Fatigue likely plays a significant role in defensive performance across the NFL. Maintaining a fresh defense helps players give a higher level of effort on quarterback rushes along with rush and pass prevention.

It makes sense that defenses are more susceptible to fatigue. The offense controls the play selection and pace of the game meaning that the defense is forced to use energy while waiting for the snap and anticipating the play call.

One key advantage for the offense is that they know the snap count. The quarterback runs through dummy calls and signals as the defense burns energy. The offense also knows the play call that allows some offensive players to “take it easy” for the play depending on their role. For example, on a running play, the wide receiver can often run his route at less than maximum effort but the cornerback is forced him at full effort. Further, the offense has the option to rest a tired running back or receiver after consecutive plays. It is harder for the defense to make player substitutions in the middle of the drive.

Based on these built in fatigue factors on defense, we hypothesize that the amount of rest that a defense gets between drives significantly impacts performance. To test our hypothesis, we built a multinomial logistic regression model with play-by-play data from the 2009 through 2016 NFL seasons (including the postseason) using the drive outcome as the response and teams’ offensive rating, defensive rating, defensive rest, the time when the drive started (to control for cumulative fatigue effects), and offensive home field advantage as the predictors.

As a response, a categorical score variable was assigned depending on whether the offense punted the ball (0 points), kicked a field goal (3 points), scored a touchdown (6 points), lost an interception or fumble (-6 points), suffered a safety (-2 points). Any other outcome was also assigned an outcome of zero points.

We calculated the offense and defensive ratings for each team (for each season) using an algorithm based on the final score margin and whether the team was home or away. The defensive rest period is defined as the time difference between when the defending team’s offense stared and ended on the previous possession. The play-by-play data was split into training and testing sets as a measure for cross validation.

According to the multinomial logistic regression model, the defensive rest period did significantly influence defensive performance allowing us to reject the null hypothesis.

The most significant variables in the model were the team’s offensive rating (p=0.0133), defensive rating (p=0.0135), and defensive rest (p<2e-16). We found that home field advantage and the time when the drive started as non-significant predictors of defensive performance.

Figure 1: The coefficient output for the multilevel logistic regression model.

Along these lines, we also built a logistic regression model to determine if a drive ended in a score or not using the same predictors as in previous model (multinomial logistic regression model). For reference, scoring drives were classified as those that resulted in a field goal or touchdown for the offense.

For this model, we found that all variables were significant predictors of a scoring outcome. Overall, the logistic regression model accurately classified 73.2% of drives as scoring or non-scoring.

The logistic regression model was further evaluated through a receive operating characteristic curve (ROC), which measures how well a classifier separates true or false outcomes.

Figure 2: Area under the curve (AUC) for classifying scoring and non-scoring drives.

The area under the curve (AUC) is 0.71 suggesting that our model does a fairly good job of classifying scoring and non-scoring drives.

Using the model, we also compared the actual percent of scoring drives and the predicted percent of scoring drives. We found that teams scored a field goal or touchdown an average 18.5% more than predicted by the model. For example, the Green Bay Packers scored on 36.7% of drives between 2009-2016 but were predicted to score at a 14.3% rate according to our logistic regression model.

There a few limitations in our model. First, we did not account for penalties on drives (i.e. false starts), which gives the defense additional rest time before the snap. In addition, defenses (and offenses) have a built-in rest period on drives that run into the two-minute warning that was not measured in our model. Despite these limitations, our model does suggest that NFL defenses tend to perform worse with limited rest between drives regardless of the time in the game. In other words, having an offense that can stay on the field longer likely gives the defense an edge on the next drive.

Github Code:

https://github.com/Fremont28/nfl_rest/blob/master/nfl_rest.R

https://github.com/Fremont28/nfl_rest/blob/master/team_ratings.py

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