The trigger for me starting a blog was an analysis I came up with on Belichick’s decision to go for it on fourth down. I posted it on someone’s blog and, of course, nothing – ah the plight of brilliance unrecognized! Ok, not really brilliance, but hey, I thought it was pretty clever.
In general, conventional football wisdom says punt the ball. Recently, several economists (e.g., David Romer, Steve Levitt) have looked on sports conventional wisdom and judged it to be too conservative. So Belichick makes a call on fourth-and-2, and the rest is history.
This is the kind of stuff quantoids live for. And one of them, Brian Burke, immediately came to Belichick’s defense, which got great play by ESPN and NYT. Burke runs a website called Advance NFL Stats (www.advancednflstats.com) which has tons of interesting quantoid stuff on football.
QUANTOID MAGIC!
I won’t go through Burke’s whole analysis. But here are a few relevant points:
1) The probability of the Patriots converting fourth down and winning = 60%
2) The probability of the Patriots failing to convert fourth down and winning = 19%
3) The probability of the Patriots punting and winning = 70%
So you add 1) and 2) and you come up with 79% chance of winning by going for it on fourth compared with 70% chance of winning by punting. Now it all makes sense. Quantoids rejoice! Belichick’s not only right, he’s the quantoid patron saint!
I admit, I am a quantoid (how I became one is a story for another day). I’m also a fan of decision theory, which is that branch of quantitative analysis that deals with decision making under conditions of uncertainty. Brian Burke essentially used a decision theoretic framework to make his point.
According to decision theory, the rational choice for a decision maker is the choice that maximizes her or his expected utility. The general form for calculating expected utility is the probability of a good event happening times the consequence, (read payoff) of that good event happening plus the probability of it not happening times the consequence (read payoff) of it not happening.
It terms of the Belichick decision, the payoff for the good event (winning) is 1 while the payoff for the bad event (losing) is 0 such that:
Expected utility of going for it = 0.79*1 + 0.21*0 = 0.79
Expected utility of punting = 0.7*1 + 0.3*0 = 0.7
This way of formulating the decision, not to mention Belichick’s decision itself, has caused a bit of outrage, especially on the part of sports writers who can't stand all this numbers BS. The quantoid response is to say that the outrage is about emotion more than rational assessment. Maybe that's right. But I wanted to see if there was a way to use a decision analytic framework to argue against Belichick’s choice. Here’s what I came up with.
WHY HOW YOU LOSE MATTERS
Suppose there were two types of coaches, the percentage coach and the conventional coach. A percentage coach doesn't care how you win or lose since its all about maximizing your chances of winning.
In contrast, for a conventional coach, it does matter how you lose. A conventional coach wants to win, but prefers to lose conventionally rather than lose unconventionally. That is, for a conventional coach, the payoff values are the following: win = 1; lose conventionally = 0; lose unconventionally = -1.
Why would anyone care how they lose. They care because of the uproar involved. If you play it the conventional way, you may not win, but you won't be blamed for losing by doing something "stupid" or "risky" or "arrogant." So it's not that a conventional coach plays not to win, but, rather, plays so that they can't be blamed. Losing unconventionally is more humiliating then losing conventionally.
Using these payoffs impacts the expected utility calculations in the following way:
Going for it = 0.79*1 + 0.21*-1 = 0.58
Punting = 0.7*1 + 0.2*0 = 0.7
Factoring in the new payoffs of the conventional coaches lowers the expected utility of going for it by 0.21 or the percentage chance of going for it and losing. Furthermore, punting now becomes the optimal choice.
I think most football coaches and most fans are conventional in just this way. Belichick is not conventional, though, of course, this experience may change that. At any rate, at least this model gives a (rational) base for an emotional (outrageous) response.
