Justin Wolfers provides sort of the ultimate defense of Carroll and Bevell, in its total focus on abstractions and ignorance of the specific facts of the situation:
Here’s what I would do: Call a game theorist, someone who specializes in the branch of economics that analyzes strategic interactions. Game theory is the tool used to understand how global superpowers respond to each other, how large companies compete with each other and how grandmasters play chess. It also describes the strategic tussle between Bill Belichick, the coach of the New England Patriots, and Pete Carroll, the coach of the Seattle Seahawks, who found themselves facing difficult decisions in the final seconds of Sunday’s Super Bowl.
The key insight of game theory for an N.F.L. coach is that when you think about what choice you should make, you need to also consider the response from the opposing coach, understanding that he is also thinking strategically. This line of thinking suggests that you should not necessarily call a run play, even if you’re blessed with a great running back. Likewise, it’s not clear that you should definitely pass. Rather, your choice should be somewhat random — a choice that game theorists call a “mixed strategy.”
Game theory points to the possibility that Carroll’s decisive call was actually the result of following the best possible strategy, and that this is a strategy that involves an element of randomness in play-calling. This leads to the intriguing possibility that if that fateful final play were to be run in a dozen parallel universes, with each coach continuing to play the same mixed strategy, the actual plays called would differ, as would their outcomes.
The basic argument here — that optimal strategy isn’t always the optimal strategy because other players will respond to it — is familiar and true enough in some circumstances. If a poker player establishes that she always plays the percentages, she’s actually not likely to be profitable against other good players because nobody will bet into her unless they have the nuts. (Part of what makes poker interesting to many people is that it’s not enough to have the best hand — you need to get other people to pay you for it.)
This is a genuine game theory insight, but it’s also one of limited applicability. The first problem, which Wolfers alludes to but doesn’t consider nearly enough, is that the value of intentionally suboptimal* strategy depends on the time horizon. If you play poker with the same players every week and they know what they’re doing, it’s important to vary your betting strategy. If you’re sitting down at a one-shot game for an hour or two, the value of intentionally bad play is limited to non-existent. It’s generally dumb to waste a hand so you can flip over your 3-8 unsuited and establish your reputation as a wild bluffer when you might not get a hand that allows you to make use of it and will never see the other players again.
The applicability of this to Carroll’s decision should be obvious. The potential long-term advantages gained by using sub-optimal strategy in an iterated game should be given no consideration whatsoever. It’s the last minute of the goddamned Super Bowl. You don’t make a suboptimal tactical choice to slightly increase the chances that a running play will succeed at the goal line in a game next October.
As for the potential short term advantages of a suboptimal choice, the proof is in the pudding and again Wolfers’s argument obviously fails. Remember that that the other player matters. In poker, there’s no point in making intentionally irrational bets against players who aren’t sophisticated enough to follow your betting patterns. Carroll had the opposite problem. His post game comments suggested that he thought that sending out a formation with one tight end and three wideouts would cause Belichick to keep his basic defensive package on the field. The problem is that Belichick — regrettably for the Seahawks — was thinking like a great football coach and not like a freak, and hence was focused on the talent matchups. Given that a running play would put the best running back in the league against a lousy short-yardage defense, and a pass play would involve one decent wideout covered by a first-ballot Hall of Fame corner and two other wideouts who may be working in the insurance industry this time next year (the slightly better of whom would also be covered by an excellent corner), Belichick sent a goal-line defense onto the field, presumably reasoning that if he guarded against the run he could live with man coverage and no safety help against Seattle’s weak receiving unit. It’s possibly true that given Belichick’s response and only one time out a pass play was the best call out of that formation, but of course Carroll and Bevell screwed up by sending a formation that have New England an advantage against the run if they (as one should expect) sent their goalline defense onto the field. There was a game theory advantage here — but it was Belichick’s. His response meant that Bevell was either running into a run defense without enough blockers, or was taking the ball out of the hands of his best player and putting it into the hands of replacement-level players.
And I’ve already written too much on this so I won’t go into elaborate detail again, but the other problem with Wolfers’s analysis you is that you get an advantage from deception only if you try to deceive the opponent. There’s no deceptive strategic advantage being gained when you run a plain-vanilla inside slant out of an obvious passing formation.
Wolfers’s analysis, in other words, is the kind of thing that gives both sabermetrics and pop ecomomics a bad name — abstractions that fail to take into account the specific details of the choices at hand.
*I won’t correct every instance, but as a commenter notes this is obviously a poor choice of words. Obviously, you always want to play an optimal strategy. What I mean is that an apparently poor percentage play can be part of an optimal strategy because predictability gives a strategic advantage to your opponents.