The “delay-the-reckoning heuristic” in pro football?

Paul Campos tells this story of an NFL coach making a bad decision:

Denver kicked a field goal with 1:54 to go to make the score 13-6 Pittsburgh. Denver had one time out remaining. At this point [Denver coach] Payton elected to kick the ball off through the end zone rather than try an onside kick. If you do the math, this meant that the reasonable best case scenario for Denver was that they would stop Pittsburgh from getting a first down after three running plays, and get the ball back after a punt deep in their own territory with about ten seconds left and no time outs. This is in fact what happened. Since the odds of scoring a game-tying TD in this situation are almost zero, the question that naturally arose after the game is why Payton didn’t try an onside kick. . . .

Now the dumbest part of all this is that the downside of a failed onside kick in this situation is trivial. If the kick fails, Pittsburgh gets the ball around the 50 rather than on their own 30 after the kick through the end zone. If Pittsburgh makes a first down in either situation the game is over so that’s irrelevant. But what’s the downside of Pittsburgh punting from the Denver 44 instead of, as they did, from the Pittsburgh 36? This is a 20-yard difference, but, because the end zone serves as a constraint on punters since a punt that goes into the end zone comes out to the 20, the real difference in field position as a practical matter is probably more like ten yards, with the likely outcome being Denver getting the ball on its own 20 rather than its own ten. So Payton passed up a chance to get the ball back at midfield with nearly two minutes and a time out left — a very manageable situation if you need a TD — for a realistic best case scenario that would have required something tantamount to a miracle to result in a TD.

Campos’s framing of the decision, a framing that seems reasonable to me, is that Denver, down by 7 points with 1:54 to go, had two options with their kickoff:

1. Deep kick, then try to keep Pittsburgh from getting a first down, then try to score a touchdown with the one or two plays remaining after the punt recovery.

2. Onside kick, then in the unlikely event that Denver recovers (approximately 6% chance, according to this source), they have more than a minute and a half to try to reach the end zone.

Campos argues that option 2 is better because, even conditional on stopping the first down and getting the ball back, the probability of scoring a touchdown in one or two plays, starting from deep in your own territory, is so much lower than the probability of scoring a touchdown from closer to midfield with a minute and a half to go. If Denver has a 60% chance of stopping Pittsburgh from getting the first down, then this would imply that Campos thinks that Denver would be much less than 1/10th as likely to get the touchdown in one or two plays than with a minute and a half and one time out. I don’t know these probabilities, but I assume a pro football coach would have an assistant who’d be able to access these numbers instantly. As Campos says, “all of this happened immediately after the two minute warning, so he and his staff didn’t have to make snap decision: they had three minutes of beer and ED commercials to figure out this statistical puzzle.”

Assuming that (a) Campos is correct about the probabilities, and (b) that the decision isn’t even close, the question then arises, why did the coach make the wrong decision (which, again, we’re assuming was wrong prospectively, not just retrospectively)?

Campos offers three explanations:

(1) When choosing between a course of action that creates a very slim chance of winning — onside kicks are rarely recovered — and one that creates a much slimmer chance, coaches tend to treat the decision in an irrational way, because what’s the difference between a one in 50 chance of winning and a one in 200 . . . when the baseline is low enough it’s like it doesn’t even matter. Now this is very likely true in this one particular instance, but it’s very much NOT true in the long run, when making many similar decisions over time.

(2) Coaches have a strong and strongly irrational preference for delaying the arrival of certain defeat for as long as possible, even at the cost of greatly reducing the odds of actually winning. . . . [This fits] Payton’s mentality throughout this game, including the decision to kick a field goal while down 13-0 with ten minutes to go, and even more so the decision to punt on fourth and eight from the Denver 33 while down by ten with seven and half minutes to go. Such decisions are both more likely to cause the moment of certain defeat to arrive later than it would arrive otherwise, and seriously suboptimal in terms of increasing the chances of actually winning the game.

(3) A third factor in such decisions is that coaches would prefer defeat while pursuing the conventional course of action to defeat while doing something unconventional, since the latter makes them prone to heavier criticism, even if the criticism is wrong. . . .

Let’s get that third factor out of the way first, as it often comes up in this sort of discussions of coaching decisions. We talked about it a few years ago in the context of fourth-down decisions in the NFL (with followup here). The short answer is yeah, most coaches have a motivation to be conservative, as it looks worse if you do something bold and it fails, but in this case the decision seems so clear that I don’t think the onside kick is particularly controversial.

As for the first factor . . . sure, I guess the point is that when a decision seems unimportant (in this case, raising the probability of tying or winning from near-zero to higher but still very low), then there is less motivation to make the rational decision. But, I don’t really buy this. Think about it the other way. From the coach’s perspective, if the probability of winning is tiny, then the game is already basically lost, so at that point the team is playing with the house’s money. So why not roll the dice? From a psychological standpoint, this seems fundamentally different from if you’re almost certain to win and you make a seemingly-more conservative play even if it slightly increases your probability of losing, because if you’re gonna lose, you don’t want it to happen from what would be considered a weird play.

So then it comes down to Campos’s second argument, which interests me because it seems related to other decision-analysis paradoxes. But, like other ideas in the always-confusing heuristics-and-biases literature, it introduces its own challenges.

The delay-the-reckoning heuristic

I’m gonna label this idea identified by Campos, that “Coaches have a strong and strongly irrational preference for delaying the arrival of certain defeat for as long as possible, even at the cost of greatly reducing the odds of actually winning,” as the delay-the-reckoning heuristic.

The general scenario is that you are at a fork in the decision tree, where one branch will give you decisive, or near-decisive, information right away, while the other branch will take you down further steps until the uncertainty is resolved.

Which fork will you take?

Just speaking in general terms, I feel like it could go either way. Let me break the scenario into two sub-scenarios: potential good news (as in the football example when you’re behind but there’s an outside chance you could get lucky and win) or potential bad news (if you were leading in the football game and there’s an outside chance you could get unlucky and lose). Or you could think of medical examples: you have a serious disease but there’s a potential miracle drug with a small chance of working, or you’re healthy and you’re going to take a blood test that might reveal you have an incurable cancer.

In the potential-good-news scenario, I agree with Campos that it somehow seems more natural (whatever that means) to delay the reckoning. The idea is that you’re pretty sure it’s gonna be bad news, so you’d like to prolong the period of hope for as long as possible. From a pure decision-analysis standpoint, it’s always better to get information sooner, as it can inform later steps in the decision problem, but from an emotional standpoint, I understand the appeal of keeping hope alive for as long as possible.

On the other hand, what about the “Give it to me straight, Doc?” attitude? If you’re in bad shape, maybe you want to just know already and move on. So I’m not sure.

Also, I kind of understand the emotional logic to delaying the reckoning . . . but this is all happening within two minutes of a football game! Is it really worth lowering your win probability just to gain an additional minute and a half of hope? That doesn’t seem quite right. I feel like there’s something more going on here.

What about the potential-bad-news scenario? There I feel like it’s natural to want the information as soon as possible so as to rule out the unlikely bad outcome. Or maybe not. I feel like I’m working in the grand tradition of judgment and decision making research, which is to theorize based on personal impressions of hypothetical scenarios.

I sent the above to Dan Goldstein, an expert in judgment and decision making, and he pointed us to the book, Deliberate Ignorance: Choosing Not to Know, edited by Ralph Hertwig and Christoph Engel. So maybe there’s something there that’s relevant to our discussion.

The delay-the-reckoning heuristic interests me for its own sake and also for its connection to other time-related decision analysis issues such as the base-rate fallacy and its opposite, the slow-to-update problem.