Why football coaches should be more aggressive on 4th down

According to Brian Burke, an NFL statistical analyst who runs Advanced NFL Stats,

Every single serious study of 4th-down decisions has found that, in most situations, teams would be better off by going for the conversion attempt rather than kicking. I’ve recently completed a study of 4th-down decisions that confirms what some fans already know, that it pays to be more aggressive. Those short on time might want to skip ahead to the bottom line.

In normal football situations, when neither team is ahead by much, and when the clock is not yet a factor, we can weigh the costs and benefits of each possible decision. Field-goal attempts, punts and conversion attempts can be valued by using a concept called Expected Points. A 1st down at any given yard line has an equivalent point value based on the average of the next score in the game. For example, a 1st down at midfield is worth 1.9 expected points.

Since we know the average punt distances and field-goal percentages from various field positions, we can accurately estimate the expected point values of kicks. And since we know the conversion percentages on 4th-down attempts, we can value those, too. When the values are compared, it becomes clear that going for the first down is the better decision far more often than most people, and most coaches, think.

The graph below charts the “recommended option for each field position and distance to go combination. On the line or below it, a coach should go for the 1st down:”

The bottom line, Burke says, is that coaches should “normally be far more aggressive on 4th down.” But what prevents them from doing so?

You might ask: If it’s so obvious, then why don’t coaches go for it more often? There are a number of good explanations. The authors of the football research classic “The Hidden Game of Football” note that in the early days of the sport, it was rare for a team to score more than once all game. A punt basically guaranteed the opponent wouldn’t score on the next drive. Professor David Romer, author of one of the definitive papers on the subject, theorized that coaches are worried more about job security than winning. If a coach goes for it and fails, it’s his fault. But if he punts and loses, well, that’s just football, and his players take the blame.

I buy those explanations, but I also think it has something to do with what economists call Prospect Theory. In short, almost all people tend to fear losses far more than they value equivalent gains. In this perspective, a punt is considered the “break-even” decision. A failed conversion attempt is seen as a loss, and a successful attempt is seen as a gain. But the loss is feared disproportionately, and the result is clouded decision-making.

Above, I wrote “in normal football situations.” When time becomes a factor, or when a team falls far behind, we need a different way to analyze decisions. For these situations we need to rely on a Win Probability model, an index of how likely a team is to win based on all relevant game variables.

What this does suggest, however, is that an arbitrage opportunity has arisen in the NFL. The first coach who “takes advantage of a more aggressive 4th-down doctrine” could bring in far more victories. But if probably doesn’t go his way, he will be out of a job.

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