Guest column by Ben Baldwin

Whenever I ask why teams run the ball so frequently, a common response is that by running the ball and chewing up clock, a team can keep its defense off the field and rested for the next drive, thereby allowing it to perform at its highest level.

Anecdotes supporting the idea that rested defenses are more effective come to mind quickly. In Super Bowl LII, the Brandon Graham strip sack -- the only sack of the game -- came after a 15-play drive (counting the attempted two-point conversion) that chewed up more than seven minutes of game time. In the AFC Championship Game, the Jaguars' defense finally showed cracks after a series of three-and-outs by the offense, with the game-deciding New England touchdown following a Jacksonville three-and-out that used less than a minute of game clock. And of course, in Super Bowl LI, Atlanta's defense looked gassed in the second half on the way to spending 93 snaps on the field.

Do we remember specific defensive performance following exceptionally long or short drives because of confirmation bias? Or is a given defense's time to rest actually predictive of how it will perform?

The only piece of research I could find is this piece from Football Outsiders in 2011, in which Daniel Lawver found no relationship between a team's average offensive plays per drive and defensive DVOA over the course of a season. However, it could be the case that using team-level averages over a season obscures a real effect (perhaps, for example, at the end of games). This piece will go a step deeper and look at every single drive and the relationship between defensive rest and its performance.

For this piece, I used the public play-by-play data from the wonderful nflscrapR project that collects statistics from 2009 to 2017 (with special thanks to Ron Yurko). I excluded the first drives of each half (defenses are well-rested for those drives), drives beginning in the last four minutes of the game (when teams are substantially less likely to score due to the clock being a factor), and sample sizes with fewer than 10 drives. Code is here.

The question addressed in this piece is whether the number of plays or amount of time that a defense has recently rested predicts how many points it allows on the subsequent drive, all else being equal. However, a simple look at points per drive versus time of rest (or plays of rest) isn't quite what we want, because drives that follow extremely short drives are more likely to begin after turnovers and thus have better field position.

Every figure in this piece will look at the same four factors as shown in the following graph. Starting from the upper left and moving clockwise, we have:

defensive rest time on the most recent drive by number of plays run;

defensive rest time on the most recent drive by time of possession;

the number of plays faced by a defense as of the start of the drive;

and time of possession faced by a defense as of the start of a drive.

The first two factors measure the amount of rest a defense has had since the last time it was on the field, and the last two measure how long a defense has been on the field to that point in a game.

The above figure is interesting and could be a piece by itself. The two top graphics show that teams start closer to the opponent's end zone following short drives, whether measured by number of plays or time of possession. This is due to two factors. First, defenses that take the field after a very short drive (i.e., fewer than four plays run) have typically seen their offense go three-and-out or turn the ball over, both of which tend to place the defense in poor field position. Second, teams are more likely to pin their opponents deep following longer drives than shorter drives. The R-squared values of about 0.1 mean that about 10 percent of the variation in starting field position can be explained by the length of the previous drive.

The two bottom graphics in the figure above show that starting field position is mostly constant throughout the game (close to the-30 yard line). The exceptions come at the very beginning (because the game opens with a kickoff, rather than a punt or turnover) and the very end (probably due to teams who have run a lot of plays tending to be in the lead and having opponents taking greater risks).

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A technical note on the R-squared values listed throughout the piece (feel free to skip this paragraph): R-squared is obtained through a drive-level regression of the outcome of interest on a cubic polynomial in the explanatory rest variable of interest (the order of the polynomial doesn't turn out to matter). The R-squared is small in, for example, the lower left graphic above despite the appearance of a relationship because the collapsed data in the graph obscures the tremendous variation at each point. For example, for the point (1, 74) -- the far left point on the lower left graph -- the vertical coordinate of 74 is the average of more than 4,600 drives which range in starting position from the 1-yard line to the 99-yard line. In technical terms, the variation in field position within previous plays run is enormous relative to the variation across previous plays run.

The following figure shows expected points per drive by defensive rest time, where expected points is defined relative to starting field position. For those interested, I performed a drive-level regression of points scored on a fifth-order polynomial in field position (yards from opponent end zone) to obtain expected points for a given drive based on starting field position. For those familiar with expected points added (EPA), this is not quite the same calculation, because EPA takes into account possible scores on subsequent drives, while I am only interested in the number of points scored on a given drive.

Because drives following very short drives tend to begin with better field position, we would expect more points to be scored based on field position effects alone. This is shown in the following figure:

Since the goal is to gauge the extent to which a more rested defense is a more effective defense, holding field position constant, for the remainder of the piece I show points per drive relative to expected points per drive (I also experimented with holding field position constant by looking at sample of drives following kickoffs or drives starting on one's own 20- to 30-yard line, with similar results).

Points Per Drive Versus Defensive Rest Time

Here is actual points per drive minus expected points per drive, where expected points per drive is based on starting field position as described above:

This is the main relationship of interest. The key points:

1. Running a lot of plays on a drive does not make your defense perform better on the subsequent drive (as shown in the upper left).

2. Chewing up a lot of clock on a drive does not make your defense perform better on the subsequent drive (upper right).

3. Running a lot of plays against a defense does not make it easier to score against that defense as the game goes on (lower left).

4. Running up a lot of time of possession against a defense does not make it easier to score against that defense as the game goes on (lower right).

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Despite working with enormous sample sizes (nearly 38,000 drives are used to construct the upper left figure, for example), the error bands always include zero (except for the very end of the time of possession graph, where offenses are less likely to score once they've reached high time of possession), and the R-squared values are always 0.000. This includes about 3,300 drives with 11 to 15 plays of defensive rest and more than 300 drives with 16-plus plays of defensive rest. In the upper right figure, there are more than 2,300 drives with defensive rest time exceeding six minutes.

If it were the case that rested defenses performed better, we would expect the top two graphics in the above figure to be downward-sloping (more rest = harder to score) and the bottom two graphics to be upward-sloping (defense on the field longer = easier to score). Instead, we see little relationship for any of the measures. The one possible exception would be the lower right figure, where defenses that have been on the field for a long time tend to allow fewer points at the very end of games (likely because at that point some offenses are trying to run out the clock).

I could stop here and conclude that there is no evidence that how long a defense has rested affects its performance. However, when digging into the numbers, I noticed that the flat relationship in the bottom two graphs of the above figure is the result of two factors: teams with the lead being less likely to score and teams trailing being more likely to score. Here is what the figure looks like when excluding drives that began in the fourth quarter with a lead:

We now see an upward slope at the end of games. Is this evidence that tired defenses perform worse as the game goes on? While this seems plausible, another possibility is that we are seeing the impact of teams trailing late in the game making more of a concerted effort to score (by, for example, passing the ball more and taking more risks). Here is the ratio of pass plays to all plays when excluding teams who are leading in the fourth quarter:

And indeed, we see in the bottom two graphs that teams that are tied or trailing late in games pass substantially more often. Since passing is more efficient than rushing, we would expect teams to be harder to stop once they start passing more, whether defensive rest time is important or not.

Let's isolate situations where the run/pass ratio isn't changing dramatically to investigate whether defensive rest time matters late in games. Here is the ratio of passes to total plays on drives that begin with four to 10 minutes left in the game, with the offensive team trailing:

Much better! We have isolated a situation where the run/pass ratio is roughly constant regardless of defensive rest time. In this game state (four to 10 minutes left in the fourth quarter with the possession team trailing), do rested defenses perform better? Let's take a look:

If drives beginning with four to 10 minutes left in the game were more likely to score because of their aggression rather than the defense being tired, we would expect these drives to score more points regardless of defensive rest time. A look at the above figure reveals that this is exactly the case: teams in this situation are nearly universally more likely to score, regardless of how rested the opposing defense is. However, while the confidence intervals in all four figures are mostly above zero (more likely to score), the lines are mostly flat, and less than 1 percent of the variation in adjusted points per drive can be explained by defensive rest time. Thus, the increase in likelihood of scoring when excluding teams who are leading in the fourth quarter appears to be due to the aggressiveness of trailing teams rather than defenses being tired.

For defenses trying to protect a lead with four to 10 minutes left in the game, the number of plays or time of possession they have already been on the field tells one nothing about how they will perform (R-squared of less than 1 percent). For example, a defense that has already been on the field for 55 plays is no better at holding a lead in the fourth quarter than a defense that has been on the field for 65 plays. A defense that has been on the field for 32 minutes is no worse at holding a lead in the fourth quarter than one that has been on the field for 25 minutes, or even 20 minutes. A team that allowed its defense to rest for eight minutes should expect its defense to perform just as well as one that only rested for one minute.

On Rushing and Defense

If rushing carried inherent value relative to passing in improving defensive performance, we would expect time of possession (the graphs on the right of all figures shown) to be more important than plays run (the graphs on the left) because the clock is more likely to continue running after a rushing play. In reality, neither matters, and we can cross off another purported benefit of rushing.

Conclusion

Putting this all together, the main -- and perhaps only -- channel through which an offense can help a defense on a per-drive basis is through field position. Turnovers and quick three-and-outs make a team more likely to give up points on the following drive, but this appears to have everything to do with field position and nothing to do with defensive rest time. In other words, whether it's one minute or eight minutes, knowing how long a defense has had to rest tells one nothing about how the defense will perform given its starting field position.

Why is the myth that a running game can help a defense so prevalent? I suspect that a contributing factor is the conflation of pace effects (in which defenses allow fewer points if they take the field on fewer drives) with actual changes in defensive efficiency. If two teams possess the ball an equal number of times, there is nothing inherently valuable about making the other team possess the ball fewer times, because your own team will also possess the ball fewer times (unless, perhaps, an underdog is pursuing a high-variance strategy). In the end, barring defensive or special teams scores, the team with more points per drive will win, whether there are a lot of drives or few drives. But there is no evidence that time of possession helps a defense perform better when it is on the field.

An economist by trade, Ben Baldwin uses large datasets to try to learn about human behavior. His work can be found on Field Gulls and GridFE; reach him on Twitter at @guga31bb.