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Adjusting for strength of schedule is important

Adjusting for strength of schedule is important.

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.

1Peyton ManningDEN45065954775510181206778.872037
2Nick FolesPHI2033172891272281733459.181145
3Drew BreesNOR44665051623912372446877.511130
4Philip RiversSDG37854444783211301505747.791107
5Aaron RodgersGNB1932902536176211173118665
6Josh McCownCHI149224182913111372358.54629
7Russell WilsonSEA2574073357269442724517.1555
8Tony RomoDAL34253538283110352725706.54384
9Colin KaepernickSFO2434163197218392314556.65358
10Matthew StaffordDET37163446502919231686576.4355
11Andy DaltonCIN36358642933320291826156.29265
12Ben RoethlisbergerPIT37558442612814422826266.24238
13Tom BradyNWE38062843432511402566686.13175
14Michael VickPHI7714112155315991566.93166
15Jay CutlerCHI22435526211912191323746.23136
16Andrew LuckIND3435703822239322276026.06120
17Sam BradfordSTL159262168714415972776.166
18Alex SmithKAN3085083313237392105475.9441
19Matt McGloinOAK1182111547886532175.9622
20Jake LockerTEN111183125684161051995.68-36
21Matt CasselMIN153254180711916852705.69-46
22Brian HoyerCLE5796615536481025.22-66
23Cam NewtonCAR29247333792413433365165.69-88
24Thaddeus LewisBUF93157109243181001755.35-89
25Ryan FitzpatrickTEN21735024541412211093715.62-90
26Matt RyanATL43965145152617442986955.72-103
27Carson PalmerARI36257242742422412896135.67-119
28Matt FlynnGNB124200139285241352245.32-121
29Case KeenumHOU137253176096192012725.4-126
30Kellen ClemensSTL142242167387211382635.25-162
31Jason CampbellCLE1803172015118161043335.32-182
32Robert GriffinWAS27445632031612382744945.48-188
33Christian PonderMIN152239164879271192664.75-296
34EJ ManuelBUF1803061972119281593344.87-330
35Josh FreemanTAM63147761248611553.61-349
36Kirk CousinsWAS81155854475321603.67-351
37Brandon WeedenCLE141267173199271802944.51-398
38Mike GlennonTAM2474162608199403144564.98-405
39Matt SchaubHOU21935823101014211623794.53-504
40Terrelle PryorOAK1562721798711312033034.09-537
41Chad HenneJAX30550332411314382435414.86-544
42Ryan TannehillMIA35558839132417583996465-559
43Eli ManningNYG31755138181827392815904.53-788
44Geno SmithNYJ24744330461221433154864.17-824
45Joe FlaccoBAL36261439121922483246624.5-904

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.1

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.

NameTmANY/ASOSSOS RkAdj ANY/AAdj ANY/A RkAdj ValueAdj Val Rk
Peyton ManningDEN8.87-0.44398.43217401
Drew BreesNOR7.510.3877.89513892
Nick FolesPHI9.18-0.36358.82110203
Philip RiversSDG7.79-0.28347.5169454
Aaron RodgersGNB80.18148.1837225
Russell WilsonSEA7.10.3397.4277036
Colin KaepernickSFO6.650.4847.1385787
Josh McCownCHI8.54-0.55437.9944998
Matt RyanATL5.720.6436.36123449
Tom BradyNWE6.130.25136.371133910
Matthew StaffordDET6.4-0.17266.241424411
Ben RoethlisbergerPIT6.240236.251324012
Andrew LuckIND6.060.14186.21520213
Andy DaltonCIN6.29-0.13246.161618314
Kellen ClemensSTL5.251.1616.411014415
Tony RomoDAL6.54-0.43386.111714116
Carson PalmerARI5.670.4266.091813717
Michael VickPHI6.93-0.41366.52910218
Cam NewtonCAR5.690.3486.04218919
Jay CutlerCHI6.23-0.17276.06207220
Matt CasselMIN5.690.32106.01223921
Thaddeus LewisBUF5.350.7226.08193722
Sam BradfordSTL6.1-0.15255.95232423
Brian HoyerCLE5.220.14175.3530-5224
Ryan FitzpatrickTEN5.620.03215.6524-8025
Matt McGloinOAK5.96-0.5425.4726-8626
Jake LockerTEN5.68-0.27335.4227-8927
Jason CampbellCLE5.320.1195.4228-14928
Case KeenumHOU5.4-0.2285.231-18029
Alex SmithKAN5.94-0.44405.525-20030
Mike GlennonTAM4.980.4355.4129-20931
Matt FlynnGNB5.32-0.84464.4839-31032
Josh FreemanTAM3.610.15163.7643-32533
Christian PonderMIN4.75-0.25324.5138-36134
EJ ManuelBUF4.87-0.21304.6636-40135
Chad HenneJAX4.860.25125.132-41136
Matt SchaubHOU4.530.17154.7135-43837
Kirk CousinsWAS3.67-0.57453.146-44338
Brandon WeedenCLE4.51-0.22314.2941-46139
Robert GriffinWAS5.48-0.56444.9334-46340
Ryan TannehillMIA50.1205.0933-49741
Terrelle PryorOAK4.09-0.47413.6344-67842
Geno SmithNYJ4.170.3114.4740-67843
Joe FlaccoBAL4.50.02224.5237-88944
Eli ManningNYG4.53-0.41374.1142-103245
  • 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.
  • 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.


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.

  • In Pennsylvania, the opposing quarterbacks were pretty easy in 2013. The Eagles and Steelers faced the two easiest slates of opposing quarterbacks. The Eagles got Kyle Orton, Scott Tolzien, and four games against Eli Manning and Robert Griffin. For Pittsburgh, it helped getting Matt Flynn, Brandon Weeden, Geno Smith, EJ Manuel, Joe Flacco twice, and Terrell Pryor (who also made Philadelphia’s schedule easier).
  • After adjusting for strength of schedule, the Falcons defense ranked 32nd in both adjusted ANY/A and adjusted Value. So if nothing else, today’s post should make you feel more sympathetic toward Matt Ryan’s 2013 season.
  1. As it turns out, Arizona’s defense was much tougher than that. []
  • Red

    In your GQBOAT article, Peyton Manning’s 2013 season had a SOS of -0.26, but here it’s listed at -0.44. Is the difference simply a matter of one being iterated while the other is not?

    That Seahawks defense was just unreal. Holy shit. As awful as Peyton looked in the SB, his ANY/A of 4.18 was still above average against that defense.

    I must say, I’m kinda surprised how much SOS variation there was among QB’s…is it like this every year? And damn, Eli had a super easy schedule and still sucked that bad. I hope 2013 will help bury his HoF chances, which he’s never deserved a sniff of to begin with.

    Typo alert – there are two instances where you typed “2012” when you meant “2013”; in the third paragraph from the top, and in the paragraph just below the Matt Ryan equation.

    Here’s a nitpicky suggestion for articles with charts: Could you display all numbers in a given column with the same number of decimal places? Visually speaking, it’s easier to compare 7.79 to 8.00 than 7.79 to 8, and it also looks more uniform and appealing.

    • I use Tablepress to make tables for my site too, and I can say that it truncates the numbers automatically. You can set everything to the hundreds decimal in Excel, but the import will just change 8.00 to 8 every time. It is a pretty easy fix on a table like this, but on something like Andreas’ estimated DVOA it would be a really tedious task.

    • Chase Stuart

      Thanks for the typo alert. Fixed.

      Re: the table suggestion, unfortunately, that’s how the tables default in table press. I can pass along your comments to the developer, though. I agree with you.

      Re: Manning, that’s interesting. At first I thought it was due to iteration, but that’s not the case (I’m rushing, but I think Manning’s uniterated SOS was also -0.44). So here’s the main difference. In this formula, the Ravens defense is considered 0.24 ANY/A better than average. In the GQBOAT formula, the Ravens defense was considered 0.63 ANY/A better than average. That’s a huge difference – and the reason is because Manning threw for 7 TDs against Baltimore. In the GQBOAT formula, I calculated the average of the defenses based on how they performed in the other 15 games. Here, that game counts for Baltimore, but it’s adjusted for SOS.

      Make sense? Thoughts?

      • Red

        Thanks for the clarification, makes sense once you explain it. If I had to choose, I’d actually pick the previous version over this one. I realize Peyton vs. BAL is an extreme example, but it doesn’t seem fair or logical to penalize a QB for his own great performance. Would it be possible to combine the two methods together, so a QB’s own games are removed but the remaining numbers are still being iterated? That seems like the best option, if it’s feasible.

  • Has this website done any entries about people who play better or worse in the playoffs (including Super Bowl) compared to the regular season? The regular season is like a 16 game first round of the playoffs.

    • Chase Stuart

      I have. Jeff Hostetler is the freakin’ man.

  • Max

    This is why pages and pages of stats are so boring. Peyton Manning on paper rocked the NFL (fantasy) world. Then the Seahawks beheaded him. That’s the lasting memory of last season. Peyton’s performance was bafflingly bad. Makes all these stats look like, well, paper.

    • Chase Stuart

      What about the pages of stats that said Seattle’s pass defense was the best in the NFL?

      • Or the pages of stats that said Seattle was clearly the better team?

    • Richie

      Excellent insight.

    • Tim

      You mean the game where Manning threw for almost 300 yards and set several SB records, including most completions? I submit that you did not watch the entire game, and have never watched another SB. There have truly horrendeous performance by All-Pro and even MVP QBs in the Super Bowl (see Morrall, Gannon for starters) that WAY worse than Manning’s. Your “last memory” is of something that really didn’t happen.

    • Red

      I love how people who hate statistics come to a statistically oriented site just to tell us how much they hate statistics.

      As I alluded to in an earlier comment, Manning’s performance was actually above average when you account for the Seahawks defense:
      Manning ANY/A = 4.18,
      Sea Def ANY/A = 3.10
      x 50 Dropbacks = 54 VALUE

      Just for fun, here’s Tom Brady in his SB 42 loss to the Giants:
      Brady ANY/A = 4.7
      NYG Def ANY/A = 5.4
      x 53 Dropbacks = -37 VALUE

      How come Brady gets a pass for having a leaky o-line vs. the Giants, but Manning gets crucified despite dealing with a pathetic o-line vs. the Seahawks?

      • Ty

        Let’s not feed the trolls, please.

      • Richie

        Because, ringz!

  • Ty

    This is something I would like to do for myself this season. How many games do you think I should wait for the SOS to “normalize” more? I’ve read that 4 games is a decent gauge of team performance.

  • Anders

    What I find crazy is that Foles is still 2nd and 3rd despite having like half the attempts of Bress and Manning

  • Nick Bradley

    Great adjustments, but you should probably adjust each individual game for opponent than jus doing it in the aggregate.

  • rob

    Chase is it possible for Excel to generate these values over say 4 game splits? Seeing the end of season results can obscure who was playing better near the end of the season and who was sliding down. I also think the SoS for defenses can change significantly as the season progresses, perhaps like KC’s D did.

    • Chase Stuart

      I suppose it could, although in general, I’m very skeptical of four-game sample sizes.