By Barrett Hansen
The existence of momentum in the NFL has been debated extensively over the past half decade, with the majority of the analytics world siding against it. Grantland (ESPN) writer Bill Barnwell has become the analytics world’s unofficial champion of the anti-momentum cause, with extensive arguments here and here. A 2012 Sloan paper showed that big plays on defense have no substantial effect on future offensive performance. And Advanced Football Analytics’ Brian Burke added to the debate by explaining that streaks of success in football are about what you’d expect from random chance. Yet it’s hard to shake the idea that recent triumphs breed future success, especially when we see extraordinary comebacks like the one Andrew Luck engineered against the Chiefs last winter.
In this study, I will attempt to quantify how momentum manifests itself within offensive drives, specifically targeting these two questions: 1) Does gaining first downs make it more likely to achieve future ones, and 2) How much are these missed first downs worth in points? Answering these questions will shed some light on whether we can discard the idea of momentum or if it’s worth another look.
As evidenced by Brian Burke’s post, the answer to my first question is more or less “no.” I answer tentatively because though momentum does not appear to exist across the board, it’s possible it exists in certain places, such as between a first event and the subsequent ones. This effect might seem anecdotally familiar; in a game or competition, starting off on the right foot—or the wrong one for that matter—can really set the tone for what follows.
And this is exactly what we find in football with first downs. Table 1 illustrates how the success rate (where success is defined as achieving a first down or touchdown) of a drive becomes larger after achieving one first down conversion. The jump from 65.2% to 68.1% doesn’t seem like anything worth calling home about, but given the large sample size (40,511 drives going back to 2009) the difference is significant to well below the 0.01% level.
In words, this table says that when offenses have a first down on their 1st first series of a drive (when they just got the ball), they have about a 65% chance of getting a first down or touchdown on that series (meaning a 35% chance of going three and out or conceding a turnover in the first three plays). Given that a first down is achieved, teams are roughly three percent more likely to get another first down. Table 2 shows the rate for each consecutive series in the drive:
The 1st first down refers to when teams just got the ball, the second after one conversion is achieved, the third after two conversions, and so forth. This sample of about 45,000 does not comprise all drives; it includes only drives that began outside the two-minute warning and with the score difference at 16 points or lower, meaning the offense was likely trying to score. I also only used drives originating inside the offense’s 35-yard line to control for the possible change in play-calling from being close to field goal range.
“What about offensive and defensive strength?” you may ask. “Won’t good offenses get more first downs to begin with, which biases the subsequent samples?” Turns out the bias isn’t very strong. Running a logistic regression of success rate on an indicator of being the 1st series of a drive, offensive DVOA and defensive DVOA (taken yearly for each team), we see that key coefficients barely change. A league average offense (off DVOA=0) generates first downs 65.4% of the time (up from 65.2%) on their 1st first down of a drive against a league average defense (def DVOA=0). This figure bumps up to 67.9% (down from 68.1%) the rest of the way. Adjusting for DVOA shrinks our effect from 2.9 to 2.5, which is still highly significant.
Calculating how these additional first downs translate to points was a little more complicated. To measure the effect, I compared the point output of drives just starting out to ones that had achieved one first down already. The biggest confounder here was field position; drives on their second series are on average closer to the opponent’s goal line, and therefore more likely to result in points.
I used the same dataset of drives originating inside the 35, but excluded drives starting inside the ten because, barring a penalty, it is impossible to gain a first down and still be inside the ten. Here we can run a regression of a drive’s points on the same covariates as the last one (including DVOA metrics), we get the following results:
Against the average NFL defense, an average offense scores 6.5% more points relative to their field position after having secured their 1st first down on drives starting inside the 40, a significant difference. Trends for having achieved two or three first downs were not significant, but this is likely due to the small sample sizes (we must further restrict the field to allow space for two first downs to be gained). To understand how this translates to points, consider that the average offense had 581 drives fitting this study’s criteria over the five-year span, meaning 123.2 drives per season. If teams could convert their 1st first down at the elevated rate of subsequent first downs, they would add (0.11 points) * (123.2 drives/season) = 13.6 points per year. Holding points allowed constant, these 13.6 extra offensive points would translate to an additional 0.34 pythagorean wins for the average team in 2014.
So are these additional 13.6 points proof of momentum? While it’s certainly possible that offensive morale is boosted (or defensive morale drained) when the offense converts its 1st first down, there is a more visible explanation: run versus pass play-calling. Former HSAC President Kevin Meers explained in his senior thesis that it is optimal for teams to pass more, especially on first down, even accounting for defensive response. Bill Barnwell wrote a few weeks ago ago that in 2012, teams could expect just over two and a half yards per play more from passing plays than running plays.
This discrepancy, combined with a lower passing rate on the first series, likely explains the scoring gap. Teams pass the ball 58% of the time on their first series, but up that to 61% for all subsequent series (including 60.7% on their second series). T-tests show both these differences to be highly statistically significant. Though not necessarily explaining the entire gap, these results indicate offenses are too conservative on their first three plays of drives, often calling runs instead of more effective passing plays they eventually turn to later in the drive.
In this analysis, we saw how teams receive a boost in first down conversion percentage after having achieved one first down, which they maintain for the duration of their drive. Controlling for field position, offensive strength and defensive strength, the potential gains of converting first downs at that elevated level is worth a third of a win per season. Though factors such as morale (both on the offensive and defensive side), and fatigue on defense could contribute to this phenomenon, it appears the primary culprit is the 3% lower rate of passing plays called during the first series. Consequently, if teams pass 3% more on the first three plays of drives starting inside their own 40, they can expect to gain just under a point per game.
Note: Edited to reflect observation by Michael Lopez.