In light of my recent post on the difficulty of changing our decision-making habits - even when we're aware that our habits are biased and flawed - I thought it might be interesting to look at two examples from professional football. Why sports? Given the intense competitive pressure in the NFL - there's a thin line between victory and ignominy - you'd expect head coaches to have corrected many of their decision-making mistakes, especially once those mistakes have been empirically demonstrated. But you'd be wrong.

Consider some research done by David Romer, an economist at UC Berkeley, who published a 2001 paper entitled "Do Firms Maximize? Evidence From Professional Football". The question Romer was trying to answer is familiar to every NFL fan: what to do on 4th down? Is it better to bring on the kicking team for a punt or field-goal attempt? Under what conditions should coaches risk going for it?

To answer this immortal mystery, Romer analyzed every fourth down during the first quarter in every NFL game between 1998 and 2000. (He had help from a computer program.) The first thing Romer did was figure out the fluctuating value of a first down at each point on the football field. After all, a first down was more valuable for a team if it occurred on an opponents two yard line than on their own twenty yard line.

Then Romer calculated the statistical likelihood of going for it on fourth down under various circumstances and actually getting a first down. He also calculated the probability of kicking a successful field goal from various spots on the field. So let's say you are NFL coach, and you have a fourth and three on your opponent's 30 yard line. Romer could tell you that 1) you have a 60 percent chance of getting a first down, and that teams with 1st downs inside the thirty yard line score a touchdown 40 percent of the time, for an expected point value of 1.7 and 2) that field goal attempts from the 32 yard line failed almost 65 percent of the time, which meant that going for a field goal only had an expected point value of 1.05. In other words, it's almost twice as effective to go for it than to attempt a field goal.

So what do most coaches do? Well, NFL coaches consistently make the wrong decision. According to Romer's analysis, teams would have been better off going for it on fourth down during the 1st quarter on 1100 different drives. Instead, coaches decided to kick the ball 992 times. This meant that NFL coaches made the wrong decision over 90 percent of the time. Romer summarized his counterintuitive results: "This analysis implies that teams should be quite aggressive. A team facing fourth and goal is better off on average trying for a touchdown as long as it is within 5 yards of the endzone. At midfield, being within 5 yards of a first down makes going for it on average desirable. Even on its own 10 yard line - 90 yards from a score - a team within three yards of a first down is better off on average going for it." Romer conservatively estimates that a more aggressive approach on fourth downs would make a team 5 percent more likely to win the game. This is a significant advantage: a coach willing to endure the risks would win one more game in three seasons out of every four.

But if kicking a field goal or punting on fourth down is such a bad idea, then why do coaches always do it? To explain the consistently bad decisions of NFL coaches, Romer offered two different answers. The first is risk aversion. If coaches followed Romer's strategy, they would fail about half the time they were within ten yards of the endzone. This means that instead of kicking an easy field goal and settling for three points, they would come away empty handed. Although that's a winning strategy in the long-run, it's awfully hard to stomach. (As Daniel Kahneman notes, "Worst case scenarios overwhelm our probabilistic assessment, as the mere prospect of the worst case has so much more emotional oomph behind it.") After a long drive down the field, fans expect some points. A coach that routinely disappointed the crowd would quickly get fired.

The second reason coaches stink at making decisions on fourth down is that they stink at statistics. As Romer politely writes, "Many skills are more important to running a successful football team than a command of mathematical and statistical tools...It may be that individuals involved want to make the decisions to maximize their teams' chance of winning, but that they rely on experience and intuition rather than formal analysis."

So how have coaches reacted to this data? In 2001, before Romer published his findings, the average team went for it on fourth down 15.1 times per season. During the 2005 season, the average NFL team went for it on fourth down 14.5 times. Learning about our mistaken decisions led to even worse decisions.

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Why does this not surprise me? To quote you, "Knowledge has diminishing returns, right up until it has negative returns".

Great article. Passed it along to my football loving buddies.

Romer is only correct if his study is correct. His study can only be correct if the data used is relevant. Using 4th down data from the current NFL to predict behavior in a future NFL can only work if the two NFLs will be the same. However, I doubt 4th down data from an NFL where it is rare and only done when desperate (at least when more than 1 yd is needed), many times against a defense more interested in preventing a touchdown than a first down, will translate to a time when defenses are routinely asked to defend 4th down all over the field all the time.

I don't know how Romer could have accounted for this bias in the data. How many 4th and 8's does a team try a decade? How many times is it at the end of games against a prevent defense?

Garbage in = garbage out.

His study probably is better when it comes to near the opponent's goal or around the 35 yard line.

A point similar to Patrick: If you assume a basic level of competence in NFL coaches, then they would only attempt a 4th down conversion in situations their experience tells them is likely. Thus because you already have the coaches avoiding bad 4th down conversions, the 4th down conversions attempted would in fact have a higher degree of success, not because it's a good strategy but because coaches only attempt them when their experience tells them they have a better-than-50/50 chance of succeeding. You'd need to control for that by having a coach randomly go for conversions or field goals and then compare the results.

Another point that probably skews the results-

The study doesn't appear to account for the somewhat intangible detriment to a team when it fails to convert a 4th down play. A defense getting a stop on 4th down is one of the largest momentum swings in a football game. It energizes the team that made the stop and it depresses the team unable to convert a 4th down. It would be difficult to quantify this effect, but a start might be to analyze what the opposing team's offense does after their defense gets a stop on 4th down. If the offense scores a touchdown 40% of the time, you could subtract that from the expected point value. Momentum is key in a football game. Tough to define but essential to victory.

very good point Patrick

One thing coaches have to deal with is the second guessing of owners, sports writers, and fans. (Try selling these ideas to Al Davis or Jerry Jones for example.) A failure when going for it that leads to extreme criticism can be worse than the hoped for and temporary success. And even that occasional success can be criticized as a matter of pure luck that overcame the coach's otherwise bad judgement. Reputation can be as important to winning as an extra player on the field.
And if a coach thinks he can win by the usual methods, he will not chance the backlash that can come from doing the unusual. Playing the untraditional odds can get you lasting blame for the inevitable losses as opposed to some temporary credit for what may occasionally be a winning strategy. The fans and their expectations may have as much an effect on the odds as that particular strategy.

Travis wrote

A defense getting a stop on 4th down is one of the largest momentum swings in a football game.

Only because going for it on 4th down is perceived as a desperation tactic. When it's routinely expected it's a different morale game.

Patrick wrote

I don't know how Romer could have accounted for this bias in the data. How many 4th and 8's does a team try a decade? How many times is it at the end of games against a prevent defense?

That's the best question I see here. Note that it's at least partly answered by the Sports Illustrated story linked in Kyle's first comment. The opponents know what's coming because the Pulaski Academy team does it consistently, yet their record is good:

The Bruins have won 100 games this decade, including the Arkansas 5A championship last year. In the waning minutes of the 2008 title game, as the Bruins nursed a 35--32 lead, they still went for it four timesâeach successfullyâon their final drive before running out the clock.

Clearly that's not dispositive, but it is suggestive.

Jonathan wrote

If you assume a basic level of competence in NFL coaches, then they would only attempt a 4th down conversion in situations their experience tells them is likely.

Except that humans are lousy at integrating over experience to derive probabilities.

I love this kind of stuff, but it doesn't follow that NFL coaches are bad at or ignorant of statistics. Unless the entire team are sufficiently rational and cold to ignore the emotional cost of failure to score, the effect on arousal (upside down U curves, etc, etc) is likely to more than counterbalance the 5% benefit of going for it more often. I know the NCAA has some good scholar athletes, but somehow I can't imagine this working all that well.

I think the decisions made are rational, even if not optimal. The reason being coaches are fired, even winning coaches, if they break from the mold and suffer any kind of set-back the fan pressure to fire the coach can be over-whelming.

Just to clarify... whilst I think Romer has the value function used by coaches slightly wrong and hasn't taken into account a couple of (potentially unobservable) effects and there is some endogeneity (go for it on more fourth downs and expect defense to do better at stopping fourth down plays...), there is no way on the face of the Earth these decisions are going to be rational within the meaning traditionally used in decision theory and economics. (See, eg, every psychology, experimental decision theory, empirical economics, neuroscience of decision... etc... paper ever published bar about two).

The way I understand it, Romer did not use actual 4th down attempts in his study. He derived a point value for every location on the field if you were to give the other team a first down at that point. He then used 3rd down data from the first quarter of every NFL game for 3 years. The 4th down data talked about is him saying that 1100 times that his study says to go for it on 4th down, coaches punted 982.

Some of you have brought up a great point about the momentum factor of losing the ball on 4th down. Romer admits this flaw himself. However, what about the momentum of the offense for converting these 4th downs? How devastating would it be for a team to hold a team to a 4th and 3, think they're sending they're return unit out only to have to play another down and give up a 1st down? I don't know that the momentum swings would "equal" out in real games, but I don't think you can consider one while ignoring the other.

I think Shakey's got it right. Only way to get the sample to anything approaching useful in a 3 year window.

Jacksonville would be an interesting study. Between 06 and 07, seems Del Rio had a substantial shift in his approach towards going for it on 4th downs.

By Uncle Rico (not verified) on 18 Oct 2009 #permalink

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