Every year at Footballguys.com, I publish an article called Rearview QB, which adjusts the fantasy football statistics for quarterbacks (and defenses) for strength of schedule. I’ve also done the same thing for years (including last season) using ANY/A instead of fantasy points, which helps us fully understand the best and worst real life performances each year. Today I deliver the results from 2014.

Let’s start with the basics. Adjusted Net Yards per Attempt is defined as (Passing Yards + 20 * Passing Touchdowns – 45 * Interceptions – Sack Yards Lost) divided by (Pass Attempts plus Sacks). ANY/A is my favorite explanatory passing statistic — it is very good at telling you the amount of value provided (or not provided) by a passer in a given game, season, or career.

Let’s start with some basic information. The league average ANY/A for quarterbacks in 2014 was 6.13, the highest in NFL history. Aaron Rodgers led the way with a 8.65 ANY/A average, the highest rate in the league among the 39 quarterbacks who started at least five games. Since the Packers quarterback had 520 pass attempts and was dropped for 28 sacks, that means he was producing 2.52 ANY/A (i.e., his Relative ANY/A) over league average on 548 dropbacks. That means Rodgers is credited with 1,383 Adjusted Net Yards above average, a metric labeled “VALUE” in the table below. That was the most in the NFL last year:

Given how much time we’ve all had to look at the 2014 data, I doubt there’s much in here that’s surprising to regular readers. So let’s get to the point of today’s post, which is to adjust those numbers for strength of schedule. The methodology, which I’ve labeled Rearview adjusted net yards per attempt, adjusts those numbers for strength of schedule. The system is essentially the same as the one used in the Simple Rating System. Let’s look at Derek Carr, who averaged an unimpressive 4.82 ANY/A last season, on 623 dropbacks. If we want to find Carr’s SOS-adjusted rating, we need an equation that looks something like this:

Rating_Carr = 4.82 + (94/623) * (Rating_KAN-D) + (86/623) * (Rating_DEN-D) + … (17/623) * (Rating_MIA-D)

In other words, we need to adjust his rating for the ratings of the defenses he faced, based on the number of dropbacks he had against each defense. Carr’s true rating should equal his ANY/A plus the rating of each defense he played, multiplied by the number of pass plays he had against that team. Each of the 32 defenses is assigned a rating based on how much tougher or easier they are on opposing QBs than the league average. Carr had 94 dropbacks against the Chiefs, the most of any time he faced. Kansas City has (initially) a +0.33 rating in 2014, because opposing QBs averaged 0.33 fewer ANY/A than league average against the Chiefs. Carr had 86 dropbacks dropbacks against the Broncos, who (initially) have a rating of +1.20, because opposing QBs averaged 1.20 fewer ANY/A against the Broncos than league. And so on.

If Carr played a schedule that was exactly average, the sum of all the numbers to the right of the first plus sign would be zero, and Carr’s rearview rating would be the same as his actual rating. If Carr played a hard schedule (which he did), all the numbers on the right would sum to a positive number, and Carr’s rearview rating would be better than his actual rating.

This is easier in theory than it is in practice. We need to know the ratings of Kansas City, Denver, Miami, and all of the other defenses Carr faced, but we can’t figure those ratings out until we’ve figured out the ratings of all the quarterbacks those teams faced. But we can’t do that until we figure out the ratings for the defenses that those quarterbacks faced. As you can see, each quarterback’s rating depends on each team’s defensive rating, and vice versa.

Fortunately, there is a relatively simple way to do this using Excel. I iterate this strength of schedule adjustment (adjusting each QB’s SOS for each defense, adjusting each defense’s rating for each defense’s SOS (i.e., the QB), then adjusting each QB again, and then each defense again, and so on) process over and over again until the ratings converge. That’s when we know we’ve finally reached the true strength of schedule adjusted ratings.

With that out of the way, the table below shows the same 39 quarterbacks from above. Here’s how to read the Tony Romo line. The Cowboys quarterback averaged 8.11 ANY/A last year against a strength of schedule that was 0.32 ANY/A easier than average. That ranked as the 36th hardest SOS among these 39 quarterbacks (for SOS, 1 means the toughest and 39 the easiest). ^[1]And, of course, the reason Romo’s schedule was easy is not because those defenses faced Romo; that is filtered out in the iterative process. Romo’s Adjusted ANY/A is therefore 7.79 (i.e., 8.11 – 0.32), which means he ranked 4th in Adjusted ANY/A. Finally, we can compute each quarterback’s Adjusted VALUE, based on his Adjusted ANY/A and number of pass plays. Romo’s Adjusted Value is 772 adjusted net yards, which places him at #4 in the league.

• This site has not always been so kind to Derek Carr’s 2014 season, but facts are facts: the Raiders rookie faced the toughest schedule in the NFL last year. On a schedule-adjusted basis, he was about as efficient a passer as Cam Newton or Colin Kaepernick, and yes, the intent of this sentence was to praise Carr.

• The other rookie quarterbacks don’t benefit from any bump in this analysis. Both Blake Bortles and Teddy Bridgewater had slightly easier-than-average schedules.

• Drew Stanton faced the second toughest schedule in the NFL; Carson Palmer faced the easiest. Yes, the two Cardinals quarterbacks had wildly different schedules, as Stanton faced a brutal slate of opponents, while Palmer missed all four games against the 49ers and Seahawks.

• AFC East and AFC West quarterbacks faced the hardest schedules last year: among quarterbacks with at least ten starts, the quarterbacks for those eight teams had the six hardest schedules and eight of the nine toughest schedules, with only Jay Cutler breaking up the group (as he’s prone to do).

Defenses

What about the defenses? After adjusting each defense for strength of schedule (i.e., talent of the opposing quarterback), we get the following ratings. Here’s how to read Buffalo’s line: the Bills allowed 4.50 ANY/A last year and faced a schedule that was 0.02 ANY/A easier than average. That ranked as the 15th most difficult schedule; after adjusting for SOS, the Bills allowed 4.52 Adjusted ANY/A, which still ranked 1st. Over the course of the 613 dropbacks the team faced, that means the Bills pass defense finished 986 adjusted net yards above average (this is the statistic by which the table is sorted).

The Jets had, by a good margin, the toughest schedule in the NFL when it comes to facing opposing passers. In other words, it was not a good year for the Jets secondary to get decimated by injuries and departures. New York faced Rodgers, Roethlisberger, Peyton Manning, Brady, and Philip Rivers… and that was all before the bye week!

The Cowboys, meanwhile, had the easiest schedule in the NFL, courtesy of games against Blake Bortles, Jake Locker, RG3, Kaepernick, Austin Davis, and Colt McCoy.

Finally, take a look at those bottom three rows. One, it’s always startling to see the Bears and the Steelers at the bottom of any defensive rating system, although we may need to get used to that. But how about Washington? Allowing 35 touchdown passes against just 7 interceptions is a remarkable split, but the defense also ranked in the bottom three in pure net yards per attempt. Ouch.