Every year at Footballguys.com, I publish an article called Rearview QB, which adjusts quarterback (and defense) fantasy numbers for strength of schedule. I’ve also done the same thing using ANY/A instead of fantasy points, and today I revive that concept for the 2012 season.

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 2012 was 5.93. Peyton Manning averaged 7.89 ANY/A last year, the highest rate in the league among the 39 passers with at least 75 attempts. Since the Broncos star had 583 pass attempts and 21 sacks in 2012, that means he was producing 1.96 ANY/A over league average on 604 dropbacks. That means Manning is credited with 1,185 Adjusted Net Yards above average, a metric I simply call “VALUE” in the table below. Manning led the league in that category, with Tom Brady, Drew Brees, Aaron Rodgers, and Matt Ryan rounding out the top five. Remember, the ANY/A and VALUE results aren’t supposed to surprise you, so it makes sense that the best quarterbacks finish near the top in this category every year.

At the bottom of the list is Mark Sanchez, although that’s partly a function of the fact that he kept his job most of the year: both quarterbacks in Arizona and Kansas City averaged fewer ANY/A, but since those quarterbacks shared reps, none of them individually produced as much negative value as Sanchez.

We can also do the same thing for team defenses. These stats differ slightly from official numbers, because I am only including pass attempts by opposing quarterbacks (and not all opposing players). Kansas City’s pass defense was the worst in the NFL in 2012, which helps to explain why they ended up with the number one pick.

But you guys can get the information in the above tables anywhere (but should get it from PFR). The point of today’s post is to adjust those numbers for strength of schedule. It’s not really fair to compare Peyton Manning when he plays the Chiefs to Aaron Rodgers against the Bears. Sure, over 16 games the variance in the strengths of opposing defenses gets pretty small, but it does not even out. 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 Tom Brady, who averaged 7.48 ANY/A last season, on 664 pass plays. If we want to find Brady’s SOS-adjusted rating, we need an equation that looks something like this:

Rating_Brady = 7.48 + (68/664) * (Rating_SF-D) + (59/664) * (Rating_SEA-D) + … (35/664) * (Rating_DEN-D)

What’s that formula say? Brady’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. Since Brady threw 65 passes and was sacked three times against the 49ers, had 59 pass plays against the Seahawks, and 35 against the Broncos, those numbers must be weighted accordingly. 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 49ers defense gets (initially) a +1.09 rating in 2012, because opposing QBs averaged 4.84 ANY/A, which is  1.09 fewer ANY/A than league average. So the Rating_SF-D variable would (initially) be +1.09 in the above formula.

If Brady 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 Brady’s rearview rating would be the same as his actual rating. If Brady played a hard schedule (which he did), all the numbers on the right would sum to a positive number, and Brady’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 49ers, Seahawks, Broncos, and all of the other defenses Brady faced, but we can’t figure those ratings out until we’ve figured out the ratings of all the quarterbacks those teams faced; after all, a team like the Giants played Aaron Rodgers, Robert Griffin III (twice), Drew Brees, Alex Smith/Colin Kaepernick, Matt Ryan, Ben Roethlisberger, Cam Newton, Tony Romo (twice), Joe Flacco, Josh Freeman, Andy Dalton, Mike Vick (twice), and Brandon Weeden. New York’s defense shouldn’t be penalized for facing such a difficult schedule, so we have to adjust the Giants defensive rating for strength of schedule as well. But we can’t do that until we figure out the ratings for Rodgers, Griffin, Brees, etc. 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 D, adjusting each D’s rating for each D’s SOS, then adjusting each QB again, and then each D against) 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 75 attempts last season. Here’s how to read the Brady line. He averaged 7.48 ANY/A last year against a strength of schedule that was 0.26 ANY/A tougher than average. That ranked as the 9th hardest SOS in the league (for SOS, 1 means the toughest and 39 the easiest). Brady’s Adjusted ANY/A is therefore 7.74 (7.48 + 0.26). Brady ranked 2nd in Adjusted ANY/A behind only Kaepernick (who had only 35% as many attempts). Finally, we can compute each quarterback’s Adjusted VALUE, based on his Adjusted ANY/A and number of pass plays. Brady’s Adjusted Value is 1,203 yards (it was 1,028 before adjusting for SOS), which ranked him #1 in the league.

Peyton Manning drops from 1st in VALUE to 3rd in Adjusted VALUE, by virtue of having faced the 2nd easiest schedule in the league. Some other items that stuck out to me from the above table:

• The Arizona quarterbacks were terrible last year, but they also faced a brutal schedule. In fact, the five NFC West quarterbacks faced the five toughest schedules last year, playing each other, the NFC North, and the AFC East.
• Adrian Peterson was a worthy MVP choice last year, but based on this analysis, Tom Brady would have been a legitimate candidate. His campaign had little juice last year, but the difference between his and Manning’s schedules was particularly significant in 2012. As a reminder, you can get in on the latest Football Perspective contest by projecting Brady’s 2013 numbers here.
• Chad Henne certainly seemed better than Blaine Gabbert last year, but after adjusting for SOS, Gabbert actually ranked above him in both Adjusted ANY/A and Adjusted Value. Henne had one absurdly incredible performance — more on that tomorrow — but he also had five games where he “produced” more than 100+ Adjusted Net Yards below average (the worst being a 21/43, 185-yard, 0 TD, 2 INT, 3 sack game against the Jets).
• Matt Ryan had a career season in 2012, but it was certainly inflated by an easy schedule (not to mention superstar teammates). Ryan had only four games against above-average defenses. One of them was the five-interception disaster against the toughest pass defense he faced (Arizona). He played well in the other three games (againts Denver and Carolina twice), but still finished with fewer than 7.0 ANY/A in those games.
• Like the NFC West, the NFC North quarterbacks generally had it tough, especially those who had to play the Bears defense (Jay Cutler had to instead deal with the Chicago offensive line). In this light, Matt Stafford’s efficiency numbers go from slightly below average to slightly above, giving more ammunition to the pro-Stafford crowd.

Adjusted defenses for Strength of Schedule

In the process of adjusting quarterback numbers for strength of schedule, we have done all the work we ned to adjust each defense’s numbers for strength of quarterback. And as hinted to above, no defense faced a harder schedule than the Giants in 2012. But strength of schedule adjustments only serve to make the Bears defense look even better. The Bears allowed 4.25 ANY/A last year against an Aaron Rodgers and Matt Stafford-fueled schedule that was 0.10 ANY/A tougher than average (Chicago faced the 13th toughest schedule). That means the Bears allowed only 4.15 Adjusted ANY/A, easily the best rate in the league. Chicago’s 1,123 adjusted net yards of value was also the highest mark in the league.

• Many Jets fans have begun treating Darrelle Revis like a cheating ex-girlfriend, which comes with it the usual lies and misinformation. The most often-cited statistic is that even without Revis in 2012, the Jets pass defense was still the 2nd best in the league. But that’s hardly the case: New York ranked 2nd in passing yards allowed, sure, but that’s because the Jets were often losing (ranking 26th in Game Scripts and 6th in time spent trailing) and faced an easy schedule. The Jets ranked 10th in ANY/A allowed (from the earlier table) against the 21st toughest (or 12th easiest) schedule in the league. In terms of Adjusted ANY/A and Adjusted VALUE, the Jets defense was 12th, a much more accurate representation of the Jets pass defense without Revis than New York’s 2nd-place ranking in passing yards allowed.
• Like the Jets, the rest of the AFC East defenses had easy schedules (and also got to play Mark Sanchez). The Bills had the easiest SOS in the league: outside of games against the Patriots, 49ers, and Seahawks, Buffalo faced game managers or worse every week. The three high-attempt games came against Brandon Weeden, Chad Henne, and Matt Cassel, while the team also got to enjoy against Arizona, Kansas City, and two against the Jets.
• Remember that the five NFC West quarterbacks faced the five hardest schedules? All four NFC West defenses ranked in the top six in both Adjusted ANY/A and Adjusted Value.
• The Colts defense was really bad last year. In addition to finishing 31st in yards per carry allowed, the Colts pass defense ranked 28th in Adjusted ANY/A allowed, too. Only an easy strength of schedule covered that fact, and the Colts rode the league’s easiest overall schedule (along with some luck and some Andrew Luck) to an 11-5 record and the playoffs.

Previous “Random Perspective On” Articles:
AFC East: Buffalo Bills, Miami Dolphins, New England Patriots, New York Jets
AFC North: Baltimore Ravens, Cincinnati Bengals, Cleveland Browns, Pittsburgh Steelers
AFC South: Houston Texans, Indianapolis Colts, Jacksonville Jaguars, Tennessee Titans
AFC West: Denver Broncos, Kansas City Chiefs, Oakland Raiders, San Diego Chargers
NFC East: Dallas Cowboys, New York Giants, Philadelphia Eagles, Washington Redskins
NFC North: Chicago Bears, Detroit Lions, Green Bay Packers, Minnesota Vikings
NFC South: Atlanta Falcons, Carolina Panthers, New Orleans Saints, Tampa Bay Buccaneers
NFC West: Arizona Cardinals, San Francisco 49ers, Seattle Seahawks, St. Louis Rams