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Friend of the program Bryan Frye is back for another guest post. As regular readers know, Bryan operates his own fantastic site, http://www.thegridfe.com. You can view all of Bryan’s guest posts here, and follow him on twitter @LaverneusDingle.

Floating around the internet, there are copious metrics for measuring quarterback performance. Some are very basic (passing yards, completion rate), while others are quite complex (EPA, WPA). Some are open-source (passer rating, ANY/A), while others are proprietary (DVOA, Total QBR). It seems there is a stat to cover just about every aspect of QB play, so the last thing we need is another useless number.

Well, I didn’t get that memo.

Today, I’m going to look at a somewhat abstract measurement for career value, based on adjusted yards per attempt relative to league average. I prefer ANY/A and my own TAY/P (and the different iterations of both metrics), but gaps in the record books mean we can only go so far with either.1 With AY/A, we can go back to 1932, the very first season of the “official stat” era in the NFL.

The methodology is simple and straightforward. I took Pro Football Reference’s AY/A Index Scores for every quarterback with at least 1500 career pass attempts. If you are familiar with PFR’s advanced passing stats, you know they are based on three seasons’ worth of data (years n-1, n, and n+1), and a score of 100 represents league average output.2 To find the AY/A+ score itself, you simply multiply a player’s z-score by fifteen and add the product to 100. Using this knowledge, I reverse engineered the passing Index Scores in order to find the number of standard deviations above or below average each quarterback’s AY/A was. I then multiply that number by pass attempts to come up with an abstract career value metric. I also did this for replacement level, using one standard deviation below average as the baseline for replacement play.

The formulas:

Value over average = [(AY/A Index Score – 100)/15]*Attempts

Value over replacement = [(AY/A Index Score – 85)/15]*Attempts

Like I said, this isn’t forking any lightning in the realm of quarterback analysis. It’s just a quick and dirty way to approximate career productivity based on a well-known metric.

The Results

The table below shows the abstract career value of the 182 quarterbacks who met the 1000 attempt threshold. Read it thus: Peyton Manning played 266 career games and had 9380 pass attempts. His career AY/A+ score was 116. This gives him a total value of 10005 above average and 19385 above replacement (this is the metric by which the table is sorted). Note that the table below does list all 182 quarterbacks, but for ease of scrolling, only the top 25 are displayed by default. You can change that using the dropdown arrow on the left, or you can search for your favorite passer.

1Peyton Manning26693801161000519385
2Tom Brady2257792115779215584
3Dan Marino2428358112668615044
4Drew Brees2178085112646814553
5Brett Favre30210169106406814237
6Joe Montana1925391118646911860
7Steve Young1694149125691511064
8Fran Tarkenton2466467110431110778
9Aaron Rodgers1264047124647510522
10Ben Roethlisberger1715423114506110484
11Dan Fouts1815604113485710461
12John Elway2347250106290010150
13Warren Moon2086823107318410007
14Philip Rivers164533911346279966
15Johnny Unitas211518611138038989
16Tony Romo155433111646208951
17Kurt Warner124407011643418411
18Ken Anderson192447511338788353
19Jim Kelly160477911031867965
20Donovan McNabb167537410725087882
21Len Dawson211374111639907731
22Otto Graham126262612950777703
23Boomer Esiason187520510724297634
24Sonny Jurgensen218426211131257387
25Roger Staubach131295812243387296
26Carson Palmer160544310518147257
27Dave Krieg213531110517707081
28Y.A. Tittle204439510926377032
29Phil Simms164464710721696816
30Mark Brunell193464010721656805
31Trent Green120374011229926732
32Sammy Baugh165299511835946589
33Roman Gabriel183449810617996297
34Eli Manning185622710006227
35Rich Gannon157420610719636169
36Steve McNair161454410515156059
37Craig Morton207378610922726058
38Randall Cunningham161428910617166005
39Troy Aikman165471510412575972
40Bob Griese161342911125155944
41John Hadl224468710412505937
42Jim Everett15849231039855908
43Jeff Garcia125367610922065882
44Drew Bledsoe194671798-8965821
45Vinny Testaverde233670198-8935808
46Matt Ryan126453010412085738
47Terry Bradshaw168390110718205721
48Bart Starr196314911225195668
49Norm Van Brocklin140289511427025597
50Jim Hart20150761013385414
51Daunte Culpepper105319911021335332
52Matt Hasselbeck209533010005330
53Neil Lomax108315311021025255
54Joe Theismann167360210614415043
55Jeff George131396710410585025
56Ron Jaworski18841171038234940
57Chris Chandler18040051038014806
58Ken O'Brien129360210512014803
59Matt Schaub141327110715264797
60John Brodie20144911012994790
61Joe Namath140376210410034765
62Bobby Layne17537001049874687
63Steve Beuerlein147332810613314659
64Jay Cutler13443541012904644
65Brad Johnson17743261012884614
66Steve Bartkowski129345610511524608
67Steve Grogan14935931049584551
68Neil O'Donnell125322910612924521
69Bernie Kosar126336510511224487
70Brian Sipe12534391049174356
71Steve DeBerg206502498-6704354
72Daryle Lamonica151260111017344335
73Danny White166295010713774327
74Earl Morrall255268910916134302
75Ken Stabler18437931025064299
76Bert Jones102255111017014252
77Marc Bulger96317110510574228
78Kerry Collins198626195-20874174
79Russell Wilson64173512124294164
80Sid Luckman128174412023254069
81Billy Kilmer17029841059953979
82Chad Pennington89247110914833954
83Jim Harbaugh177391810003918
84Charley Johnson16533921024523844
85Charlie Conerly16128331059443777
86Jim Plunkett157370110003701
87Michael Vick14332171024293646
88Joe Ferguson186451997-9043615
89Cam Newton78241910711293548
90Joe Flacco122407098-5433527
91Mark Rypien10426131058713484
92Norm Snead178435397-8713482
93George Blanda340400798-5343473
94Jeff Blake11932411012163457
95Matthew Stafford93369199-2463445
96Don Meredith104230810710773385
97Jay Schroeder11828081035623370
98Aaron Brooks9329631023953358
99Lynn Dickey15231251012083333
100Jake Delhomme10329321023913323
101Jeff Hostetler15223381069353273
102Frank Ryan126213310811383271
103Bill Kenney10624301058103240
104Greg Landry14623001069203220
105Tommy Kramer129365198-4873164
106Archie Manning151364298-4863156
107Alex Smith126361998-4833136
108Jim McMahon11925731035153088
109Brian Griese9327961011862982
110Jim Zorn140314999-2102939
111Bobby Hebert118312199-2082913
112Jake Plummer143435095-14502900
113Gus Frerotte147310699-2072899
114David Garrard8622811046082889
115Babe Parilli189333098-4442886
116Jack Kemp122307399-2052868
117Billy Wade12825231023362859
118Gary Danielson10119321067732705
119Doug Williams8825071011672674
120Bill Nelsen9019051067622667
121Jon Kitna141444294-17772665
122Andy Dalton7724971011662663
123Elvis Grbac10524451011632608
124Stan Humphries88251610002516
125Chris Miller98289298-3862506
126Wade Wilson125242810002428
127Milt Plum129241910002419
128Tom Flores10617151066862401
129Tobin Rote149290797-5812326
130Doug Flutie9221511011432294
131Bob Waterfield9116171066472264
132Frankie Albert9015641066262190
133Scott Mitchell99234699-1562190
134Erik Kramer83229999-1532146
135Ed Brown15419871011322119
136Bill Munson10719821011322114
137Tony Eason9015641055212085
138Jason Campbell90251897-5042014
139Kyle Orton87271296-7231989
140Richard Todd119296795-9891978
141Andrew Luck55210699-1401966
142Rodney Peete104234697-4691877
143Eddie LeBaron134179610001796
144Tony Banks96235696-6281728
145Ryan Tannehill64224896-5991649
146Cotton Davidson111175299-1171635
147Ryan Fitzpatrick113347392-18521621
148Charlie Batch81160410001604
149Jay Fiedler76171799-1141603
150Mike Livingston91175197-3501401
151Bubby Brister99221294-8851327
152Byron Leftwich60160597-3211284
153Don Majkowski90190595-6351270
154Steve Bono88170196-4541247
155Mike Tomczak185233793-10911246
156Matt Cassel100257492-13731201
157Marc Wilson126208193-9711110
158Sam Bradford63229292-12221070
159Josh McCown77195693-9131043
160Eric Hipple102154695-5151031
161Dan Pastorini140305590-20371018
162Vince Ferragamo75161594-646969
163Josh Freeman62204892-1092956
164Kordell Stewart125235891-1415943
165Trent Dilfer130317289-2326846
166Tim Couch62171492-914800
167David Carr94226790-1511756
168Mark Sanchez75226789-1662605
169Derek Anderson68154390-1029514
170Billy Joe Tolliver79170789-1252455
171Rex Grossman54156289-1145417
172Chad Henne64195488-1563391
173Frank Tripucka75174588-1396349
174Dave Brown73163488-1307327
175Mike Pagel132150986-1408101
176Kyle Boller67151983-1722-203
177Jack Trudeau67164483-1863-219
178Mike Phipps119179983-2039-240
179Mark Malone73164882-1978-330
180Joey Harrington81253882-3046-508
181Rick Mirer80204381-2588-545

I normally like to point out a few curiosities I notice in the data, but I’d rather just present the numbers and leave the comments to the readers. What sticks out to you? Oh, and one note: back in 2006, Chase did some back-of-the-envelope calculations that had Rick Mirer as the worst quarterback of all time. 10 years later, not much has changed.

  1. Pro-Football-Reference doesn’t have ANY/A prior to 1969. I don’t have TAY/P prior to 1991; even without including first down data, I can only go back to 1963 before I run out of complete sack data. []
  2. Except in 1932, when there is no year n-1, and the current year, when there is no n+1. []
  • Adam

    Sometimes the quick and dirty method can still tell us a lot, which I think this does. Says a great deal about Manning and Marino that they rank 1st and 3rd despite ignoring their best statistical attribute (sack avoidance).

    • Yea, they were basically good at everything a QB can do with his arm. Great Y/A, great completion rate, great TD%, and good INT%. I don’t have all of Marino’s career on a granular level, but even after 1992 (well past his statistical prime), he fares quite well in career New TAY/P http://www.thegridfe.com/2016/04/01/career-ntayp-since-1992/

      If you look at the PFR Index stats for each player, it’s pretty nuts. They have no rating below 105, between the two of them (Manning’s int%). While Peyton has the low number, he is over a full standard deviation ahead of the league is every other index stat. Great quarterbacks.

  • WR

    I was going to post a comment about how Rodgers was being overrated because of his strong rate stats, and then I realized that I was looking at the value over average column. The val over replacement column does a good job of minimizing the impact of strong AY/A+ figures, and moves Brees and Montana back ahead of Rodgers, where I feel they belong.

    But anytime you do an exercise like this, you’re going to run into the rate stats v. volume conundrum. This exercise rates Marino significantly ahead of Montana, but also shows that when Montana was actually on the field, he was outperforming the Dolphins quarterback. And Montana was already ahead by AY/A+ before Marino’s mini-decline after 1996. So do you reward the guy with the longer career, or the higher rate of production? It’s a tough one.

    • I’d say that Rodgers might be a bit overrated from his rate stats, but that has a lot to do with the fact that he doesn’t have a great deal of early career volume, which mitigates the effect of what is often poorer play. He also is still in his prime and hasn’t hit the downturn of his career (presumably). His entire career basically comprises prime years, so I expect his index stats to fall as he plays some non-prime seasons (or more seasons like 2015).

      The volume vs rate conundrum always comes into play on exercises like this. I recall Chase asking the commenters for their input on how to deal with the significantly increased volume of modern passers versus older ones. I personally think that the way the value and replacement columns rank Montana and Marino is fine, given the aim of the two metrics. While Montana did produce at a higher rate when on the field, he was on the field a lot less; the difference in pass attempts between Marino and Montana is almost equal to Sammy Baugh’s entire career. Those extra attempts are extra value added.

      It’s kind of like this: when I was in high school, I used to charge $25 an hour for general maintenance work. I also had an actual job that paid $12.50 an hour. The higher paying gigs were rarer, whereas the lower paying job was steady and guaranteed. Despite my side project earning me twice the money per hour, I made much more money from my steady job. This is overly simplistic, obviously; Montana wasn’t twice the QB Marino was. But for the sake of example, Marino was my steady job.

      • WR

        If you want to rate Marino ahead of Montana because of the diff in volume, I’m Ok with that. But let me try to illustrate why I’m not convinced. For his career, Marino is at 112 ay/a+ and 8358 attempts. But from 1997-1999, Marino was at 100 ay/a+. If you take away those final 3 seasons and look at Marino from 83-96, his ay/a+ figure improves to 115, but his number of attempts is reduced to 6904. Now that’s still significantly more than Montana, who has 5391, but it’s significantly closer, and Montana is still ahead by rate stats. So when evaluating a player, how much is 3 seasons at league-average production really worth? Those last 3 years of Marino clearly weren’t vintage Marino, but if you’re putting big emphasis on volume, 8358 attempts looks a lot better than 6904. But that increase in volume for Marino is not indicative of Marino maintaining a high level of production, but of sticking around for a few years as an average QB.

        One way to account for this might be to look at each player’s 10 best consecutive seasons, or best 150 consecutive games, which would serve to eliminate drops in rate stats due to decline at the end of a career, or weaker seasons at the start of a career.

        • Believe me, I don’t “want” to rate Marino ahead of Montana; Montana is my favorite quarterback, and I’d love to put him at the top of every list. However, with the very limited scope of this metric, Marino belongs ahead. His volume gap was enormous, and he was clearly adding more value to the Dolphins then Montana was to the 49ers and Chiefs by mere virtue of the fact that he started 76 more career games. Montana was generally better when he was on the field (excepting 1984), but he only played two 16-game seasons in his entire career. He wasn’t the same, physically, after 1986, and he missed way too much time (and was often outplayed by Steve Young in relief).

          When we’re talking about Dan Marino playing three seasons at the end of his career at a “league average level,” we are in implicit agreement that he played three seasons above replacement level. His last two seasons, in particular, weren’t good, but they did have value. League average QB play is important and is often underrated.

          I don’t have AY/A+ on a game by game level, but I can give you the ten best consecutive seasons from each player. From 1983-1992, Marino’s Val was 5122 and his Repl was 10406. From 1981-1990, Montana’s Val was 5864 and his Repl was 10147. However, outside of his ten best seasons, Montana only had another 1108 pass attempts, compared to Marino’s 3074. There was much value above replacement in those extra 1966 passes.

          We’ll call years not in their top 10 “non-prime” years. Looking at Repl, Marino had non-prime seasons with 1107, 1028, 845, and 767 abstract AY/A+ points. Montana’s best non-prime season was worth 657 such points. Again, this is strictly referring to total value above replacement (and ignoring playoffs, which would likely swing some seasons to Montana).

          Here’s a chart with each individual season from their careers. Note that the way the formula works causes the result from using entire career inputs to be different from the result of summing individual season inputs. I included both so you could decide which you prefer.

  • I think this methodology — which you emphasized is quick-and-dirty — mostly makes sense, but it cries out for era regression or length-of-season adjustment. I realize AY/A+ is compared to league, but holy cow, this list is dominated by current players.

    * Three of the top four, and five of the top 10, were active from 2005-15.
    * None of the top 14 ever played 12-game seasons, even though those make up more than a third of the seasons surveyed.
    * Fran Tarkenton is the only one in the top 14 who never played 16-game seasons, which account for less than half of the seasons surveyed.
    * Sammy Baugh (32), Norm Van Brocklin (49), and Sid Luckman (80) are the only players in the top 100 who never played 14-game seasons.
    * Russell Wilson is ranked ahead of Luckman, who won as many championships (4) as Wilson has seasons.
    * This is an 84-year project, but 10 of the top 20 were active in 2008. Zero of the top 20 were active in the first 20 years surveyed. Two of the top 20 were active in the first 40 years surveyed.

    Using number of pass attempts as a key part of the formula favors QBs who played longer schedules, and it favors those from eras when rule changes facilitated passing. That’s probably appropriate up to a point, because QBs are probably more important now, but I don’t think it works to compare disparate eras. I would take numbers 127-132 over 63-68, easily. I’d be cautious of framing this as an all-time ranking. I’d rather see a better metric over a shorter time period — going back to 1932 didn’t really get you anything.

  • Hamiltonian_Conservative

    The total value above average (“Val”) figure adds to the mountain of statistical data, traditional and advanced, indicating John Elway tends to be grossly overrated in “greatest QB” lists and discussions. Elway is only 25th in total value above average, behind guys like Romo, Anderson, Kelly, Moon, and even Trent Green. He fares better (12th) when the baseline is lowered to total value above replacement (“Repl”), though he is about to be surpassed by both Rivers and Romo. Both AY/A+ metrics suggest Elway’s Hall of Fame career owed more to longevity than brilliance.

    Great player nonetheless, but his reputation is significantly inflated.

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