Economics in Football
Here are excerpts from ESPN’s story about a paper written by David Romer, an Economics professor at Cal-Berkely, who analyzed fourth-down situations in football to determine the optimal game-time decisions. [Read the full text of the paper HERE]
Ei Di(gt) Vi = Pgt + Bgt Ei Di(gt+1) Vi - egt
This, in the unimpeachable terms of the Bellman Equation (CR note: Wikipedia article), is the definitive proof that NFL head coaches should go for it more on fourth down. Really, no kidding.
Bill Belichick is one of several NFL head coaches who has studied David Romer’s work.
“Teams should be a lot more aggressive on fourth down,” Romer says with the precise air of a scientist. “On average, you’d be better off going for it, essentially, in any short-yardage situation, and then there are some cases even in longer yardage when you’re in that position where neither punting nor a field goal looks very attractive.“The usual assumption of profit-maximization implies that in their on-field behavior, teams should act to maximize their probabilities of winning. This isn’t happening.”
…Based on statistics from actual NFL games from 1998 through 2000, Romer assigned a value to having the ball first-and-10 on each of the yard lines of the football field in terms of points scored. Since teams rarely go for it on fourth down — last year, the league’s 31 teams went for it a collective 468 times, an average of less than once per game — Romer decided it was not a representative sample. He elected instead to use third-down statistics in assessing probability. In addition, he used only first-quarter statistics because, generally speaking, score and time left did not influence decisions that early in a game.
The findings of Romer’s analysis:
A team facing fourth-and-goal within five yards of the end zone is better off, on average, trying for a touchdown.
At midfield, on average, there is an argument to go for any fourth down within five yards of a first down.
Even on its own 10-yard-line — 90 yards from the end zone — a team within three yards of a first down is marginally better off, on average, going for it.
Of the 1,575 fourth downs in the sample where the analysis implied that teams were, on average, better off kicking, teams went for it only seven times. However, on the 1,100 fourth downs where the analysis implied that teams were, on average, better off going for it, they kicked 992 times.
Translated, in the 1,100 instances where teams had more to gain in Romer’s estimation by going for it, they did so only 108 times, or less than 10 percent.
Romer’s findings have been met with mixed reactions:
Romer freely admits there are many variables he doesn’t account for. This is the area football coaches wonder about.
“Where are you in the game?” Fassel asked. “What’s the score of the game? Are you running the ball or passing?”
“ It’s easy to sit there and apply a formula, but it’s not always the easiest thing to do on a Sunday. There’s so much more involved with the game than just sitting there, looking at the numbers and saying, ‘OK, these are my percentages, then I’m going to do it this way,’ because that one time it doesn’t work could cost your team a football game, and that’s the thing a head coach has to live with, not the professor. â€
— Bill Cowher, Steelers head coach“Do we have the personnel to get that yard?” Walsh asked. “Do we have the personnel to stop the play they may run?”
“Do we punt and use our timeouts?” Belichick asked. “Do we have confidence in our field-goal kicker? Are they going to blitz or not?
“If I don’t get the first down, what are the repercussions?” asked Packers head coach Mike Sherman. “Are they moving the football? If you’re on the road and don’t get that fourth down the momentum is going to change over to the other team.”
Momentum, according to coaches (see sidebar), is a matter of some consequence in fourth-down situations. But Romer — a man as serious as an economist can be — doesnt’ pretend to offer an infallible system, just a guideline. That’s why he couches his conclusions with the words “on average.”
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