When to Go for It on Fourth Down: What the Analytics Actually Say

The best-known research on fourth downs reaches a blunt conclusion: teams kick far more often than the arithmetic supports. In David Romer's study of the 1998 to 2000 NFL seasons, published in the Journal of Political Economy in 2006, going for it was the better choice on average whenever a team on its own half needed fewer than about 4 yards. The threshold rose to almost 10 yards around the opponent's 33-yard line, and inside the opponent's 5 going for it was always better. Teams kicked on 959 of the 1,068 fourth downs where his analysis said going for it was better.

A later research note by Michael Lopez, written from the NFL and Skidmore College, adds the necessary caveat. Measured with tracking data, the benefit of aggression is smaller than play-by-play studies suggested. It does not disappear.

How the question is framed

A fourth down offers three choices: punt, kick a field goal, or try to convert. Each produces some points now, possibly none, and a new situation next. The analytic approach puts all of them on one scale, the expected point difference between the two teams from whatever situation results.

Romer built that scale from the play-by-play of virtually every regular-season game in 1998, 1999 and 2000. He used first quarters only, because score and clock distort decisions later in a game, which left 11,112 situations. Using dynamic programming, he estimated the value of a first-and-10 at every yard line, the value of kicking from each spot, from 2,560 first-quarter kicking plays, and the value of going for it. Teams went for it only 118 times in the sample, too rarely to measure directly, so he estimated the payoff from third-down plays, which face the same yardage problem.

He also assumed that teams are risk-neutral over points, so that a point is a point whenever it is scored. He shows this is an excellent approximation early in a game and says plainly that it is not a good one late.

What the research found

Two forces shape that curve. Between midfield and comfortable field-goal range lies the dead zone, where a field goal is unlikely and a punt nets little, so the value of kicking dips. And the chance of converting falls only slowly as the distance grows: away from the end zone, teams in the sample converted third downs 64 percent of the time with 1 yard to go, 44 percent with 5 and 34 percent with 10.

Romer's cleanest example is fourth-and-goal from the 2 early in a game. A field goal is close to a certain 3 points, while a touchdown try has roughly a three-in-seven chance of 7. The immediate payoffs are about equal, but a failed try leaves the opponent pinned at its own 2, whereas any score hands it a kickoff. His estimates make the two choices equal at about an 18 percent touchdown chance, and put the gain from going for it at roughly three percentage points of win probability. Teams in his sample faced that situation nine times and kicked all nine.

Midfield works the same way. On fourth-and-3 or 4 at the 50, a team has about an even chance of converting and gains about 6 yards on average when it tries; a punt typically leaves the opponent with a first-and-10 around its own 14. Going for it leaves the team better placed on average than its opponent; punting does not.

What teams actually did

On the 1,604 fourth downs where kicking was better, teams went for it nine times. On the 1,068 where going for it was better, they kicked 959 times. Romer tested complications such as momentum and risk aversion about points and reports that none of them changes the basic conclusions.

He is also honest about the stakes. Being more aggressive was worth about 0.23 points per game in the first quarter alone, which he scales to roughly 2.1 percentage points of win probability over a whole game, or slightly more than one extra win every three seasons in the 16-game schedule of the time. That is real, but small enough to be invisible from one week to the next.

What any fourth-down model needs

You do not need a calculator to follow the logic, but it helps to know what one has to estimate. The open-source models rest on the same pieces Romer used.

1. A value for every situation. The nflfastR package's expected-points model takes the season, which team is at home, the roof type, the seconds left in the half, the yard line, the down, the yards to go and both teams' timeouts, and returns the probability of each possible next score in the half, from a touchdown to no score at all.
2. A conversion probability for the yards needed from that spot, and the value of the first down that follows a success.
3. The cost of failure, which is the opponent's value with the ball at the spot of the stop.
4. The kicking alternatives: the chance a field goal is good from that distance, and where a punt is likely to leave the opponent.

Then the comparison is mechanical:

• Go for it: chance of converting × value after converting, plus chance of failing × value of the opponent's ball at the spot.
• Field goal: chance of making it × (3 points plus the value of kicking off afterwards), plus chance of missing × value of the opponent's ball after the miss.
• Punt: value of the opponent's ball where the punt is likely to leave it.

Late in a game, swap expected points for win probability. nflfastR carries a separate win-probability estimate for every play for exactly that reason: the value of a game-tying field goal in the final minute lies in the chance of winning it adds, not in its three points.