Aaron Rodgers is the best quarterback in the NFL, and should be the highest-paid. We can all agree on that. But this guest column by Kevin Kolbe explains why salaries for other quarterbacks are all out of whack.
Guest column by Conor McGovern
You hear it all the time from commentators on TV: the closer you get to an opponent’s goal line, the easier it is to tighten up and make a stop. Of course, the caveat here is that it seems to become much easier to punch the ball in when you have a first down inside the opponent’s 5-yard line. But what about scoring touchdowns from farther out, say six to 15 yards from the goal?
On most of the football field, gaining more yardage on a given play is always desirable. For example, a play that goes for a first down on your own 45 is better than a play that goes for a first down on your own 43. But inside the opponent’s red zone, things start to get hazy. For one, according to the wisdom of the commentators, the closer the offense gets to the goal line, the less territory the defense has to cover. This is often summed up in the "bend but don’t break" mentality that some teams like to exhibit. (Patriots, I’m looking at you.)
A second potential wrench in the idea that being closer to the end zone is always better is that a first down from 11-to-15 yards out offers the opportunity for a team to get a first down inside the opponent’s 5-yard line, where the probability of scoring a touchdown is very high. What football fan hasn’t cringed as a running back bulls just inside the 10 rather than falling down at the 12, where the former results in first-and-goal and the latter would offer the opportunity for another first down inside the 2?
I decided to investigate whether there was anything to the idea that closer may not always be better. Using complete play-by-play from the 2000 through 2011 regular seasons and playoffs, I tested if a team with a first down 15 to 11 yards from their opponent’s goal is, on average, more likely to score a touchdown than a team with a first down 10 to 6 yards from the goal line (first-and-[long]-goal) because of more open field and the opportunity to get another first down inside the 5.
For the most part, closer is better. As shown in the bar chart, an offense with a first-and-goal between the opponent’s 6-to-9 yard line can expect to score touchdowns at a higher clip than those offenses outside the 10 who can still get a first down inside the 5. While the probability decreases at a gradual pace over that interval, it remains higher at the 9-yard line than at any subsequent yardage marker. Typically, teams with a first-and-goal from inside the 10 score a touchdown 64 percent of the time. On average, those with a first-and-goal right at the 10 reach the end zone on about 53 percent of drives, while offenses with a first-and-10 between the 11 and 15 will go on to score a touchdown 57 percent of the time.
That said, there is something to that cringing feeling that we get from the running back described above. An offense facing first-and-goal with 10 yards to the opponent’s end zone typically has the lowest probability of scoring a touchdown. Had he fallen down at the 12 instead of diving forward, his team could expect to score a touchdown about 9.1 percent more often on average –- a difference that is highly statistically and substantively significant.
Additionally, having a first-and-10 from the opponent’s 11 is only marginally better (3.8 percent higher probability of scoring a touchdown) than a first-and-goal from the 10. While some of this is probably statistical noise, we can be 95 percent certain that there is a systematic difference. One possible explanation for this odd finding is that this difference is a result of the unlikelihood of getting a first down at or inside the 1-yard line. Instead, offenses generally either score or get stopped. A drive with first-and-10 at the 11 is about 10 percent less likely than one with first-and-10 at the 12 to get a new set of downs by gaining ten yards, and the odds of getting a new set of downs increases from there.
While it appears that the probability of a drive ending in a touchdown for an offense with first-and-10 from the opponent’s 12 is only 1.35 percent lower than that for an offense with first-and-goal from the opponent’s 9-yard line, and the probability of scoring with a first down from the 15 is actually two percent higher than from the 14, we cannot be confident that these small differences are not just noise resulting from the selection of the sample.
Once an offense has a first down inside the 5-yard line, the end zone has to be the goal of every play. The chart shows the probability of scoring a touchdown based on down, yard line, and play choice.
At first glance, this hardly tells us anything we don’t know about today’s NFL. Except at the opponent’s 1-yard line, a passing play is typically preferable to running on any given play, and the probability of scoring a touchdown on any given play is lower the farther a team gets from the opponent’s end zone.
However, because running plays are more likely to result in a positive gain that does not score, probability may dictate that certain combinations of play choices are preferable to passing. For example, electing to pass on all three downs from the 5-yard line results in a 66.4 percent chance of scoring a touchdown on average, assuming that no play ends in a sack and field position does not change due to penalty. On the other hand, running three times from the 5 seems like it would be a worse choice. However, if the play can be assumed to achieve a positive result -– either gain two yards or score –- on each of first and second down, the probability of scoring a touchdown increases to 74.6 percent if a running play is called on third down, or 70.7 percent if a passing play is called.
Of course, this all rests on the competence of the rushing player and his offensive line. If you expect that a running play will gain one yard or score from the 5 and then pass on third down from the 3-yard line, the probability of scoring a touchdown is only 58.9 percent -- in other words, the offense with a below-average running game would be significantly better off passing three times from the 5.
While many teams choose to pass the ball on third-and-goal from the 1-yard line, the chance of scoring a touchdown is actually 12 percent lower when passing on third down as opposed to running. The standard selection of plays on first through third down from the 1 results in a touchdown 88.9 percent of the time, but running on all three downs increases this to 90.4 percent -- a small but not insignificant difference.
Therefore, inside the opponent’s 5-yard line, running is generally preferable to passing assuming a coach has some confidence in the ability of his running back and offensive line to gain positive yardage on a given play. Moreover, the chance of a catastrophic loss of yardage that would make scoring a touchdown on subsequent plays very unlikely is much lower for rushing plays than for passing plays, not only because of sacks, but because of the possibility of offensive holding penalties.
Conor McGovern is a lifelong Patriots fan who remembers days when trips to the red zone were rare enough that any bit of help for Tommy Hodson or Hugh Millen was a godsend. He works in DC as a policy wonk on social and economic justice issues. If you are interested in writing a guest column, something that takes a new angle on the NFL, please email us your idea at info-at-footballoutsiders.com