I'd like to go back to my previous post about punters in danger of losing their jobs. I'd like to focus this time on one of the papers mentioned by the source. David Romer analyzed why the behavior of National Football league (NFL) teams on fourth down situations depart from the behavior that would maximie their chances of winning in a way that is highly systematic, clear-cut, and statistically significant.
Let me restate his findings clearly and in detail:
1. What is the situation?
The choice on fourth down between kicking (either for a punt or field goal) or going for it and trying for a first down (or better yet, a touchdown).
2. So what would teams do to maximize their chances of winning?
Like any rational agents in an economic system, NFL teams maximize their objective function, which is simply to win the game. Now going for it on fourth down or simply kick the ball would depend on the attractiveness of the distributions of ball possession and field position, but Romer came up with what could be considered objective-maximiing decisions using dynamic programming analysis:
"On the team's own half of the field, going for it is better on average if there is less than 4 yards to go. After midfield, the gain from kicking falls, and so the critical value rises [the critical value is the yardage-treshold where a value lesser than this treshold means that the team should go for it]. It is 6.5 yards at the opponent's 45 and peaks at 9.8 on the opponent's 33. As the team gets into field goal range, the critical value falls rapidly; its lowest point is 4 yards on the 21. Thereafter, the value of kicking changes little while the value of going for it rises. As a result, the critical value rises again. The analysis implies that once a team reaches its opponent's 5, it is always better off on average going for it."
3. So now that we have some scientific metersticks on how "rational" teams would maximize their objectives during fourth downs, what did Romer's empirical findings show on how NFL teams actually decided on these situations:
"Team's actual choices are dramatically more conservative than those recommended by the dunamic-programming analysis. On the 1,604 fourth downs in the sample for which the analysis implies that teams are on average better off kicking, they went for it only 9 times. But on the 1,068 fourth downs for which the analysis implies that teams are on average better off going for it, they kicked 959 times... Over most of the field, teams usually kick even with only 1 yard to go. Teams are slightly more aggressive in the [red] one, but are still far less aggressive than the dynamic programming analysis suggests."
Romer attributes these not-so rational behaviors to two some-what "eccentric" qualities: NFL teams could have more complicated objective functions as merely just winning the game, like through "subtle" channels--their risk aversions could come from the fans, it could come from owners, even coaches or players. The other attricbute of this "irrational" behavior is that these NFL teams are just simply imperfect maximizers. Rather than use mathematical and statistical tools, decision makers rely mostly on experience and intiotion than formal analysis in their quest to maximize the team's chances of winning.
It's a good thing the Missouri Tigers turn out to be less "eccentric" and more "rational" in last night's game against the Bowling Green Falcons. In the fourth quarter, the Tigers were down 20-13 and they find themselves in a situation where the had the ball and they're facing fourth down at the opponent's 39 yard line. Did they go for it? You bet they did, and they converted it successfully. They eventually scored during that drive that tied the game. They scored another one on a run after the Mizzou defense stepped up and stopped the Falcon's next offensive drive.
They maximied their objective.
And they won the game.
I have to thank a good friend of mine, Dottie Heibel, for bringing me to that game--the first live football match of my life (also enjoyed my first tailgate party! Thanks to Dottie's sister Nancy and his husband Ed). And what a game it was. Spirits were way down at half-time with the Tigers trailing behind the Falcons with 13-6 at the score board. But I guess the Tigers were just experiencing the jitters of having to play on home turf for the first time this season. Coach Gary Pinkel might have one hell of a motivational talk with the team as quarterback-sensation Blaine Gabbert and his crew got back in high spirits from the locker room and managed a comeback win. What a game.
Romer's original intention for his study may have been to analyze an eccentric behavior among firms by using NFL teams as an illustration. But I think he showed us that he can become a very good NFL coach. And I wouldn't be surprised if Coach Pinkel managed to read Romer's paper before the game.
Reference:
David Romer (2006) "Do firms maximize? Evidence from professional football." Journal of Political Economy 114(21): 340-365.