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Rearview Adjusted Yards per Attempt

Posted by Chase Stuart on August 23, 2007

In March, I ranked the 2006 NFL quarterbacks based on how many adjusted passing yards they accumulated. Adjusted passing yards are calculated by starting with raw passing yards, subtracting 45 yards for each interception thrown and adding 10 points for every touchdown pass. Adjusted yards is nothing new -- PFR has always posted lists of the top ten leaders in several statistics, and adjusted yards per attempt is one of those categories. Here's the list from this past season:

D McNabb 8.09
D Huard 7.96
P Manning 7.72
D Brees 7.55
T Romo 7.44
C Palmer 7.17
M Bulger 7.11
P Rivers 6.96
M Brunell 6.50
T Brady 6.26

If you have to use one statistic to rank quarterbacks, adjusted yards per attempt is probably the best one. It's "better" than quarterback rating in the sense that it more closely mirrors what quarterbacks are supposed to do to win games. But as we all know, not every quarterback faces the same schedule. It's not really fair to compare Peyton Manning to Drew Brees if one is playing the Ravens and the other the Bengals. Sure, over 16 games the variance in the strengths of opposing defenses gets pretty small, but it does not even out. The solution? Rearview adjusted yards per attempt, which adjusts for strength of schedule.

Doug and I have written a rearview QB article for our other website,, each of the past two years using fantasy points per game as our statistic. Finally, the light bulb went off in our heads to do the same process here, but using adjusted yards per attempt.

The system is essentially the same as the one used in the Simple Rating System. Let's look at Tony Romo, who averaged 7.44 yards per attempt last season, on 337 attempts. If we want to find Tony Romo's true rating, we need an equation that looks something like this:

    R_Romo = 7.44 + (29/337) * (R_phi) + (23/337) * (R_clt) + ... (36/337) * (R_was)

What's that formula say? Romo's true rating should equal his AY/A plus the rating of each defense he played multiplied by the number of pass attempts he had against that team. Since Romo threw 29 passes against the Eagles, 23 against the Colts and 36 against Washington, those numbers should be weighted accordingly. Each of the defenses will be assigned a rating based on how much tougher or easier they are on opposing QBs than the league average. Philadelphia had a +0.57 rating last year, which means that opposing QBs averaged 0.57 fewer yards per pass against them than against the rest of the league. So the R_phi would be +0.57. It's simply Romo's AY/A plus the weighted average rating of his opponent's adjusted yards per attempt allowed rating.

Therefore, an average quarterback playing an average schedule would have the league average 5.825 adjusted yards per attempt. If Romo 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 Romo's true rating would be the same as his actual rating. If he played an easy schedule (which he did), all the numbers on the right would sum to a negative number, and Romo's "moral" rating would be worse than what he actually did.

It wouldn't be that difficult to find Romo's rating if we knew all of his opponents’ ratings. But we can’t figure those out until we’ve figured out the ratings of all the QBs they've faced; after all, a team like Tennessee played Peyton Manning twice, Donovan McNabb, Tom Brady and Philip Rivers. They shouldn't be penalized for that, so we have to adjust Tennessee's defensive rating for strength of schedule, as well. But we can't do that until we figure out the ratings for Manning, McNabb, Brady and Rivers. As you can see, each QB's rating depends on each team's defensive rating, and vice versa.

Fortunately, Doug whipped up a formula that will iterate this strength of schedule adjustment process over and over again until the ratings no longer change. That's when we know we've finally reached the "morally accurate" ratings for each QB and each team defense.

With that out of the way, here's a list of all QBs with 100 attempts last season, with their SOS adjusted yards per attempt on the left, their actual adjusted yards per attempt in the middle column, and their SOS adjustment on the far right. A positive number indicates a hard schedule, and a negative number indicates an easy schedule.

player adjAY/A actAY/A SOS rating
Donovan McNabb 7.92 8.09 -0.17
Peyton Manning 7.87 7.72 0.15
Damon Huard 7.73 7.96 -0.24
Carson Palmer 7.37 7.17 0.20
Drew Brees 7.36 7.55 -0.19
Tim Rattay 7.23 6.91 0.32
Tony Romo 7.02 7.44 -0.42
Jeff Garcia 6.99 7.02 -0.02
Philip Rivers 6.98 6.96 0.02
Marc Bulger 6.91 7.11 -0.21
Mark Brunell 6.78 6.50 0.29
Kurt Warner 6.69 7.21 -0.52
Tom Brady 6.47 6.26 0.22
J.P. Losman 6.33 6.09 0.25
Chad Pennington 6.12 5.78 0.35
Daunte Culpepper 6.07 6.07 -0.01
David Garrard 6.05 5.93 0.12
Ben Roethlisberger 5.89 5.67 0.22
Jay Cutler 5.88 6.32 -0.44
Jon Kitna 5.81 5.75 0.06
Matt Leinart 5.69 5.61 0.08
Steve McNair 5.68 5.70 -0.02
Trent Green 5.68 5.09 0.59
David Carr 5.64 5.29 0.35
Jake Delhomme 5.41 5.75 -0.35
Brett Favre 5.27 5.31 -0.04
Byron Leftwich 5.25 5.49 -0.24
Drew Bledsoe 5.18 5.17 0.01
Michael Vick 5.16 5.38 -0.22
Vince Young 5.16 4.86 0.30
Alex Smith 5.16 5.27 -0.12
Matt Hasselbeck 5.12 5.25 -0.13
Eli Manning 5.06 5.12 -0.06
Jake Plummer 5.05 4.79 0.26
Jason Campbell 5.04 5.44 -0.41
Rex Grossman 5.01 5.26 -0.24
Seneca Wallace 4.85 4.91 -0.06
Brad Johnson 4.82 4.93 -0.11
Joey Harrington 4.72 4.33 0.38
Charlie Frye 4.55 4.56 -0.02
Derek Anderson 4.21 4.13 0.08
Andrew Walter 4.00 4.06 -0.07
Bruce Gradkowski 3.93 4.10 -0.17
Aaron Brooks 3.71 4.04 -0.32
Chris Simms 2.21 2.64 -0.43

If I was going to make a guess as to how many adjusted yards per attempt each QB would average this season, the above list would be my starting point. Manning, McNabb and Palmer, three of the best QBs in the league, come out on top. It's a bit surprising to see Damon Huard rank highly, but it's hard to argue with his numbers from last year. He had the lowest interception rate of any quarterback since 1960, throwing just one interception in 244 pass attempts.

Perhaps a more interesting way to look at the QBs would be to check just their schedule:

Trent Green 0.59
Joey Harrington 0.38
David Carr 0.35
Chad Pennington 0.35
Tim Rattay 0.32
Vince Young 0.30
Mark Brunell 0.29
Jake Plummer 0.26
J.P. Losman 0.25
Ben Roethlisberger 0.22
Tom Brady 0.22
Carson Palmer 0.20
Peyton Manning 0.15
David Garrard 0.12
Derek Anderson 0.08
Matt Leinart 0.08
Jon Kitna 0.06
Philip Rivers 0.02
Drew Bledsoe 0.01
Daunte Culpepper -0.01
Charlie Frye -0.02
Jeff Garcia -0.02
Steve McNair -0.02
Brett Favre -0.04
Seneca Wallace -0.06
Eli Manning -0.06
Andrew Walter -0.07
Brad Johnson -0.11
Alex Smith -0.12
Matt Hasselbeck -0.13
Donovan McNabb -0.17
Bruce Gradkowski -0.17
Drew Brees -0.19
Marc Bulger -0.21
Michael Vick -0.22
Damon Huard -0.24
Byron Leftwich -0.24
Rex Grossman -0.24
Aaron Brooks -0.32
Jake Delhomme -0.35
Jason Campbell -0.41
Tony Romo -0.42
Chris Simms -0.43
Jay Cutler -0.44
Kurt Warner -0.52

Jay Cutler had the second easiest schedule in the league last year, while Jake Plummer had one of the harder ones. Tony Romo and Jason Campbell were young QBs that put up impressive numbers, but both played easy schedules. Really, we don't know too much about either QB just yet. And maybe, just maybe, Trent Green isn't finished after all. His numbers were very close to the league average last season, he just faced an impossible schedule -- while Damon Huard got to play the easy opponents. He's not exactly moving into an easy division, though. Look at the AFC East QBs last year -- Harrington, Brady, Pennington and Losman all had very difficult schedules. None had great numbers, and a tough schedule was one of the reasons why.

What about the defenses? The table below shows how many yards per attempt each defense allowed last year, relative to the league average. The middle column shows that the Bears actually allowed 1.56 AY/A below the league average last season. But since Chicago faced an easier than average string of QBs, their SOS rating was -0.13. Therefore, the Bears were "morally" just 1.43 adjusted yards per pass better than the league average. The Jaguars move the other way; Jacksonville faced Peyton Manning twice, Donovan McNabb, Damon Huard and a bunch of pretty good QBs. Despite that, they still were 1.04 AY/A better than the league average, but they shoot way up and almost catch the Bears when adjusting for strength of schedule.

team adjR actR SOSR
chi 1.43 1.56 -0.13
jax 1.36 1.04 0.32
rai 1.00 1.03 -0.03
rav 0.89 1.13 -0.25
nwe 0.76 0.82 -0.06
phi 0.57 0.76 -0.19
clt 0.57 0.43 0.15
den 0.49 0.28 0.21
cle 0.48 0.27 0.21
nyg 0.36 0.14 0.21
gnb 0.33 0.32 0.01
pit 0.31 0.29 0.02
buf 0.27 0.20 0.07
min 0.25 0.42 -0.17
ten 0.24 -0.28 0.52
sdg 0.10 0.19 -0.09
nyj 0.08 0.32 -0.24
car 0.04 0.19 -0.15
dal -0.15 -0.38 0.23
mia -0.28 -0.48 0.20
cin -0.39 -0.33 -0.06
sea -0.46 -0.54 0.08
kan -0.50 -0.16 -0.33
sfo -0.54 -0.81 0.27
nor -0.61 -0.27 -0.34
ram -0.67 -0.26 -0.41
hou -0.70 -0.86 0.15
tam -0.73 -0.85 0.12
crd -0.87 -0.83 -0.05
det -1.06 -0.84 -0.22
atl -1.36 -1.09 -0.27
was -1.43 -1.62 0.18

The Redskins last year were just pitiful against the pass, but at least they had a tough schedule to take (a small) part of the blame. Washington pulled off the rare double 32s, ranking dead last in interceptions (6) and touchdown passes allowed (30). That might explain why LeRon Landry, the defensive back out of LSU, was Washington's first round draft pick in April. Atlanta goes the other way; the Falcons looked bad against the pass in '06, but were actually even worse than they looked. Only a historically bad year by Washington kept Atlanta out of the basement.

The Titans' pass defense looked below average at first glance, but Tennessee was actually one of the better pass defenses last year. The 49ers added Tully Banta-Cain, Nate Clements, Michael Lewis and Patrick Willis in the off-season, in the hopes of giving their weak defense a boost. And while those additions will get the credit if San Francisco improves this year, note that the 49ers weren't that bad against the pass in 2006, either. They just looked awful because they played McNabb, Huard, Brees and Rivers, along with facing Bulger and Warner twice. Across the Bay, the Raiders look legit. Sure, Oakland allowed the fewest passing yards in the league because the Raiders had a miserable offense and opposing teams never needed to pass on them. But Oakland also ranks third here in SOS-adjusted yards per attempt allowed, which indicates that on a per-attempt basis, they were extremely very effective. Remember, that unit intercepted 18 of the 401 passes thrown against them last year, one of the best five rates in the league.

This entry was posted on Thursday, August 23rd, 2007 at 2:47 am and is filed under General. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.