End of Half Clock Management

I'm watching a game right now where there's over a minute left in the 2nd quarter. The ball is at midfield and it's 4th and long. Both teams have all three timeouts, but neither team used any. The punting team is standing around letting the seconds tick away, while the receiving team is patiently waiting for the snap.

I think this is irrational. Football is a zero-sum game. Whatever is good for me is equally bad for you, and vice versa. So if stopping the clock right now is not what you want, then it must be what I want. It can't be possible for both teams to benefit from allowing the clock to run down. One or the other team derives an advantage, however small, from stopping the clock.

The only plausible exception I can think of is when the possibility of either team scoring is so remote that the cost of potential for injury on the remaining plays exceeds the value of whatever advantage could be squeezed from trying to pursue a score. In this sense, the game becomes non-zero-sum.

But I think it's more likely that one or both of the teams are excessively pessimistic. The punting team is worried that the receiving team might have enough time to put together a scoring drive, and the receiving team is worried they might turn the ball over or be forced to punt again from deep in its own territory.

This phenomenon might be related to Prospect Theory, which says people weight potential losses more heavily than equivalent gains. In this model, both coaches would be overly gun-shy about stopping the clock because their pessimistic mental calculations tell them both that stopping the clock is bad.

But I'd guess it has more to do with the a large degree of uncertainty surrounding the probabilities. As the Ellsberg Paradox demonstrates, people prefer known risks to unknown uncertainties, even when the more uncertain option has higher expected value. Rather than pursue the overall optimization of their chances winning, coaches seek out the choice with highest minimum plausible chance of winning, within the band of uncertainty. In other words, they are selecting the option with least-bad worst case scenario. In this situation, the highest minimum plausible expected value for both coaches is to allow time to run out. After all, letting time run out is the least uncertain option of all.

In 'normal' situations when time is not a factor, if the punt can be downed inside the 15 yard line, the punting team will probably be the next to score. Outside the 15, it's probably the receiving team who will be the next to score. But in this particular situation near the end of the half, the numbers aren't so clear. The one thing we do know is that the answer isn't none of the above.

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20 Responses to “End of Half Clock Management”

  1. Adam H says:

    Good simple analysis of a frustratingly common phenomenon. It's like both teams (both coaches, rather) believe they are worse than the other team. Because if you had confidence in your team, you'd want to extend the game. The more plays you run, the more control you have over the outcome of the game.

  2. Brian Anderson says:

    It's not like stopping the clock is costless. It could be that, even if there is a small benefit to one team of stopping the clock, that it's not worth the cost of using one of their remaining timeouts.

  3. Jim Glass says:

    But in this particular situation near the end of the half, the numbers aren't so clear

    The numbers aren't clear to the coaches either, so they don't know what is best to do, and they both are risk averse (don't want to hand a score to the other team at the last minute -- and be pilloried for it later) -- so they both play cautiously to run out the clock.

    I don't see what is irrational about it. There is nothing irrational about acting with caution in conditions of uncertainty when possessing insufficient information.

    OTOH, one might criticize them for not knowing more about what is best for their teams in that situation, so the numbers are clearer to them than to anyone else, here or elsewhere -- after all, they are being paid a lot of money to know that.

    And, perhaps, if they do have some idea of that, for being too risk averse to follow through on it. (Although being risk averse isn't necessarily the wrong idea, depending....)

  4. Brian Burke says:

    I should have been more precise. I don't mean to say coaches are making irrational decisions individually. (After all, at least one of them is acting rationally.) I guess I'm really saying the process or system is irrational in an abstract sense that it's impossible for both coaches to truly benefit from the same outcome.

  5. Brian Burke says:

    The discussion at Tango's blog is good. As MGL writes (I'll summarize):

    reasonable != rational

    From a maximin perspective, it might be reasonable to fall back on the choice with the best worst-case, but that doesn't make it rational. Strictly speaking, in a 2-player zero-sum game, the only 'rational' thing to do do is maximize expected value at all times.

  6. Anonymous says:

    I'm not sure I agree with the analysis here. If both teams were choosing between "Team A's offense runs a play" and "Team A's offense doesn't run a play", then it's a zero-sum game. But that's not what they're choosing between. If Team B uses their time outs while Team A has possession, they're not forcing Team A to run a play, they're just getting the opportunity to run a play themselves. So if the risks outweigh the rewards for running an offensive play when there is less than a minute left on the clock (or whatever amount of time) from most places on the field, then it's perfectly rational for both teams to let the clock run down.

  7. Stat Guy says:

    I say that the best way to run out the clock is to play like Chip Kelly's offense plays. Chip Kelly ran out the clock by playing at a high tempo rate, and even getting into FG position. Most teams get to maybe 1 first down if they're lucky, then punt it, and then the other team gets a shot at winning the game. If I were to choose a coach to burn out the clock, it would be Chip Kelly.

  8. Anonymous says:

    I think you hit the nail on the head with the potential of injury. Injuries are common enough in the NFL, and the potential costs of them so enormous, that every additional contested play induces a tangible risk. It seems very rational to me for that risk to outweigh calling a timeout which might bring an imperceptible increase in WP.

  9. Brian Burke says:

    A few thoughts...

    1. Regarding the costlessness of stopping the clock: True, but *it's not just about using a timeout*. If the punting team wanted to maximize time remaining it wouldn't have stood around for 20 sec waiting for the play clock to tick down. If the receiving team wanted to maximize time remaining it would certainly have called a timeout. Using a timeout is always best on defense when you can't control the clock by hurrying, going out of bounds, incomplete passes, spikes. The point was that both teams demonstrated they wanted the clock to run out with the fewest snaps played.

    2. Team A and Team B commenter: I don't get your point. Whether or not you're in a zero-sum game isn't optional. An NFL game is zero-sum whether you want it to be or not (with very rare exceptions noted above).

    3. If the point was that teams don't call timeouts on the vast majority of plays in a game, then I agree. But at this stage of the 1st half, the laws of zero-sum games require that it would have either made sense for the punting team to not fritter and punt as soon as ready or the receiving team to call a timeout.

    4. Regarding injuries: I obviously agree with the consideration, but I wonder about the magnitude of the consideration. If teams were truly that worried about injuries, wouldn't they behave very differently than they do when the game is out of hand, like sending in backups, running very low risk plays, etc?

  10. Anonymous says:

    It could be that the break-even point is at 2.5 timeouts for the team receiving the punt. So the punting team does not want to call a timeout, because then the receiving team would be left with 3 timeouts. And the receiving team does not want to call a timeout, because then it would be left with 2 timeouts. Of course, it is highly hypothetical that this situation is actually the reason, why noone called a timeout.

  11. Phil Birnbaum says:

    Maybe both coaches are maximizing their reputations. That's another aspect that's not zero-sum.

  12. Anonymous says:

    You're right. I wasn't clear with my Team A and Team B discussion. I'll try to be a little more explicit.

    Let's say that the three options, ranked by how good they are for Team A, are:

    1. Team B receives a punt and runs a play (top of the list because the current game state makes the risk of an offensive play greater than the reward)
    2. clock winds down
    3. Team A runs a play (bottom of the list because the current game state makes the risk of an offensive play greater than the reward)

    Then the same three possibilities would be in the opposite order if ranked by how good they are for Team B. This is because, as you said, what's good for one team must be equally bad for the other.

    But each team only has so much in their control. Team A can't force Team B to run a play and vice versa. This means that Team A is choosing between:

    1. Team A runs a play
    2. Team A doesn't run a play and gives Team B the choice of running one (they could do this by punting or by letting the clock run down)

    Since we are in a situation where Team A's worst option is to run an offensive play, it makes sense for them to choose #2. Once they do that, Team B can choose to run a play or not. Team B's worst option was to run an offensive play, so it makes sense for them to choose not to as well.

    So even though it's zero-sum, there are three things that can happen and the first team only has enough control to choose between one of them (they run a play) and the opponent's preference of the other two. And in that situation, it's very reasonable for both to choose to let the clock run down.

  13. Anonymous says:

    I think that one thing this analysis is missing is that using a timeout uses a resource. It could be the case stopping the clock then gives the advantage to whichever team has more timeouts to alter the game length in the future, as they now have more control over the amount of future plays run.

    By this way of thinking, the ideal scenario for both teams could be having the other team calling timeout, leaving more game time where you have more timeouts to change the game length depending on the future results

  14. Tyler Heewai says:

    As an example of this, take an example a scenario where it is 3rd down, with 1:30 left, and both teams have 1 timeout, at some arbitrary yard line out of field goal range (say their own 35). If the defensive team takes a timeout, then the offensive team, if it picks up the first down, has more clock and still has a timeout to drive to field goal range. If it doesn't pick up the first down, the defensive team no longer has a timeout, hampering its ability to drive after a punt.

    If the offense calls timeout and picks up the first down, then it no longer has the timeout to help it reach field goal range. If it fails, it punts, and the other team still has a timeout to aid its drive

  15. Anonymous says:

    So, depending on the propability that the team converts the 3rd down it might be both teams that would benefit from calling a timeout.

  16. Brian Burke says:

    Yes, a timeout is a resource, and its cost diminishes to near zero as the possibilities for their uses dwindle. And there is no value to unused timeouts at the end of the half. Plus, if you want to save time, it is always better to use timeouts on defense when you cannot control the clock otherwise.

    But I'll repeat what I wrote above: this isn't just about using a timeout. It's about both teams simultaneously and deliberately allowing the clock to run down. Timeouts are only a part of that.

    It is impossible, under zero-sum assumptions, for both teams to want the punt to occur later. One team should want the punt to occur as early as possible. The other team should want it to occur as late as possible. In this case, both teams agreed that the punt should take place later rather than sooner.

  17. Zyzzyva says:

    Actually, I can see why neither team would want to call timeout. Three timeouts on defense has much more value than having two timeouts. If the punting team calls timeout, the other team can run a couple "discovery" plays, forcing the defense to burn the rest of their timeouts. Now the offense can make an informed decision whether to continue the drive (with plenty of timeouts of their own) or head to the locker room.

    On the other hand, if the receiving team uses a timeout, the defense still has three and threatens to get the ball back with time still on the clock.

  18. Anonymous says:

    This is a very strange post. Yes, it is a zero sum game but advantage is only gained if one of the teams actually manages to score. What is the probability of the offensive team making it? What are the options for the defensive team - what are their chances of making it? How about some stats on the situation here on Advanced NFL stats? Field position gained isn't carried over into the second half.

  19. Brian Burke says:

    The chances of scoring a FG with 1 min left and 2 timeouts is far from zero.

    What a strange comment...

  20. Ian Simcox says:

    Just picked this one up from your review of 2013 and one of the anons I think has it, but I’ll try to explain how I think it could make sense.

    Say the home team is offense which is facing 4th down and suppose their win probability is a function of the score differential, time remaining in half, and home and away timeouts.

    P(Home Win) = f (score differential, time remaining in half, home timeouts, away timeouts)

    Say that ‘c’ is current time left on the clock and ‘t’ is the amount of time run off the clock if neither team calls a timeout.

    Suppose then that the following cases are true

    p(HW | 0, c - t, 3, 3) = 0.50
    p(HW | 0, c, 3, 3) = 0.49
    p(HW | 0, c, 3, 2) = 0.51
    p(HW | 0, c, 2, 3) = 0.48

    So that is 1) game is a 50/50 proposition if we let time tick down, 2) if the home side chooses to punt now then then they are giving the away side the ball with more time but no timeout advantage, 3) if the away team calls timeout now, the home side has the advantage by virtue of having more timeouts and 4) similar to 3, if the home side calls timeout now, the away team has the advantage of time and having more timeouts.

    Because you cannot force the other team to use a timeout, the away side can only choose between scenarios 1 and 3, while the home side can choose between 1, 2 and 4. If that is the case then both sides are right to let the clock wind down.

    I would be amazed if this was the case though, but it might prove an interesting analysis were it possible.

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