Does QB Performance Decline Over A Season?

On average, how does the most important player on the football field fare throughout the course of a season? There are innumerable ways to measure how quarterbacks perform in a single game, and an average of these will tell you how they did overall in a season. But how do quarterbacks' performances trend over the course of sixteen games? 

Total Quarterback Rating (QBR) is a metric designed by ESPN to grade quarterback performance on a scale of 0-100. This stat is also structured to incorporate the different contexts in which quarterbacks make their passes. A high pressure drive in the fourth quarter impacts QBR differently than a short pass in garbage time. 

All things considered, QBR correlates with other metrics of quarterback performance pretty well and can be used to judge performances effectively. I will use it here to see how quarterback performance moves during a season. 

The plots below track the average QBR of all starting quarterbacks through seventeen weeks in 2014 and the first seven weeks of 2015:

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Overall QBR shows a slight downward trend in both years, with 2014's being more reliable than 2015's. The relevant question, of course, is why QBR trends downward throughout the course of a season. Statistically pinpointing the actual causal mechanism of this trend lies beyond the reaches of this article. However, let's consider some possible explanations for decreasing QBR. 

1) Defenses make adjustments.

This explanation makes sense at first glance. Defensive coordinators and theirs staffs have more film to analyze over the course of a season. The defense can therefore make better adjustments, and quarterback play will get worse (i.e. QBR decreases). Unfortunately, the data don't quite tell that story.

To measure defensive performance, I've used Football Outsiders' Defensive DVOA, which is a measure of efficiency that adjusts for situational pressure (much like ESPN's QBR). I've taken the average of every team's Defensive DVOA for each week and plotted them below. Note that since DVOA is usually recorded with negative numbers (the lower the better), I used negative DVOA so that an upward trend means better performance:

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In 2014, defenses, like quarterbacks, played worse as the season went along. This trend troubles the defensive adjustment narrative posited above. Here's the plot for 2015:

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The data for 2015 so far support the defensive adjustment narrative. Defenses have played better as quarterbacks have played worse. Or is it the other way around? Quarterbacks could be playing worse and so defenses look better. Perhaps the biggest problem with the defensive adjustment explanation, aside from the contradictory data in 2014, is that it could only establish correlation at best. We cannot say whether defenses cause quarterbacks to look worse or quarterbacks make defenses look better. As we continue, you'll notice that this correlation/causality problem keeps coming up.

2) Everyone fatigued.

Admittedly, this explanation is somewhat lazy, as it is basically unfalsifiable with the data I've assembled. How exactly one would measure fatigue is uncertain, but it is clear that only a third variable could explain the trends in QBR and Defensive DVOA. Fatigue from the season's games makes as much sense as any other possible cause. If Defensive DVOA for 2015 turns downward in the next couple of weeks, we may have found the culprit. 

3) Quarterback-Defense Equilibrium

This idea proposes that the relationship between quarterback and defense is a sort of arms race. Both sides are studying the other meticulously in hopes of gaining an edge. As one side makes progress (big week for quarterbacks), the other side evolves (big week for defenses). The general movements of a line connecting the points suggest this equilibrium, at least for 2014: 

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The mirroring effect noticed between these two lines could be attributable to the quarterback-defense equilibrium, which makes sense intuitively. In this scenario, both sides of the ball make adjustments throughout the season and pull each other towards the center of the plot (i.e. average play). As noted earlier, however, I do not have statistical causality for this idea. For now, it's just a thought.

What does all of this mean for our teams? Our quarterbacks will play worse as the season goes on, but so will the opposing defenses. Why exactly this happens we cannot say for sure, but if your QB is playing poorly, I wouldn't expect any miracle turnarounds in the second half of 2015.  

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