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 2013.

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 in 2013 was 5.86, a slight downgrade from 2012 (5.93). Nick Foles led the way with a 9.18 ANY/A average last year, the highest rate in the league among the 45 passers with at least 100 dropbacks. Since the Eagles quarterback had 317 pass attempts and 28 sacks in 2013, that means he was producing 3.32 ANY/A (i.e., his Relative ANY/A) over league average on 345 dropbacks. That means Foles is credited with 1,145 Adjusted Net Yards above average, a metric labeled “VALUE” in the table below. Of course, Peyton Manning led the league in that category last year, with a whopping 2,037 Adjusted Net Yards over Average.

Manning paces in the field in Value over average, of course: that’s not surprising when the future Hall of Famer set the single-season record for passing yards and passing touchdowns. Foles, Drew Brees, and Philip Rivers formed the next tier of quarterbacks, far behind Manning but well ahead of the rest of the league.

And at the bottom of the list was the defending Super Bowl MVP, Joe Flacco. With a 4.50 ANY/A average, Flacco only edged out four other quarterbacks in that statistic, and none of the other passers came close to accumulating as many dropbacks as Flacco. After him comes the two New York quraterbacks, Geno Smith and Eli Manning.

But the point of today’s post is to adjust those numbers for strength of schedule. The solution is this post — a methodology I’ve labeled Rearview adjusted net yards per attempt, which 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 Matt Ryan, who averaged 5.72 ANY/A last season, on 695 dropbacks. If we want to find Ryan’s SOS-adjusted rating, we need an equation that looks something like this:

Rating_Ryan = 5.72 + (62/695) * (Rating_ARI-D) + (54/695) * (Rating_NE-D) + … (35/695) * (Rating_GB-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. Ryan’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. The Cardinals defense gets (initially) a +0.79 rating in 2013, because opposing QBs averaged 5.07 ANY/A against the Cardinals, which is 0.79 fewer ANY/A than league average.

If Ryan 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 Ryan’s rearview rating would be the same as his actual rating. If Ryan played a hard schedule (which he did), all the numbers on the right would sum to a positive number, and Ryan’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 the Arizona, New England, Green Bay, and all of the other defenses Ryan 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 all QBs with 100 attempts last season. Here’s how to read the Matt Ryan line. He averaged 5.72 ANY/A last year against a strength of schedule that was 0.64 ANY/A tougher than average. That ranked as the 3rd hardest SOS in the league (for SOS, 1 means the toughest and 45 the easiest). Ryan’s Adjusted ANY/A is therefore 6.36 (i.e., 5.72 + 0.64), which means he ranked 12th in Adjusted ANY/A. Finally, we can compute each quarterback’s Adjusted VALUE, based on his Adjusted ANY/A and number of pass plays. Ryan’s Adjusted Value is 344 yards (it was -103 before adjusting for SOS), which put him at #9 in the league.

Ryan had a brutally difficult schedule last year — he faced the insanely difficult Seahawks defense, along with two games against the 3rd hardest (Carolina). Throw in eight more games against defenses ranked 4th and 10th, and an incredible eleven of Ryan’s opponents were ranked in the top 10 in adjusted ANY/A allowed.

Kellen Clemens, Carson Palmer, and Colin Kaepernick all faced really difficult schedules. It seems like those guys probably have something in common.

Clemens and Sam Bradford provide an interesting comparison. They nearly evenly split Rams starts and pass attempts in half, but faced drastically different schedules. Bradford had the edge in ANY/A, 6.10 to 5.25, but Clemens faced a schedule that was the hardest in the league, while Bradford’s was easier than average. As a result, Clemens actually had the highested Adjusted ANY/A, 6.41 to 5.95. There’s a pretty simple explanation for that: Clemens was the quarterback for both Seahawks games (and fared miserably in both games), while Bradford was the quarterback for the four easiest games on the St. Louis schedule (Atlanta, Jacksonville, Dallas, and Houston).

Mike Glennon, like Ryan, faced a very difficult schedule, although he got to have two games against the anemic Atlanta defense. Along with Andrew Luck, Glennon was the only quarterback to produce an above-average game (without adjusting for SOS) against Seattle in 2013.

Peyton Manning had a very easy schedule last year, even after adjusting those defenses for the fact that they had to face Peyton Manning. He had five games against bottom five defenses (San Diego and Oakland twice each, Jacksonville), and just three games against top 12 defenses — with none of those games coming against top eight defenses! Of course, in his games against the #9, #11, and #12 defenses — i.e., the three best defenses he faced in the regular season — Manning threw for 1,166 yards, 13 touchdowns and no interceptions.

Eli Manning, Robert Griffin III, Tony Romo, and Alex Smith all had super easy schedules, too. That’s what happens when the NFC East and AFC West are on the schedules.

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 Seattle’s line: Seattle allowed 3.16 ANY/A last year and faced a schedule that was 0.05 ANY/A tougher than average. That ranked as the 15th most difficult schedule; after adjusting for SOS, the Seahawks allowed just 3.10 ANY/A, which ranked 1st. Over the course of 567 dropbacks faced, that means the Seattle pass defense finished 1,565 yards above average.

Tm ANY/A SOS SOS Rk Adj ANY/A Adj ANY/A Rk Adj Value DB Adj Val Rk SEA 3.16 0.05 15 3.1 1 1565 567 1 CIN 4.39 0.01 17 4.38 2 977 657 2 ARI 5.07 0.58 2 4.49 4 922 672 3 CAR 4.61 0.21 9 4.4 3 913 623 4 SFO 4.99 0.3 6 4.69 5 728 622 5 BUF 4.52 -0.26 27 4.79 6 664 618 6 MIA 5.24 0.02 16 5.21 8 404 621 7 NOR 5.31 0.15 12 5.15 7 393 554 8 NYG 5.08 -0.31 28 5.39 9 299 635 9 TAM 5.96 0.48 3 5.47 10 227 581 10 TEN 5.73 0.2 10 5.53 11 194 581 11 BAL 5.84 0.22 8 5.62 12 141 590 12 CLE 5.35 -0.32 29 5.67 13 124 642 13 KAN 5.46 -0.26 26 5.72 14 90 638 14 NWE 5.59 -0.26 25 5.85 15 11 637 15 STL 6.38 0.45 4 5.93 16 -40 574 16 IND 5.99 0.01 18 5.98 17 -69 577 17 CHI 6.27 0.12 14 6.15 18 -157 538 18 HOU 6.51 0.34 5 6.17 19 -159 514 19 WAS 6.83 0.58 1 6.25 20 -212 550 20 DET 6.19 -0.19 22 6.38 21 -310 604 21 PIT 5.83 -0.58 31 6.41 22 -330 603 22 NYJ 6.22 -0.21 23 6.43 24 -352 624 23 DEN 5.89 -0.52 30 6.41 23 -359 653 24 PHI 6.06 -0.59 32 6.64 25 -551 707 25 MIN 6.92 0.16 11 6.76 26 -618 688 26 GNB 6.93 -0.04 19 6.96 28 -640 582 27 DAL 6.98 0.13 13 6.85 27 -645 655 28 JAX 6.95 -0.12 21 7.07 29 -701 582 29 OAK 7.41 0.25 7 7.16 30 -759 587 30 SDG 7.04 -0.24 24 7.28 31 -824 583 31 ATL 7.45 -0.11 20 7.56 32 -927 546 32