved in the second-half? Or second-half runs? A team applying this advice would be a huge blunder because the advantages you claim exist, do not.

[Great Bustard]

But if you're talking about two teams who are otherwise evenly matched, it does seem to hold. If two teams are otherwise evenly matched (and after awhile, most teams who play in HSNCT matches are quite close to each other in difficulty), then even a short lead (say 50 points) is worth defending through stalling. It provides a minor advantage early in the game, to be sure, but why throw away even a small edge?

Because "evenly matched" doesn't mean equal chance of getting every question. It's not a minor advantage at all because it has the potential to screw you, hard - consider if a run of questions goes to Team B (formerly down 50) and Team A (formerly up 50) now finds itself down by 70 [say, 2/1/0 20,30,30 on three questions] - they've hurt their chance of winning (according to your analysis, anyway) by stalling. I'm sure you can find some cases where a team who was up stalled and won - at the end of a game. But stalling all game when you don't know how the questions will turn out is a recipe for disaster. How many first-half runs have you seen that dissolved in the second-half? Or second-half runs? A team applying this advice would be a huge blunder because the advantages you claim exist, do not.

You're missing the point. It's all about averages here. Your hypothetical scenario could certainly occur, and you're right - in that instance, it would hurt. But on average the strategy would benefit the team using it, as long as the caveats that I listed in the original post are taken into account. This is not complicated, and yes, the advantages on average do exist. Citing one example of many where it might not work is not a valid argument if the strategy gives an edge, even, say 51% of the time. Sure, 49% of the time it would hurt. But, still, you're more likely to help yourself than not. And of course, once the lead increases, and the game gets closer to the end, the benefits become readily apparent. My point is simply that this strategy can be extended much farther back towards the start of the game than people currently use it.

[Cody]

You're missing the point. It's all about averages here. Your hypothetical scenario could certainly occur, and you're right - in that instance, it would hurt. But on average the strategy would benefit the team using it, as long as the caveats that I listed in the original post are taken into account. This is not complicated, and yes, the advantages on average do exist. Citing one example of many where it might not work is not a valid argument if the strategy gives an edge, even, say 51% of the time. Sure, 49% of the time it would hurt. But, still, you're more likely to help yourself than not. And of course, once the lead increases, and the game gets closer to the end, the benefits become readily apparent. My point is simply that this strategy can be extended much farther back towards the start of the game than people currently use it.

No, you're missing the point. Let me quote myself:

Playing to averages sounds good, but there aren't 162 games in the tournament here - much less that many where it truly matters. Stalling is only going to hurt your team if you're applying it blindly.

If it gives you an edge 51% of the time – it's not going to help you win a game.

You also give me no reason to buy that this actually gives a team an advantage. You're extrapolating from unsupported suppositions and it makes very little sense to me, as someone who has played many tournaments - including timed.There are times to stall and that time is not "whenever you happen to be up".

[jonpin]

One additional point of order that can complicate the matter is protests. First, an NSC example, then an HSNCT example.

I gave my team two pieces of advice in final preparations for NSC. Since it has bouncebacks, there are very specific times when answering a tossup can be bad. Advice #1 was that they had explicit permission to spike (or maybe a better analogy is "take a knee") tossup 20 (or 23, in OT) if they led by exactly 10 or 20 and the other team had already negged. Advice #2 was that if there was ANYTHING in the match that their opponents might conceivably protest, then that permission was revoked.

The analog in HSNCT is the case where you've just converted a tossup with, say, 30 seconds to go. You can generally take your time on the bonus and run out the clock, or if you answer each part in 1-2 seconds, there will be enough time for another cycle (Thankfully, the instantly-game-ending buzzer which led to some amusing but bad moments in quiz bowl history is now gone). However, if there was something your opponents are going to protest, you may regret running out the clock.

[Great Bustard]

I think the words that are needed here are ceteris parabus - everything else being equal. Now, fine, go ahead and make the argument that it never is, and that every situation must be judged uniquely on its merits as well it should. My theory is of the sort of an economic model that makes sense to illuminate a concept more than provide an all-pervasive theory of every contingency. But still, there are certainly many situations where it's in one team's statistical advantage to stall based on if they are in the lead. In fact, if we could do a perfect analysis of all the variables, it would always work out that one team would be better off playing more tossups, and one team playing fewer at any given point in any given match. Trying to calculate that to the nth degree is obviously impossible during a game. But it can be estimated, and doing so, even if imprecise, can give a team an advantage. Perhaps I should have worded my original statement differently (though I thought couching it with the caveats would make this clear enough), but the fact that some team should probably be stalling, and some team should be trying to speed up a game at any given time seems blindingly obvious to me (even if the estimation process is imprecise, and the advantage it confers is more readily apparent and increases later in the game / once a team gets a big lead). If I have two options available (stall or not stall), and stalling confers on average a .00001 % greater likelihood of winning, and not stalling by definition confers on average a .00001% greater likelihood of losing, I think I'll stall. Not that I anticipate coaching a team at HSNCT any time soon, if ever.

[hokie168]

Madden's Clock Theory
So, here's a controversial notion, but one that I think has some statistical validity to it. I posit that not only towards the end of the game, but at any point, where a team takes a lead, they should then kill the clock as much as possible on bonuses (and if possible, even by drawing out the extra second at the end of a tossup). For example, if team A answers the first tossup correctly, they should stall on the bonus. Why? Well, statistically speaking, if a team is up, it's going to on average be to their benefit to have fewer tossups for the other team to mount a comeback. This principle becomes relatively clear enough late in the game, but I would hold that it's the percentage play even in the early stages.

This is incorrect. The better team will generally want to play quickly all the time, except in specific and comparatively uncommon cases near the end of the game.

Suppose Team A is slightly better than Team B. Let's assume that somehow, we have enough data that the Law of Large Numbers kicks in and we know the following:

Team A: 55% chance of getting the TU and averages 20 PPB. Avg 16.5 PPTH.
Team B: 45% chance of getting the TU and averages 18 PPB. Avg 12.6 PPTH.

We can assume for purposes of simplification that there are no powers or negs, and that every tossup is answered by one of the two teams.

Now suppose that Team A gets the TU #1 but zeroes the bonus, so that they are up 10-0. According to your theory, Team A should always stall in this situation. Let's see what happens with sample games for Stall (21 TU total) and Rush (24 TU total). Note that since we are calculating Expected Value(EV), we can have scores that are not multiples of 5. Banging on Excel for 5 minutes gives:

Game Stall's expected final score: Team A 340, Team B 252. Team A's stddev is 66.7 points.
Game Rush's expected final score: Team A 389.5, Team B 289.8. Team A's stddev is 71.6 points.

We need to find the win probabilities of each team in Game Stall and Game Rush. Again, for quick simplification, let's say that for each point Team A falls below its average, that same amount is added to Team B's average- essentially, that what Team A missed was because Team B got it. This is even tilting things in Team B's favor, as we've now assumed that they'd be converting those bonuses at 20 PPB.

Theoretical breakeven for Game Stall is 296 pts, or -0.659 stddev for Team A. Team A wins 74.5% of the time.
Theoretical breakeven for Game Rush is 339.65 pts, or -0.696 stddev for Team A. Team A wins 75.7% of the time.

It is to Team A's advantage, up 10-0 after TU #1, to play quickly. If Team A were even better- on tossups, bonuses, or both- this win % difference will widen.

There is absolutely no reason for the better team to stall in the 1st half, unless there is some non-game external event affecting the outcome. There probably isn't any reason for the better team to stall until the clock gets below 4 minutes; more realistically, they probably shouldn't even bother with considering it until under 2.5 minutes. The better team will generally want as many questions as possible so that their edge compounds. The expected gap in points will go up faster than Team A's stddev, so Team A is reducing the game outcome variance by getting more tossups in.

-Time outs should be called with timing in mind. For students focused on getting questions right, it might be better for the coach to be the one primarily focusing on the score, and what the appropriate stalling/clock strategy should be during the endgame portion.

Keeping track of the score and deciding whether to stall is the coach's job, not the students. There's no reason to distract the students. If they tried to figure out stalling tactics while playing, it seems reasonable to expect that they'll occasionally screw up questions that they would have pulled without the distraction.

[Great Bustard]

Again, in the caveats to the theory I was putting forward, I already addressed the issue of a better team wanting to hear more tossups and the other team fewer for precisely the reasons you outline. That said, often it's hard to know who the better team is (I suppose a coach could consult the Morlan rankings or whatnot, but the power matching of HSNCT means that many games are between largely comparable teams) but it's often easy enough to know who's up. I agree that if a decidedly and known better team only has a lead of 10 points after tossup 1, they shouldn't stall (but by extension - if the other team got tossup 2, then they should, right?!)
I think that everyone who's chiming into this discussion understands basic statistics and the principles at play. My original theory, as mentioned, is really only true in a vacuum; once other variables (lead size, tossup number, time left, momentum, strength of teams, even which topics have come up) come into play, then everything else needs to be taken into account. But looked at another way, the point that I'm really trying to make here is not that necessarily it should always be the leading team who stalls, but rather that statistically, it's going to be to one team's benefit to hear more tossups, and to another team's benefit to hear fewer at any point in the game. And that means that somebody, at least, should probably be stalling more often than not. Agreed that teams should primarily focus on the questions, but for high schoolers able to do NAQT math in five seconds, reasonable estimations of when stalling makes sense should not be beyond their capacity in most instances. Or, put another way, from what I saw, one of the two teams in the room was only stalling about 10% of the time, tops, in all the games I watched last weekend. Maybe expecting one of the two teams in a room to be stalling 100%, or even 80% of the time is expecting a bit much, but I think with a little situational awareness, someone should be stalling at least 50% of the time.

[theMoMA]

There is unquestionably some strategic value in stalling, even early in the game, for an underdog team. But as noted, any team thinking about stalling must weigh the potential benefit of fewer questions heard against the potential for being thrown off their game (because of a shift in momentum, the potential for saying wrong answers while trying to kill time, the general discomfort of being off your normal game, etc.). In most cases, I think that the negative gameplay effects of stalling early on would outweigh the potential value of hearing one or two fewer tossup/bonus cycles for the underdog team. In short, I say you should just play your game the way it feels comfortable to you until late in the game when strategic considerations become more immediate.

[Great Bustard]

There is unquestionably some strategic value in stalling, even early in the game, for an underdog team. But as noted, any team thinking about stalling must weigh the potential benefit of fewer questions heard against the potential for being thrown off their game (because of a shift in momentum, the potential for saying wrong answers while trying to kill time, the general discomfort of being off your normal game, etc.). In most cases, I think that the negative gameplay effects of stalling early on would outweigh the potential value of hearing one or two fewer tossup/bonus cycles for the underdog team. In short, I say you should just play your game the way it feels comfortable to you until late in the game when strategic considerations become more immediate.

This may very well be true right now, but if teams practiced more on the clock in the lead up to the event, it wouldn't necessarily be too hard for smart students to figure it out. Or at least to keep a few guidelines in play (e.g. if you're playing a team you're largely evenly matched with, and you're up by at least 100 points, then stall, even if it's only on, say bonus #4) Interestingly, as an aside, professional sports has all sorts of sabremetricians figuring out every little advantage here and there. It's way beyond my capacity, but I wonder if someone could write an algorithm that would be able to take into account all the variables in a game and then spit out the optimal scenario? Computer Science / Statistics AP project anyone?

[jonpin]

Interestingly, as an aside, professional sports has all sorts of sabremetricians figuring out every little advantage here and there.

And yet there are more than a handful of occasions each NFL season when I am yelling at my TV because the coaches can't figure out clock management.

My policy on the matter is basically, "If you have a significant but not insurmountable lead in the second half (or you can run out the first half), start delaying. If you are in the opposite situation, start rushing."

[Cody]

Again, in the caveats to the theory I was putting forward, I already addressed the issue of a better team wanting to hear more tossups and the other team fewer for precisely the reasons you outline. That said, often it's hard to know who the better team is (I suppose a coach could consult the Morlan rankings or whatnot, but the power matching of HSNCT means that many games are between largely comparable teams) but it's often easy enough to know who's up. I agree that if a decidedly and known better team only has a lead of 10 points after tossup 1, they shouldn't stall (but by extension - if the other team got tossup 2, then they should, right?!)

Okay, but 55% vs 45% is not "decidedly better". What you seem to be missing is that, sure, we agree it can be beneficial to stall or play quicker throughout the game (although let's be honest - it's mostly only towards the end that it matters), but such situations (in the first half of the game) have very little to do with whether or not you are up or up some # of points. Only at the end of the game does that consideration come into play. What should be considered is the relative level of talent - something that is hard to assess, especially on NAQT questions.

I think that everyone who's chiming into this discussion understands basic statistics and the principles at play. My original theory, as mentioned, is really only true in a vacuum; once other variables (lead size, tossup number, time left, momentum, strength of teams, even which topics have come up) come into play, then everything else needs to be taken into account.

I can think of at least one person in this discussion who does not seem to understand such. Your theory is not true in a vacuum, as Dennis has literally just shown you.

And that means that somebody, at least, should probably be stalling more often than not. Agreed that teams should primarily focus on the questions, but for high schoolers able to do NAQT math in five seconds, reasonable estimations of when stalling makes sense should not be beyond their capacity in most instances. Or, put another way, from what I saw, one of the two teams in the room was only stalling about 10% of the time, tops, in all the games I watched last weekend. Maybe expecting one of the two teams in a room to be stalling 100%, or even 80% of the time is expecting a bit much, but I think with a little situational awareness, someone should be stalling at least 50% of the time.

Well, no, someone should probably not be stalling more often than not. They should be stalling less often than not (much less). Stalling 50% of the time doesn't make any sense. (sidenote on the bolded statement: have you seen the conversion rates on comp. math?!). Also, this is not what you said in your original post! You are completely moving your target.

Interestingly, as an aside, professional sports has all sorts of sabremetricians figuring out every little advantage here and there. It's way beyond my capacity, but I wonder if someone could write an algorithm that would be able to take into account all the variables in a game and then spit out the optimal scenario? Computer Science / Statistics AP project anyone?

Professional sports are very different from quizbowl, though. For one thing, we do not even have the stats to do this. For two, what is there to adjust in quizbowl? How late you're buzzing? Sure, but the overriding factor in quizbowl (well, non-NAQT tournaments) is whether you know more. Spending your time learning more things is going to pay off 100x more than focusing on some optimal strategy that doesn't even exist.

[Sen. Estes Kefauver (D-TN)]

Let's all make up numbers and say things.