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Improving Passer Rating Differential Remains Key For Cowboys Success in 2014

The key to the Cowboys making the playoffs will be an improved pass defense, whether through a better secondary or an improved pass rush. Don't trust anybody who tells you otherwise.

Dilip Vishwanat

Over the years, I've written so many posts on passer rating differential that I haven't really talked about the subject much this season as I didn't want to sound like a broken record. Here are some previous posts on the topic:

Heck, our old friend KD Drummond even referenced one of those posts in his recent Advanced Stats Notebook in which he previewed the Sunday's Texans @ Cowboys game. Earlier this morning, rabblerouser called me "the metaphorical town crier of passer rating differential," so today I'll attend to my duties and write about passer rating differential once more.

One of the main reasons I have focused so much on passer rating differential over time is that most other stats like NYA or passing yards can't sniff the jockstrap of passer rating differential when it comes to correlation with wins in the NFL.

In statistics, the relationship between two variables is called a correlation, and the strength of that correlation is measured by the "correlation coefficient". This coefficient (r²) is expressed as a number between 1 and -1. The closer the r² number is to 1 or -1, the stronger the relationship between the two variables. The closer it is to zero, the weaker the relationship. R² between Passer Rating Differential (PRD) and wins in 2013 was 0.71, one of the highest observed correlations outside of points differential. Here's a graph that illustrates the correlation between Passer Rating Differential and wins for all 32 NFL teams in 2013:


Today, winning in the NFL is all about passing efficiency. The best offenses are those that pass the ball the most effectively, the best defenses are those that prevent their opponents from passing it effectively. The best teams in the league are those that do both most effectively, and it's no coincidence that the 2013 Seahawks and Broncos stand out on the graph above.

By themselves, offensive and defensive passer ratings had an "okay-ish" correlation with wins (0.42 and 0.41) in 2013. But combining the two into a passer rating differential is like switching on a stat turbo that drives the correlation up to 0.71. The differential works so well because it effectively tells you how much more effective a team is at passing the ball relative to its opponents.

You can see this "turbo effect" with almost every stat you look at. Here's an overview of some stats we've used in the past and what their correlation to wins in 2013 looked like. The table features the differential, the value for the offense only, and the value for the defense only.

Stat R², 2013 Offense R², 2013 Defense R², 2013
Points Differential 0.89 Points For 0.50 Points Against 0.58
Passer Rating Differential 0.71 Offensive Passer Rating 0.42 Defensive Passer Rating
ANY/A* Differential 0.69 ANY/A Offense 0.43 ANY/A Defense 0.34
Net DSR* 0.59 Offensive DSR 0.33 Defensive DSR 0.16
NY/A* Differential 0.56 NY/A Offense 0.35 NY/A Defense 0.21
Y/A* Differential 0.44 Y/A Offense 0.36 Y/A Defense 0.15
Turnover Differential 0.42 Turnovers lost 0.30 Turnovers made 0.27
Passing Yards Differential 0.08 Passing Yards Offense 0.05 Passing Yards Defense 0.03

*ANY/A: Adjusted net passing yards per attempt = (Passing Yards + (Passing TDs)*20 - (INTs thrown)*45 - Sack Yards) / (Passing Attempts + Sacks)
*DSR: Drive Success Rate measures the percentage of down series that result in a first down or touchdown = (First Downs + Touchdowns) / (First Downs + Drives)
*Y/A: Yards gained per pass attempt (Passing Yards / Passes Attempted).
*NY/A: Net yards gained per pass attempt, which is basically Y/A adjusted for sacks (Passing Yards - Sack Yards) / (Passes Attempted + Sacks).

When all is said and done, PRD may just be the Robitussin of stats (no matter what you've got, Robitussin better handle it). PRD beats almost any other available stats in terms of how closely it correlates to wins in the NFL. It follows that as a team, you should do everything you can to improve your passer rating differential, no?

Over four games this year, the Cowboys have an offensive passer rating of 98.7 and a defensive passer rating of 94.2 for a PRD of just 4.5. If we were to plug that PRD into the 2013 regression formula (PRD*0.16+8), we'd get a result that suggests the Cowboys are on track for an 8.7-win season, their 3-1 start notwithstanding.

The regression formula suggests that to reach 10 wins, the Cowboys would need a PRD of 13. Assuming the offensive passer rating remains constant at 98.7, that in turn would require the defensive passer rating to drop to 85.7, an improvement of 8.5 points. Of course, the Cowboys could also look to get that 8.5-point improvement on offense. And even though they are already one of the top teams on offense, they may have no choice, given the state of their defense.

There is little doubt that the Cowboys will need to improve their PRD if they want to reach the postseason. The question is, do you look for an improved PRD on offense or on defense, where an improved passing defense would require either an improved pass rush or an improved secondary (or perhaps both)?

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