The mathematical reason NFL teams need to be aggressive on 4th down

Ask any military historian: Tactical aggression is a game changer. Throughout history, forces who were more aggressive in combat saw a lot more success compared their predecessors. Ulysses S. Grant's determination to take the war to the Confederates led to a win for the Union in the Civil War. When Maj. Gen. Lloyd Fredenhall was soundly beaten by the aggressive Nazi Afrika Corps in Tunisia, he was replaced by the famously aggressive George S. Patton, who saw resounding success. The U.S. strategy of building an overwhelming force to push Iraq out of Kuwait led to a decisive victory in a mere 40 days during the Gulf War.

In a game of strategy like NFL football, the same kind of aggression pays off.

For anyone who saw the Bengals-Chiefs game on Oct. 21, 2018, watching Cincinnati opt to take a field goal in the 3rd quarter while down by 30-plus points was a real head-scratcher. Why not risk the turnover when you're running out of the time it takes to score the four touchdowns you need?

That call — still a bad one — is one made over and over by conservative coaches, even in situations not quite as extreme as the one Cincinnati faced that Sunday night. If a team is facing a 4th down with 4 yards to go on their opponent's 40 yard line, there's a good chance they'll still opt to punt the ball away.

They shouldn't.

Well, maybe the Bengals always should. Anyway...

Kicking the ball, either for a punt or a field goal, is the safe choice. Whenever a team opts for the kick, fans and sportscasters alike praise the coach for making that decision. Economists and statisticians, on the other hand, lose their minds.

Why? Because there's no real reason for a coach to be so conservative. Brian Burke, a former Naval aviator who used to fly the F-18C, is a nationally recognized expert on advanced sports analytics. Burke is currently an analyst for ESPN. In 2014, he published a study on Advanced Football Analytics that took a look at 4th-down decision making.

The longitudinal study assumes that coaches want to maximize the number of points they score while minimizing the number of points the other team scores. Then, it took thousands of real NFL plays on 4th down to calculate the potential value of each situation. Every down versus yardage situation has an "expected point" value and a value attached to the result of previous play, which affects the value of that play.

For example, the expected points value of a touchdown is actually 6.3 points because the opponent gets the ball back on the next play, whose value is .07. If you understand the value of the situation a team is in on 4th down, then you can find the statistically-driven decision the coach should make on that down.

If you don't understand the math, don't worry about it. People who do understand math created a handy graphic for the New York Times, based on Burke's calculation. So we can look at the Bengals horrible performance in Kansas City a different way.

The horrible ball handling that led to the turnover aside, the Bengals tried for a fake punt on 4 and 9 from their own 37-yard-line with almost the entire second quarter remaining. Bengals coach Marvin Lewis tried a play that worked against the Chicago Bears in a preseason matchup. No matter how the ball was handled, the Times' 4th Down Bot says they should have punted it away.

Later in the game, with 6:20 left in the 3rd quarter and the Bengals down 28-7, Lewis opted to kick the field goal from the Kansas City 15-yard-line. Bengals fans everywhere were livid, given the score. While the the bot created by Burke's formula and the New York Times doesn't account for what to do in a blowout situation, Lewis made the mathematically correct call.

Too bad math isn't enough to make Bengals fans hate Marvin Lewis any less.

Looking at the 2018 season, let's see if there's a correlation between game-winning success and 4th down aggression.

As of week 7, the Tampa Bay Buccaneers are a staggering 4-4 when comes to first downs on 4th down — but their record is still a measly 3-3. That doesn't correlate, but the teams with the next-highest percentages in 4th down conversions are the Saints (at 87.5 percent) and the Chiefs (at 80 percent). New Orleans and Kansas City are first in their respective divisions. Five of the ten most successfully aggressive teams on 4th down also lead in total yardage, points per game, and total points this season.

One caveat: the least successful on 4th down conversions are also the least successful teams so far this year. So... know your own limitations.