≡ Menu
Can you spot the GOAT?

Can you spot the GOAT?

In 2006, I took a stab at ranking every quarterback in NFL history. Two years later, I acquired more data and made enough improvements to merit publishing an updated and more accurate list of the best quarterbacks the league has ever seen. In 2009, I tweaked the formula again, and published a set of career rankings, along with a set of strength of schedule, era and weather adjustments, and finally career rankings which include those adjustments and playoff performances.  And two years ago, I revised the formula and produced a new set of career rankings.

This time around, I’m not going to tweak the formula much (that’s for GQBOAT VI), but I do have one big change that I suspect will be well-received.  Let’s review the methodology.

Methodology

We start with plain old yards per attempt. I then incorporate sack data by removing sack yards from the numerator and adding sacks to the denominator. [1]I have individual game sack data for every quarterback back to 2008. For seasons between 1969 and 2007, I have season sack data and team game sack data, so I was able to derive best-fit estimates for … Continue reading To include touchdowns and interceptions, I gave a quarterback 20 yards for each passing touchdown and subtracted 45 yards for each interception. This calculation — (Pass Yards + 20 * PTD – 45 * INT – Sack Yards Lost) / (Sacks + Pass Attempts) forms the basis for Adjusted Net Yards per Attempt, one of the key metrics I use to evaluate quarterbacks. For purposes of this study, I did some further tweaking. I’m including rushing touchdowns, because our goal is to measure quarterbacks as players. There’s no reason to separate rushing and passing touchdowns from a value standpoint, so all passing and rushing touchdowns are worth 20 yards and are calculated in the numerator of Adjusted Net Yards per Attempt. To be consistent, I also include rushing touchdowns in the denominator of the equation. This won’t change anything for most quarterbacks, but feels right to me. A touchdown is a touchdown.

Now, here comes the twist.  In past year, I’ve compared each quarterback’s “ANY/A” — I put that term in quotes because what we’re really using is ANY/A with a rushing touchdowns modifier — and then calculated a value over average statistic after comparing that rate to the league average. For example, if a QB has an “ANY/A” of 7.0 and the NFL average “ANY/A” is 5.0, and the quarterback has 500 “dropbacks” — i.e., pass attempts plus sacks plus rushing touchdowns — then the quarterback gets credit for 1,000 yards above average.

This time around, I’m going to incorporate strength of schedule by comparing each quarterback in each game not to league average, but to the “ANY/A” allowed by the opposing team in each of their other games.  Add up the Value relative to the defense in each game of each season, and you get season grades.  This step combines a SOS and era adjustment all in one, and frankly, I’m not sure why it took me so long to get around to this. [2]Ideally, I would iterate the strength of schedule adjustment. That’s for GQBOAT VI, I suppose.

There are three final steps. After creating season grades, we need to include two more statistics and then make one last adjustment. First, we subtract for “net fumbles” lost by the quarterback, which represents the number of fumbles by a quarterback minus the number of fumbles he recovered.  Based on prior research, a net fumble is worth about -30 yards, so -30 is subtracted for each net fumble. I calculated the average fumbles lost per “Dropback” by quarterbacks in each year (which was just north of 1.0% for most years) and then gave each quarterback credit (or a penalty) for their net fumbles above/below average. [3]If I had net fumbles lost on a per-game basis, I would simply include them in the prior step. But I don’t think much changes by simply including them in the aggregate on the season-level.

We also must add a rushing component. I have never figured out a good way to handle quarterback rushing, but what I’ve done in the past is to add all quarterback rushing yards over 4.0 yards per carry.  So 500 yards on 100 carries goes down as +100. That’s not very scientific, but the results have been noncontroversial, so I’ll continue to use it until someone suggests something better.

Finally, I made adjustments for non-16 game NFL seasons.  For seasons with fewer than 16 games, all stats have been pro-rated to 16 games.  And for the first five years of the AFL, I reduced the value of quarterback statistics. [4]In 1960, the final grade gets multiplied by 0.5; in 1961, by 0.6, in 1962 by 0.7, and so on.

Last time around, Tom Brady’s 2007 season ranked not just third, but a somewhat distant third to Dan Marino 1984 and Peyton Manning 2004. As it turns out, the SOS adjustment changes that. The table below shows the top 100 quarterback seasons since 1960. Let’s walk through Brady’s ’07 to guide you through the table. In 2007, Brady threw for 4,806 yards and 50 touchdowns, while recording just 8 interceptions, 21 sacks, and 128 sack yards lost. He had a “Relative ANY/A” of +3.63 (this includes the rushing TD bonus). He had a harder than average schedule, although that’s already been factored into his “RANY/A” (I’m including the SOS column for reference only). Brady had 601 dropbacks, and since he had fewer fumbles than average, gets an 88 yard fumble value bonus (but no rushing bonus). Add it up, and Brady produced 2,270 yards of VALUE over average, the most of any quarterback in any season since 1960.

RkQuarterbackTmYrYd-TD-INT-Sk-SkydRANY/ASOSDBFumValRushValVALUE
1Tom BradyNWE20074806-50-8-21-1283.630.266018802270
2Dan MarinoMIA19845084-48-17-13-1203.76-0.135779502267
3Peyton ManningIND20044557-49-10-13-1013.88-0.2351015202132
4Dan FoutsSDG19822883-17-11-12-942.72-0.2234316201946
5Aaron RodgersGNB20114643-45-6-36-2193.28-0.2254187171879
6Peyton ManningDEN20135477-55-10-18-1202.72-0.26678-6401780
7Steve YoungSFO19923465-25-7-29-1523.540.2343582331779
8Peyton ManningIND20064397-31-9-14-862.680.0957519301735
9Tom BradyNWE20115235-39-12-32-1732.440.0964612201696
10Tom BradyNWE20103900-36-4-25-1752.970.465189501632
11Drew BreesNOR20115476-46-14-24-1582.08-0.2268219421615
12Bert JonesBAL19763104-24-9-29-2843.32-0.3837465621564
13Tom BradyNWE20094398-28-13-16-862.50.785828401538
14Tom BradyNWE20124827-34-8-27-1822.040.4766816901532
15Steve YoungSFO19943969-35-10-31-1632.73-0.27499100611522
16Peyton ManningIND20034267-29-10-18-1072.290.1958418701522
17John BrodieSFO19702941-24-10-8-673.23-0.163887301517
18Ken AndersonCIN19753169-21-11-32-2473.150.224113301516
19Sonny JurgensenPHI19613723-32-24-25-2162.810.464417801504
20Johnny UnitasBAL19642824-19-6-35-2453.25-0.05342146141452
21Daunte CulpepperMIN20044717-39-11-46-2382.36-0.04596-22541438
22Daunte CulpepperMIN20003937-33-16-34-1812.550.3651521141432
23Randall CunninghamMIN19983704-34-10-20-1322.97-0.2544610141430
24Dan FoutsSDG19814802-33-17-19-1342.21-0.02628701393
25Drew BreesNOR20135162-39-12-37-2442.010.36690-101384
26John HadlSDG19673365-24-22-11-1072.770.42441-901384
27Drew BreesNOR20094388-34-11-20-1352.680.01536-5201383
28John BrodieSFO19653112-30-16-14-1002.750.644069401382
29Mark RypienWAS19913564-28-11-7-593.230.07429-1101373
30Ken AndersonCIN19813754-29-10-25-1402.27-0.14505851361369
31Jeff GarciaSFO20004278-31-10-24-1551.9-0.275891191261364
32Philip RiversSDG20094254-28-9-25-1672.59-0.055122901355
33Johnny UnitasBAL19673428-20-16-25-1982.330.446110611351
34Peyton ManningIND20004413-33-15-20-1312.130.145929001350
35Ken StablerOAK19762737-27-17-19-2033.840.5311-1601345
36Steve YoungSFO19984170-36-12-48-2342.110.04571-331741344
37Roger StaubachDAL19793586-27-11-36-2402.460.349789241337
38Joe MontanaSFO19843630-28-10-22-1382.65-0.2945611001318
39Milt PlumCLE19602297-21-5-29-2703.37-0.462814101317
40Matt SchaubHOU20094770-29-15-25-1491.890.1260815301299
41Joe MontanaSFO19893521-26-8-33-1983.09-0.01422-38311297
42Tony RomoDAL20094483-26-9-34-1962.070.195858501293
43Kurt WarnerSTL19994353-41-13-29-2012.54-0.57529-6301280
44Donovan McNabbPHI20043875-31-8-32-1922.430.155040561280
45Neil LomaxSTL19844614-28-16-49-3772.080.37612-42441277
46Carson PalmerCIN20053836-32-12-19-1052.150.2552913801274
47Joe NamathNYJ19674007-26-28-27-2701.830.0651816601273
48Fran TarkentonMIN19762961-17-8-25-2212.350.244388601272
49Ken AndersonCIN19742667-18-10-36-2922.490.12366591421272
50Dan FoutsSDG19804715-30-24-32-2102.090.49623-2901272
51Boomer EsiasonCIN19883572-28-14-30-2452.6-0.1541999761264
52Steve YoungSFO19934023-29-16-31-1602.24-0.22495101311250
53Drew BreesNOR20085069-34-17-13-921.75-0.0664811601249
54Jim HartSTL19762946-18-13-17-1322.580.344054501248
55Peyton ManningIND19994135-26-15-14-1162.090.25499401244
56Roger StaubachDAL19783190-25-16-32-2192.580.4444677141243
57Joe TheismannWAS19833714-29-11-34-2422.03-0.17494150861240
58Peyton ManningIND20074040-31-14-21-1242.060.2553912301231
59Peyton ManningIND20094500-33-16-10-741.870.0358114301227
60Drew BreesNOR20064418-26-11-18-1052.07-0.15724201227
61Brett FavreMIN20094202-33-7-34-2471.92056513801224
62Sonny JurgensenWAS19673747-31-16-19-1572.01-0.28529601224
63Dan MarinoMIA19864746-44-23-17-1191.73-0.2664011301224
64Kurt WarnerSTL20014830-36-22-38-2332.08-0.08584-301213
65Vinny TestaverdeNYJ19983256-29-7-19-1402.620.264414081202
66Y.A. TittleNYG19633145-36-14-26-2362.26-0.49395121271192
67Joe MontanaSFO19833910-26-12-33-2241.890.19550111401188
68Don MeredithDAL19662805-24-12-35-2512.38038431901183
69Joe NamathNYJ19683147-15-17-16-1152.320.0439810601176
70Aaron RodgersGNB20103922-28-11-31-1931.980.15510631001172
71Bernie KosarCLE19873033-22-9-22-1292.370.2841212101171
72Len DawsonKAN19662527-26-10-22-2083.17-0.06306-19711167
73Bart StarrGNB19662257-14-3-26-1913.950.24279-101201165
74Tom BradyNWE20054110-26-14-26-1881.820.3255715201165
75Aaron RodgersGNB20124295-39-8-51-2931.750.3660560431163
76Peyton ManningDEN20124659-37-11-21-1371.67-0.2460415001159
77Ken StablerOAK19742469-26-12-18-1412.94-0.153294701158
78Roman GabrielPHI19733219-23-12-31-2191.93-0.094926201157
79Roger StaubachDAL19772620-18-9-30-2192.620.11394-2301155
80Ron JaworskiPHI19803529-27-12-27-2132.180.1447910201147
81Peyton ManningIND20053747-28-10-17-812.27-0.394708001147
82Daryle LamonicaOAK19683245-25-15-26-2172.07-0.1444362221146
83John BrodieSFO19612588-14-12-20-1912.840.330513701146
84Tommy KramerMIN19863000-24-10-31-1782.760.654042701143
85Joe MontanaSFO19853653-27-13-35-2461.840.3153216301142
86Greg LandryDET19712237-16-13-29-2322.440.3293582261141
87Jim EverettRAM19894310-29-17-29-2141.75-0.1454818501141
88George BlandaHOU19613330-36-22-7-964.180.1136911801138
89Philip RiversSDG20084009-34-11-25-1512.25-0.04503301135
90Lynn DickeyGNB19834458-32-29-40-3071.960.2752710201134
91Fran TarkentonMIN19742598-17-12-17-1422.40.1837061361128
92Erik KramerCHI19953838-29-10-15-951.950.165387801125
93Dan MarinoMIA19873245-26-13-9-772.010.2245413601118
94Steve YoungSFO19912517-17-8-13-793.05-0.17296571511111
95Richard ToddNYJ19821961-14-8-23-2062.231.08285-1001110
96Trent GreenKAN20023690-26-13-26-1411.660.014971791011104
97Brian SipeCLE19804132-30-14-23-2171.67-0.1657813601100
98Philip RiversSDG20134478-32-11-30-1501.71-0.1657411401098
99Steve YoungSFO19973029-19-6-35-2202.520.1639410401095
100Johnny UnitasBAL19633481-20-12-34-2962.370.45444-130361095
101John ElwayDEN19934030-25-10-39-2931.610.3459013601089
102Boomer EsiasonCIN19863959-24-17-26-1942.250.19496-2901085
103Dan MarinoMIA19884434-28-23-6-311.560.2261212801082
104Brett FavreGNB19963899-39-13-40-2411.730.255856501079
105Trent GreenKAN20034039-24-12-20-1301.83-0.055458101078
106Roger StaubachDAL19711882-15-4-23-1753.57-0.34236-791791077
107Aaron RodgersGNB20094434-30-7-50-3061.6-0.2959629841066
108Roman GabrielRAM19672779-25-13-25-2072.220.12402-2261049
109Tony RomoDAL20114184-31-10-36-2271.60.1355915301046
110Len DawsonKAN19682109-17-9-19-1663.550.082435301046
111Brett FavreGNB19954413-38-13-33-2171.71-0.15606-17251043
112Nick FolesPHI20132891-27-2-28-1732.95-0.423481601041
113Fran TarkentonNYG19673088-29-19-33-3001.890.0741211301037
114Joe MontanaSFO19873054-31-13-22-1582.010.0942112411035
115Roman GabrielRAM19692549-24-7-14-1121.960.2141867161032
116Archie ManningNOR19783416-17-16-37-3011.790.4550971501031
117Dan MarinoMIA19924116-24-16-28-1731.490.0558216101030
118Tom FloresOAK19662638-24-14-27-2192.340.0633484301021
119Rich GannonOAK20024689-26-10-36-2141.47-0.136575601020
120Eli ManningNYG20114933-29-16-28-1991.610.096182301016
121Steve McNairTEN20013350-21-12-37-2511.750.48473721141013
122Steve DeBergKAN19903444-23-4-22-1912.13-0.1246670999
123Philip RiversSDG20104710-30-13-38-2271.68-0.32579230997
124Brett FavreGNB20074155-28-15-15-931.680.05550680992
125Steve McNairTEN20033215-24-7-19-1082.56-0.11423-910991
126Warren MoonHOU19904689-33-13-36-2521.85-0.13622-1700983
127Scott MitchellDET19954338-32-12-31-1451.56-0.06618180982
128Sonny JurgensenWAS19702354-23-10-25-2142.30.52363715979
129Frank RyanCLE19662974-29-14-28-2302.03-0.164101112979
130Daryle LamonicaOAK19693302-34-25-11-1001.74-0.31438900972
131Daryle LamonicaOAK19673228-30-20-36-3131.59-0.194658922972
132Earl MorrallBAL19682909-26-17-27-2042.6-0.05345-530962
133John ElwayDEN19873198-19-12-20-1381.75-0.024349940961
134Chad PenningtonNYJ20023120-22-6-22-1351.98-0.174231220960
135Boomer EsiasonCIN19853443-27-12-32-2891.970.03464440959
136Troy AikmanDAL19953304-16-7-14-891.970.18447750957
137Dan FoutsSDG19853638-27-20-18-1352.180.07448-230954
138Bert JonesBAL19772686-17-11-26-2211.64-0.3242110634951
139Billy WadeCHI19612258-22-13-27-2532.550.362793675941
140John HadlRAM19732008-22-11-17-1262.730.04275720941
141Tony RomoDAL20074211-36-19-24-1761.58-0.09546665934
142Sonny JurgensenWAS19663209-28-19-27-2121.630.16463610931
143Dan FoutsSDG19832975-20-15-14-1072.50.18355390928
144Randall CunninghamPHI19903466-30-13-49-4310.830.0951929470928
145Tom BradyNWE20043692-28-14-26-1621.770.51500280913
146David GarrardJAX20072509-18-3-21-992.480.37347470907
147Craig MortonDAL19701819-15-7-20-1663.230.2227610906
148Brett FavreGNB19973867-35-16-25-1761.6-0.04539440905
149Fran TarkentonMIN19652609-19-11-30-2761.530.39360103132899
150Michael VickPHI20103018-21-6-34-2101.7-0.09415-86276898
151Ken AndersonCIN19732428-18-12-24-1632.030.07353700898
152Vinny TestaverdeBAL19964177-33-19-34-2701.490.25585-2552897
153Tommy KramerMIN19822037-15-12-21-1301.310.91332680893
154Troy AikmanDAL19933100-15-6-26-1532.040.06418400892
155Norm Van BrocklinPHI19602471-24-17-14-1182.39-0.33298-430892
156Daryle LamonicaOAK19702516-22-15-15-1271.750.143711290889
157Fran TarkentonMIN19732113-15-7-31-2702.420.34306-738883
158Ken AndersonCIN19822495-12-9-26-1541.17-0.683391010883
159Donovan McNabbPHI20062647-18-6-21-1402.09-0.313409084882
160Peyton ManningIND20084002-27-12-14-861.230.075701780879
161Johnny UnitasBAL19652530-23-12-30-2292.480.39313-80878
162Boomer EsiasonCIN19893525-28-11-36-2881.620.19491-1590872
163Dan MarinoMIA19944453-30-17-18-1131.270.07634620869
164Fran TarkentonNYG19702777-19-12-36-2491.36-0.0942711464867
165Drew BreesNOR20125177-43-19-26-1901.07-0.146971180863
166Billy KilmerWAS19752440-23-16-23-1381.890.42370510859
167Y.A. TittleNYG19623224-33-20-14-1281.7-0.63914340858
168Babe ParilliBOS19621988-18-8-12-993.830.47267-1257855
169Robert GriffinWAS20123200-20-5-30-2171.47-0.22430-112335855
170Doug FlutieBUF19982711-20-11-12-781.730.1236716356855
171Warren MoonHOU19893631-23-14-35-2671.660.44503190854
172Carson PalmerCIN20064035-28-13-36-2331.80.42556-1450853
173John ElwayDEN19982806-22-10-18-1352.310.51375-140852
174Dan MarinoMIA19854137-30-21-18-1571.40.08585350851
175Mark BrunellJAX19973281-18-7-33-1891.51-0.044707565850
176Milt PlumCLE19612416-18-10-18-1592.420.22321-350849
177Ken O'BrienNYJ19853888-25-8-62-3991.67-0.03550-700849
178Russell WilsonSEA20123118-26-10-33-2031.610.4743038113844
179Joe FergusonBUF19752426-25-17-20-1531.950.11342720843
180Jake PlummerDEN20053366-18-7-22-1351.45-0.084801440840
181Matt HasselbeckSEA20053459-24-9-24-1541.54-0.264741120840
182Josh FreemanTAM20103451-25-6-28-1951.370.195026092839
183Dan FoutsSDG19782999-24-20-22-1302.210.13405-580835
184Steve BartkowskiATL19803544-31-16-35-3241.570.17500490834
185Jim EverettRAM19883964-31-18-28-1971.610.12545-420833
186Brett FavreGNB20013921-32-15-22-1511.72-0.09533-840831
187Kurt WarnerSTL20003429-21-18-20-1152.23-0.48367100829
188Johnny UnitasBAL19603099-25-24-24-2081.5-0.03402-3651824
189Drew BreesSDG20043159-27-7-18-1311.83-0.34420550824
190Fran TarkentonMIN19722651-18-13-26-2031.430.34046972822
191Rich GannonOAK19993840-24-14-49-2411.230.2956611114821
192Jeff GeorgeATL19954143-24-11-43-2701.20.226001010821
193Ben RoethlisbergerPIT20052385-17-9-23-1292.380.12941140814
194Brian GrieseDEN20002688-19-4-17-1392.19-0.37354350811
195Doug WilliamsTAM19813563-19-14-18-1351.630.06493-917811
196John BrodieSFO19683020-22-21-25-1661.440.51429910810
197Steve YoungSFO19962410-14-6-34-1601.750.3235488102810
198Ben RoethlisbergerPIT20094328-26-12-50-3481.37-0.12558450809
199Joe NamathNYJ19722816-19-21-11-1011.97-0.07335470808
200Joe NamathNYJ19692734-19-17-13-1171.760376430803

The table is fully sortable and searchable. Some thoughts:

  • San Francisco leads the way with 17 top-200 seasons: seven by Young, five by Joe Montana, four by Brodie, and one by Jeff Garcia. The Chargers are second with 12 such seasons, with Brees and John Hadl (!) each contributing one year, and Fouts and Philip Rivers delivering the rest.

And now, the huge caveat: It’s important to remember that this is just a measure of each team’s passing game, assigned to the quarterback on the field for those plays. Obviously the quality of the offensive line, the ability of the receivers, the versatility of the tight ends and running backs, the philosophy of the coaches, the strength of the schedule, and good old randomness have a significant impact on the above numbers. The reason for these posts is to accurately measure quarterback statistics, and nothing else. Once we have strong measures of QB performance, we can then judge QBs based on how much of their success (or lack thereof) we want to assign to the QB and how much to other people/factors.

And, of course, even if supporting casts are the same, numbers don’t tell the full story. The point here is simply to get the most out of the numbers we have. Anyway, I’m sure this gives you more than enough to chew on. Leave your thoughts on the methodology and the single-season leaders here; tomorrow, we get to the career list.

References

References
1 I have individual game sack data for every quarterback back to 2008. For seasons between 1969 and 2007, I have season sack data and team game sack data, so I was able to derive best-fit estimates for each quarterback in each game. For seasons between 1960 and 1969, I gave each quarterback an approximate number of sacks, giving him the pro-rated portion of sacks allowed by the percentage of pass attempts he threw for the team.
2 Ideally, I would iterate the strength of schedule adjustment. That’s for GQBOAT VI, I suppose.
3 If I had net fumbles lost on a per-game basis, I would simply include them in the prior step. But I don’t think much changes by simply including them in the aggregate on the season-level.
4 In 1960, the final grade gets multiplied by 0.5; in 1961, by 0.6, in 1962 by 0.7, and so on.
{ 41 comments }