Football Stats are hard. Statistics in all sports can be difficult to analyze, but football presents a lot of unique challenges. In baseball, for example, you have a huge sample size (162 games per year), you play every team in your league (multiple times), the teams have different pitchers (so the difficulty of playing against them will vary day to day), and every player has a similar objective at the plate (get hits). This leads to stats like WAR (Wins Above Replacement) being relatively objective, all-encompassing, and easy(er) to create. In football, though you play a small sample size each year, vs only a handful of teams, which makes the strength of schedule vary widely, and different positions have entirely different goals (you can't judge a lineman on his rushing yards), making a stat like WAR nearly impossible. This doesn't even mention how, especially offensively in football, the strength of the team around you will have a HUGE impact on your personal performance/stats whereas in other sports that impact will be far lower.
Quarterback stats are the most complex of all football stats, making Quarterbacks possibly the hardest position to evaluate numerically in all of sports. Tons of Quarterback stats exist and are used frequently, but all of them have significant flaws. The main flaw of such stats is that they measure outcome, and equate it directly to ability, which may work for a Left Fielder in Baseball, but isn't so good for a football QB.
The equation that makes up stats is “Ability X (Team Talent-Opponent Talent)= Statistical Output”. Ability plays a significant role in stats obviously, but if you made a perfect QB in a lab and put him on a PeeWee team vs the ‘85 Bears, he’d have awful stats. Does that mean he isn't talented? Of course not. The reverse is true as well, if you put a terrible QB on the 2019 Chiefs vs your high school team, he’d surely come out with a great Passer Rating.
Unfortunately though, because of how hard “team talent” and “opponent talent” are to quantify, it's not so easy to simply “factor them out” and see a numerical representation of talent.
This idea of factoring out brought me to my theory for this study. To factor out even one variable would leave us with a more accurate representation of talent, if still imperfect.
Offensive talent is just about impossible to quantify, as it is such a “chicken and the egg scenario”. Did the Eagles only pass for 207 yards per game because Carson Wentz is bad? Or was it because his receiving core is terrible. In just about all cases it's both, but “how much of each” isn't possible to determine. Did Jalen Reagor only catch one Touchdown because he’s bad or because the rest of his offense did allow him opportunities? We will never 100% know. If we were to amend Carson Wentz’s stats to account for the offensive talent around him, where would we start if we can't factually determine whose fault their lack of success was?
The inability to factor out offense leaves us with only defense remaining, and the obvious way to do this (at least what was obvious to me) is to factor in the average passer rating allowed by the defenses each QB faced, to establish a “passing strength of schedule” for each quarterback, and then use that to adjust their passer ratings. When I thought of this, it seemed to be common sense and I went to look for it on Football Reference, and then ESPN, and then RotoWorld, and every other stat site. But for the life of me, I couldn't find any stat resembling it. I had to bust open Excel and do it myself
My exact formula was to figure out the average passer rating allowed by all the NFL defenses, which is also the average passer rating. This number is 93.556. I then aggregated the schedule of every Quarterback to start 6 or more games and calculated the average passer rating allowed that they faced. These numbers ranged from 89.283 on the strong end to 101.566 on the weak end. Finally, I calculated the percent difference between each QB’s passing strength of schedule and the average, and applied that percentage to their passer ratings, to arrive at their DaPR (Defense-adjusted Passer Rating). By this I mean that if you faced a passer rating 2.5% times harder than average, your passer rating will get bumped up 2.5% to account for it, makes sense right? Now, enough with all the talk, let's get into the results!
First and foremost, what kind of difference did this adjustment have? Well, it didn't change the passer rating leader. The DaPR leader for the 2020 season is Aaron Rodgers, with 114.71. Much lower than his 121.5 standard passer rating, because his schedule was weak, but still the best. The second-place quarterback is still Deshaun Watson, third and fourth place flipped, with Josh Allen having a higher DaPR than Patrick Mahomes, and fifth place is Russell Wilson, who was seventh in standard passer rating.
The worst passer rating did change from this analysis though, with Dwayne Haskins (third-worst passer rating) having the worst DaPr of the year (72.58). He was one of only a handful of QBs to have a below-average passer rating, AND an easier than average passing strength of schedule, meaning essentially that he played bad vs bad teams. It's no secret why he was benched in only his second season.
What Quarterbacks did DaPR have the most impact on? That would be Sam Darnold and Mitchell Trubisky. Darnold, as any Jets fan remembers, played a brutally hard schedule last season. The average passer rating allowed that he faced was 89.283, the lowest (hardest) faced by any QB, largely as a factor of playing the Bills (twice), Rams, and 49ers, in an injury-shortened season. He had the worst standard passer rating in the league (72.7) but his DaPR of 76.02 was able to put him in the neighborhood of Daniel Jones and Alex Smith instead of Dwayne Haskins, which is a deserved improvement.
Mitchell Trubisky, the man who benefitted from scheduling most, faced an average passer rating allowed of 101.566, meaning the average team he faced was over 6 passer-rating-points easier than the easiest team Darnold faced. A football fan looking at Mitchel Trubusky’s stats, who has been hearing about how terrible he is all year, might be confused to see his respectable 93.5 passer rating. The strength of schedule angle helps to explain the disparity between his reputation as bad and his solid stats. Mitchell Trubisky played pretty well, vs awful teams.
Now, since all stats are flawed, especially football stats, let's be honest and talk about the shortcomings of DaPR. “Chicken and the Egg'' situations, as mentioned before, are very common in football stats and DaPR isn't immune to that. Did defenses that Aaron Rodgers faced have a high passer rating allowed because they're bad? Or because they faced Aaron Rodgers. As always the answer is “both”. The strength of Quarterbacks faced by the defense absolutely factors into these passer rating allowed stats, but over the course of each defense facing upwards of 12 QBs, AND each QB facing at least 6 defenses, it allows us a large(r) sample size and I would say it makes these stats relevant. The other major flaw is that it still doesn't factor in the offensive skill of the QB's team, which prevents it from being a truly all-encompassing stat, but I would argue that because it factors in more variables than passer rating itself, despite not being “flawless” by any stretch, DaPR is a stat that holds value.
How do you, as a football fan/analyst, use DaPR? Quarterback evaluations always have to be done holistically and DaPR doesn't change that. What it does do though is make holistic evaluation a little simpler.
Previously when determining the ability or value of a quarterback, you would look at their standards stats (completion%, yards per attempt, touchdowns, and interceptions, which are all combined to make passer rating), then you would assess how good the team around them is, then you would look at their opponents and try to estimate the impact their strength of schedule had, and you’d also look at game film, to see how well they make decisions and operate in-game situations.
With DaPR in your toolbag, although you still need to consider the offense around a Quarterback, and there's no substitute for watching a QB play, you can cut out the strength of schedule analysis, and make balancing all the factors a little easier. Cutting out even one part of the guesswork will trim your margin of error, as you'll only have to balance two things (DaPR and offensive talent) vs your eye test. This can be a valuable tool for any football analyst out there, but at the very least, hopefully, can be a little bit of fun to look at.