Bill Belichick has never been the most popular coach in the NFL, but his Sunday night decision to go for it on 4th and 2 on his own 28 with two minutes remaining in the fourth quarter has even his fans crying foul. I bring up this football decision not because I’m interested in a debate – as a Pats fan, the last five minutes of that game were excruciating – but because I think it illustrates the difficulty of making rational decisions, even when the evidence supports the call.
I’ve blogged about the research of UC Berkeley economist David Romer before, but his basic thesis, based on an exhaustive statistical analysis of 4th down scenarios, is that NFL coaches are irrationally risk-averse. They punt the ball way too frequently and kick far too many field goals.
Belichick was an econ major, and has expressed a familiarity with Romer’s research. Nicholas Beaudrot has persuasively shown how, from this econometric perspective, Belichick’s bizarre decision actually makes perfect sense:
On 4th down, with 2 yards or fewer to go, New England has gained a first down on approximately 66% of its attempts with Tom Brady as quarterback. The Colts had one timeout. If the Patriots gain a first down, the game ends; they can slowly walk to burn a few seconds, then take a knee on each down to end the game. If they don’t gain a first down, the Colts would still need to score a touchdown to win the game. Let’s give the Colts a probability P of getting the six if the ball starts at the 28 yard line. So if the Patriots try for the first, their chance of losing is
(Probability of 4th down failure) x
(Probability of Colts scoring a TD from the 28 Yard line) = 0.33P
The average New England punt nets about 40 yards. Let’s give the Colts a probability Q of scoring a TD on a driving starting at the Indianapolis 32. Then, the chance of the Patriots losing is simply Q. For Belichick’s decision to make sense, we just have to believe that he gave his team a lower chance of losing. In math terms, that would mean 0.33P < Q. Doing some algebra leaves you with P < 3Q. In other words, for the Patriots to have made the right decision, we only have to believe the Colts odds of scoring a TD on a drive starting 28 yards from the end zone are less than three times the odds of the same outcome starting from 68 yards out. The win probability graph for the game suggests that, given 1st-and-10 from New England's 29, the Colts had roughly a 51% chance of winning in the actual situation. We have to believe that their chances under the punt scenario were above 17% for Belichick to have made a bad good decision. Considering the Colts' have scored touchdowns on 30% of their offensive possessions, my guess is that this was a good one.
The reason I bring up this analysis is to demonstrate that even defensible decisions can have wrenching emotional consequences. Belichick’s call might have been statistically correct, but it felt horribly wrong.
And this kind of contradiction isn’t just relevant for football coaches. Just consider health care: the only way we’re ever going to reduce medical costs is to restrict procedures that haven’t passed evidence-based efficacy tests. Maybe that means 40 year old women don’t get mammograms, or that we treat prostrate cancer less aggressively, or that we stop performing spinal fusion surgeries. Although there’s solid evidence to question all of these medical options, such changes provoke intense debate. Why? Because our emotions don’t understand statistics. Because when we have back pain we want an MRI. Because when it’s our father with prostate cancer we want the most aggressive possible treatments. And so on.
The point is that there’s often an indefatigable gap between the rigors of cost-benefit analyses and the emotional hunches that drive our decisions. We say we want to follow the evidence, but then the evidence rubs against a bias like loss aversion, and so we make an exception. We’ll follow the evidence next time.
So here’s my cheeky proposal for lowering the cost of health care: Put Belichick in charge of Medicare. Nobody likes him anyways, and he’s clearly able to follow the math even when it feels like a mistake.
PS. Razib addresses a similar issue from a slightly different angle.
Update: Here’s more evidence that Belichick’s decision was eminently rational, and made them 9 percent more likely to win than punting the ball.