Where Statistics Meet Football: The Fourth Down Dilemma

New England Patriots coach Bill Belichick made what was, to many, a “bad” call on November 15, 2009. On the fourth down, with two yards to go from his own 28 yard line and 2:08 left on the clock, the Patriots were leading the Indianapolis Colts 34-28 and Belichick elected to go for it. The attempt failed and the Colts scored just three plays later to steal the win in dramatic fashion, with Belichick being blamed entirely for letting a game that was all but won slip away.

Historically, Belichick’s decision seems to be radical and out of place. However, with the emergence of new analytics and data science in the world of sports, we can reexamine this decision from a far more informed perspective, as I did at the Wharton Moneyball Academy, a sports analytics program for high school students. For now, sports analytics have not had nearly the same impact on football as on other sports like baseball. This is largely due to the nature of the sport. Unlike baseball, every football play involves contributions from multiple players from the same team. Thus, most statistics are representative of more than one player’s actions, making it hard to isolate and evaluate player performance. However, the fourth down dilemma is a rare area where statistical analysis has produced a concrete conclusion: coaches should be far more aggressive on fourth down.

This idea has yet to have real game impact due to resistance from NFL coaches. However, initial resistance has been common in most sports, even statistics oriented ones like baseball, and may subside as time passes and sports analysis technology improves. Former Pittsburgh Steelers coach Bill Cowher was quoted saying, “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.” However, what coaches like Cowher do not realize is that their ignorance and resistance toward the hard facts may end up costing them points, and even games.

With several respected data analysts at Wharton, I studied in depth the simple question: What should coaches do on the fourth down? It is conventional for coaches to punt the ball on fourth down from most positions on the field. It’s a somewhat risk-free play, but studies suggest that it may be better to go for it in many situations. The majority of these studies revolve around the concept of net expected points. They examine how many points teams are likely to score or allow based on their decisions on fourth down situations. These expected points numbers are calculated by multiplying the probability of one outcome by the amount of points lost or gained and adding that number to the product of the probability of the alternative outcome and the points lost or gained. This analysis takes into account factors such as fourth down conversion percentage based on field position and the number of yards left to go for a first down, as well as field goal percentage, average punt distance, and scoring percentage by field position. Looking ahead one or more drives, they do this analysis for every possible decision—punt, kick a field goal, or go for it—and with that data, extract the greatest net expected points. Whatever decision that number corresponds with is deemed optimal.

So, let’s get back to Belichick's controversial decision. The fourth and two at his own 28 yard line situation that Belichick found himself in is actually one of the three possible situations in which punting and going for it are equally effective according to the expected points model. Consequently, we must take factors such as time and score into account in order to reach a more concrete conclusion.

According to the New York Times, because it was fourth and two, the Patriots had a 60 percent chance of converting the fourth down. Given that a first down would have effectively won the game, you can start your win probability calculation by multiplying .60 by 1. Next, you must multiply the chance that they would not have converted, 40 percent, by the chance that even if they had turned the ball over on downs, the opposing team would have failed to score and the game would have been won in spite of the failed conversion. Historically, with two minutes left on the clock from the opposing team’s 28 yard line and a touchdown needed to win or tie the game, NFL teams score 53 percent of the time. Therefore, you multiply .40 by .47 and add the product to the .60 that was calculated previously. The result shows that going for it on fourth down in that situation gave Belichick and the Patriots a 79 percent chance of winning the game.

Alternatively, when teams punt from their own 28 yard line, the average punt nets 38 yards. This means that the opposing team, on average, would start their drive on their own 34 yard line. The chance of scoring from a team’s own 34 yard line in this situation is approximately 30 percent, giving the Patriots a 70 percent chance of winning if they had punted the ball.

Evidently, going for it on that fourth down gave the Patriots the best chance of winning, which means Belichick made the right call. He’s somewhat of a maverick in his departure from the conservative fourth down culture in the NFL and was met with intense criticism after the loss. But he made a statistically sound decision and maximized his team’s chance of winning the game. Ultimately, football fans, coaches, and critics alike may look back on this play in a different light as statistical analysis continues to become an increasingly important part of sports.