Guest Post: Quarterbacks and Exceeding Pythagorean Wins

by Chase Stuart on June 20, 2016

Adam Steele is back for another guest post. You can view all of Adam’s posts here. As always, we thank him for contributing.

There have been countless attempts at deducing the clutchiness of NFL quarterbacks, most of which involve tallying playoff wins and Super Bowl rings. Today I’m going to take a stab at the clutch conundrum using a different approach: Pythagorean win projection. If a quarterback’s actual win/loss record diverges significantly from his Pythagorean estimated record, perhaps we can learn something from it. I began this study having no idea how it would turn out, so there were definitely some surprises once I saw the end results. This study evaluates the 219 quarterbacks who started at least 32 games since 1950, including playoffs but excluding the 1960-64 AFL (lack of competitive depth).

Here’s how to read the table, from left to right: points per game scored by the QB’s team in games he started, points per game allowed in his starts, total starts, total wins (counting ties as a half win), Pythagorean projected wins based on the points scored and allowed in his starts (using a 2.37 exponent), and the difference between his actual win total and Pythagorean win projection.

Search:

Rank	Quarterback	PF/G	PA/G	GS	ActW	PythW	Diff
1	Peyton Manning	26.74	21.37	292	200	183.9	16.1
2	Tom Brady	27.89	18.92	254	194	181.6	12.4
3	Dan Marino	23.04	20.75	258	155	144.9	10.1
4	John Elway	23.27	19.43	252	162.5	152.5	10.0
5	Jake Plummer	19.74	21.94	142	71	62.1	8.9
6	Dan Pastorini	18.27	21.07	122	59	50.8	8.2
7	Jay Schroeder	20.16	18.87	104	64	56.1	7.9
8	Andrew Luck	24.52	24.02	61	38	31.3	6.7
9	Stan Humphries	21.62	20.40	87	53	46.5	6.5
10	Jeff Hostetler	21.06	19.31	88	55	48.5	6.5
11	Ken Stabler	22.51	18.42	158	103.5	97.4	6.1
12	Ed Brown	21.97	21.19	99	57.5	51.6	5.9
13	Matt Hasselbeck	21.99	22.27	171	90	84.2	5.8
14	Mike Phipps	17.82	19.04	73	39	33.6	5.4
15	Rodney Peete	19.48	20.85	89	46	40.9	5.1
16	Jay Cutler	22.69	24.17	136	68	62.9	5.1
17	Steve McNair	21.72	19.69	163	96	90.9	5.1
18	Jeff George	17.57	23.60	127	47	42.2	4.8
19	Fran Tarkenton	21.40	20.94	250	133	128.2	4.8
20	Brian Sipe	19.89	21.15	113	57	52.4	4.6
21	Ben Roethlisberger	23.82	18.57	186	124	119.7	4.3
22	Tony Eason	20.79	21.61	56	31	26.7	4.3
23	Marc Bulger	21.08	25.59	98	42	37.9	4.1
24	Vince Young	21.59	20.49	51	31	27.1	3.9
25	Neil Lomax	20.69	23.12	102	48	44.3	3.7
26	Frank Ryan	24.84	20.18	90	59.5	55.9	3.6
27	Eli Manning	23.84	22.90	194	105	101.6	3.4
28	Y.A. Tittle	24.39	22.21	139	80.5	77.2	3.3
29	Matt Ryan	23.92	22.06	131	75	71.7	3.3
30	Joe Theismann	21.96	18.37	132	83	79.8	3.2
31	Tony Romo	25.16	22.06	133	80	76.8	3.2
32	Jake Delhomme	21.73	19.78	104	61	57.8	3.2
33	Phil Simms	20.30	17.73	169	101	97.9	3.1
34	Jim Plunkett	20.41	20.41	154	80	77.0	3.0
35	Marc Wilson	20.39	21.25	61	32	29.0	3.0
36	Daryle Lamonica	26.47	18.00	94	70	67.1	2.9
37	Derek Anderson	18.51	22.73	45	20	17.1	2.9
38	Bill Nelson	22.81	22.27	79	43.5	40.6	2.9
39	Joe Montana	24.63	17.35	187	133	130.2	2.8
40	Dave Brown	16.72	20.30	60	26	23.2	2.8
41	Colin Kaepernick	22.11	20.89	53	31	28.3	2.7
42	Erik Kramer	19.69	22.61	70	32	29.3	2.7
43	Michael Vick	22.25	21.68	118	63.5	60.8	2.7
44	Steve Walsh	17.00	18.54	41	21	18.4	2.6
45	Bobby Layne	23.73	20.24	139	85	82.4	2.6
46	Jim Zorn	20.00	24.12	106	44	41.4	2.6
47	Joe Namath	22.42	23.10	132	66	63.7	2.3
48	Trent Dilfer	17.82	17.52	119	63	60.7	2.3
49	Sonny Jurgensen	21.54	22.61	149	72.5	70.2	2.3
50	Quincy Carter	15.71	17.00	35	18	15.9	2.1
51	David Woodley	21.67	17.93	58	37.5	35.4	2.1
52	Earl Morrall	20.97	17.04	107	68.5	66.4	2.1
53	Neil O'Donnell	19.87	19.12	107	58	55.9	2.1
54	David Whitehurst	14.89	17.95	37	16.5	14.5	2.0
55	John Brodie	21.63	22.55	164	80	78.0	2.0
56	Aaron Brooks	20.53	24.23	92	39	37.1	1.9
57	Andy Dalton	23.79	20.05	81	50.5	48.6	1.9
58	Gary Hogeboom	19.38	21.59	37	18	16.1	1.9
59	Jim Kelly	23.20	19.18	177	110	108.2	1.8
60	Carson Palmer	22.83	22.66	163	84	82.3	1.7
61	Steve Bono	20.81	17.21	43	28	26.3	1.7
62	Jim McMahon	20.75	15.59	103	70	68.3	1.7
63	Tim Couch	16.59	21.69	59	22	20.4	1.6
64	Danny White	25.23	19.73	102	67	65.5	1.5
65	Jeff Blake	20.00	24.82	100	39	37.5	1.5
66	Tommy Kramer	20.55	21.32	114	56	54.5	1.5
67	Jack Concannon	16.82	19.18	45	20.5	19.0	1.5
68	Babe Parilli	18.82	24.20	55	21	19.5	1.5
69	Jack Trudeau	15.44	20.00	50	19	17.6	1.4
70	Kordell Stewart	20.17	18.05	86	50	48.6	1.4
71	Norm Van Brocklin	26.74	22.29	105	65	63.7	1.3
72	Craig Erickson	17.60	22.34	35	14	12.7	1.3
73	Doug Williams	17.77	18.73	88	42.5	41.3	1.2
74	Pete Beathard	18.05	19.08	37	18.5	17.3	1.2
75	Mike Tomczak	20.72	18.67	78	45	43.8	1.2
76	Josh Freeman	19.95	24.08	61	25	23.8	1.2
77	Byron Leftwich	17.31	18.90	51	24	22.9	1.1
78	Bert Jones	21.56	22.91	99	47	45.9	1.1
79	Randy Johnson	15.55	28.45	49	10.5	9.5	1.0
80	Brett Favre	24.07	19.75	322	199	198.0	1.0
81	Chad Henne	18.62	25.45	53	18	17.1	0.9
82	Charley Johnson	22.23	22.19	124	63	62.1	0.9
83	Mark Sanchez	22.09	21.54	78	41	40.2	0.8
84	Bob Avellini	17.00	18.98	51	23	22.2	0.8
85	Jim Hart	21.04	21.49	182	89.5	88.7	0.8
86	Scott Hunter	16.81	16.65	43	22.5	21.7	0.8
87	Sam Bradford	19.13	22.94	63	25.5	24.8	0.7
88	Joe Ferguson	18.78	20.33	175	80	79.3	0.7
89	Dennis Shaw	15.46	26.03	37	9	8.3	0.7
90	Matt Cassel	20.41	23.00	80	35	34.4	0.6
91	Daunte Culpepper	21.48	25.15	104	43	42.4	0.6
92	Nick Foles	23.64	23.14	36	19	18.5	0.5
93	Dave Krieg	21.34	19.73	184	101	100.5	0.5
94	Billy Kilmer	20.17	19.48	121	63.5	63.0	0.5
95	Eddie LeBaron	18.17	24.31	81	27.5	27.1	0.4
96	Lamar McHan	17.82	23.73	73	25	24.6	0.4
97	Vince Ferragamo	21.58	21.46	59	30	29.7	0.3
98	Charlie Conerly	21.78	17.32	92	58.5	58.2	0.3
99	Marty Domres	16.44	20.72	32	12	11.7	0.3
100	Trent Edwards	18.42	21.21	33	14	13.8	0.2
101	Bubby Brister	19.35	19.66	77	38	37.8	0.2
102	Chris Chandler	19.72	21.68	155	69	68.8	0.2
103	J.P. Losman	15.79	22.70	33	10	9.8	0.2
104	Kent Graham	16.92	18.61	38	17	16.9	0.1
105	Ryan Tannehill	20.36	22.09	64	29	28.9	0.1
106	Steve Spurrier	16.92	21.84	38	13.5	13.4	0.1
107	Craig Morton	19.14	17.25	154	86.5	86.4	0.1
108	Mike Pagel	17.04	23.24	54	17.5	17.5	0.0
109	Cam Newton	24.68	21.63	84	48.5	48.5	0.0
110	Jim Harbaugh	18.68	19.68	145	68	68.0	0.0
111	Derek Carr	19.13	26.59	32	10	10.0	0.0
112	Matt Schaub	23.64	23.19	94	48	48.1	-0.1
113	David Carr	16.28	23.63	79	23	23.1	-0.1
114	Jay Fiedler	20.73	17.32	63	38	38.1	-0.1
115	Don Heinrich	20.73	16.70	37	23	23.1	-0.1
116	Steve Tensi	19.47	27.09	34	10.5	10.7	-0.2
117	Jim Finks	19.58	23.04	45	18	18.2	-0.2
118	Bobby Hebert	21.26	19.68	103	56	56.2	-0.2
119	David Garrard	21.65	21.09	78	40	40.2	-0.2
120	Chad Pennington	20.64	19.53	87	46	46.4	-0.4
121	Randall Cunningham	23.06	19.56	144	85.5	85.9	-0.4
122	Alex Smith	21.79	19.58	126	70.5	71.0	-0.5
123	Richard Todd	20.10	21.69	112	50.5	51.0	-0.5
124	Don Majkowski	19.44	20.33	57	26.5	27.0	-0.5
125	Christian Ponder	23.50	27.08	36	14.5	15.0	-0.5
126	Aaron Rodgers	27.82	20.90	132	87	87.5	-0.5
127	Doug Flutie	20.74	18.50	68	38	38.6	-0.6
128	Archie Manning	15.86	24.30	139	36.5	37.1	-0.6
129	Pat Haden	20.27	16.05	60	37.5	38.1	-0.6
130	Kyle Orton	20.73	20.06	82	42	42.6	-0.6
131	Wade Wilson	21.65	20.84	74	38	38.7	-0.7
132	Brad Johnson	21.26	18.52	132	76	76.7	-0.7
133	Rex Grossman	21.90	20.33	51	27	27.7	-0.7
134	Robert Griffin III	23.00	26.83	36	14	14.7	-0.7
135	Randy Wright	15.09	24.34	32	7	7.8	-0.8
136	Gus Frerotte	21.37	21.80	95	45.5	46.4	-0.9
137	Bob Berry	17.04	19.17	52	21.5	22.4	-0.9
138	Adrian Burk	20.10	22.83	41	16.5	17.4	-0.9
139	Steve Fuller	17.41	18.14	44	20	20.9	-0.9
140	Blaine Gabbert	15.49	24.31	35	8	8.9	-0.9
141	Jon Kitna	20.89	24.46	125	50	51.0	-1.0
142	Gary Cuozzo	18.85	17.76	41	21	22.0	-1.0
143	Tobin Rote	22.08	26.08	98	38.5	39.5	-1.0
144	Roger Staubach	23.82	15.31	131	96	97.0	-1.0
145	Jack Kemp	20.98	19.27	51	27	28.1	-1.1
146	Joe Kapp	19.15	17.60	52	27.5	28.6	-1.1
147	Ryan Fitzpatrick	20.64	23.42	105	43.5	44.7	-1.2
148	Kyle Boller	19.02	20.64	47	20	21.2	-1.2
149	Otto Graham	26.85	14.74	78	61.5	62.8	-1.3
150	Lynn Dickey	19.70	22.10	113	47.5	48.9	-1.4
151	Johnny Unitas	24.36	18.53	194	126	127.4	-1.4
152	Joey Harrington	17.24	21.95	76	26	27.4	-1.4
153	Kerry Collins	19.63	21.12	187	84	85.4	-1.4
154	Joe Flacco	23.60	18.82	137	85	86.4	-1.4
155	Ken O'Brien	20.19	21.46	112	50.5	52.0	-1.5
156	Rick Mirer	17.74	21.99	68	24	25.5	-1.5
157	Drew Brees	26.60	23.23	227	130	131.5	-1.5
158	Zeke Bratkowski	18.53	22.60	47	16.5	18.1	-1.6
159	Brian Griese	22.04	19.86	83	45	46.6	-1.6
160	Eric Hipple	20.05	19.64	58	28	29.7	-1.7
161	Kurt Warner	26.67	22.36	129	76	77.8	-1.8
162	James Harris	19.07	15.20	44	26	27.8	-1.8
163	Tommy Maddox	21.29	21.95	38	16.5	18.3	-1.8
164	George Blanda	21.81	25.26	42	15.5	17.4	-1.9
165	Chris Miller	19.41	23.34	94	35	36.9	-1.9
166	Billy Wade	22.47	22.05	86	42	44.0	-2.0
167	Mark Rypien	23.38	18.48	85	52	54.0	-2.0
168	Billy Joe Tolliver	18.19	22.94	47	15	17.2	-2.2
169	Jeff Garcia	22.55	22.16	122	60	62.2	-2.2
170	Bernie Kosar	20.84	20.43	115	56.5	58.9	-2.4
171	Tony Banks	19.18	19.83	78	35	37.5	-2.5
172	Charlie Batch	20.69	20.71	55	25	27.5	-2.5
173	Shaun Hill	22.06	20.50	34	16	18.5	-2.5
174	Russell Wilson	25.73	16.19	74	53	55.5	-2.5
175	Bobby Douglass	17.19	21.96	53	16.5	19.0	-2.5
176	Milt Plum	21.70	18.52	104	59	61.7	-2.7
177	Jason Campbell	19.66	21.77	79	32	34.7	-2.7
178	Bill Munson	18.68	19.05	66	29.5	32.2	-2.7
179	Len Dawson	22.63	17.42	125	78.5	81.3	-2.8
180	Dan Fouts	23.77	23.03	178	89.5	92.3	-2.8
181	Elvis Grbac	22.41	18.88	73	41	43.8	-2.8
182	Vince Evans	18.10	20.18	39	14	17.0	-3.0
183	Tarvaris Jackson	22.29	19.69	35	17	20.1	-3.1
184	Matthew Stafford	23.42	24.44	95	42	45.1	-3.1
185	Greg Landry	18.91	19.18	99	45.5	48.7	-3.2
186	Bob Griese	21.15	16.77	162	99.5	102.7	-3.2
187	John Friesz	18.76	21.18	38	13	16.3	-3.3
188	Gary Danielson	20.48	19.75	61	28.5	31.8	-3.3
189	Josh McCown	19.23	23.88	57	18	21.3	-3.3
190	Mark Malone	20.11	20.13	55	24	27.5	-3.5
191	Scott Mitchell	22.41	22.89	73	32	35.6	-3.6
192	Steve Grogan	22.38	19.86	138	75	78.7	-3.7
193	Vinny Testaverde	19.50	21.62	219	92.5	96.2	-3.7
194	Roman Gabriel	21.30	18.38	159	89.5	93.2	-3.7
195	John Hadl	21.95	20.01	150	79.5	83.2	-3.7
196	Steve Bartkowski	20.38	20.82	131	60	63.9	-3.9
197	Warren Moon	21.90	21.45	213	105	109.2	-4.2
198	Donovan McNabb	22.92	18.28	177	107.5	111.7	-4.2
199	Boomer Esiason	21.87	22.25	178	83	87.2	-4.2
200	Steve Young	25.76	18.84	157	102	106.3	-4.3
201	Steve Beuerlein	20.25	20.10	104	48	52.5	-4.5
202	Bobby Thomason	20.36	18.05	42	19.5	24.0	-4.5
203	Mark Brunell	21.61	20.08	161	83	87.5	-4.5
204	Terry Bradshaw	22.85	15.68	177	121	125.6	-4.6
205	Mike Livingston	19.45	20.01	75	31.5	36.2	-4.7
206	Jim Everett	20.19	22.01	158	66	71.0	-5.0
207	Bill Kenney	21.75	21.49	77	34	39.0	-5.0
208	Norm Snead	19.59	23.95	158	55.5	60.6	-5.1
209	Philip Rivers	25.09	21.15	169	96	101.4	-5.4
210	Drew Bledsoe	20.74	19.54	199	101	106.5	-5.5
211	Don Meredith	26.61	21.04	89	51	56.6	-5.6
212	Trent Green	25.07	23.58	115	56	61.7	-5.7
213	Steve DeBerg	19.60	22.53	144	54.5	60.2	-5.7
214	Troy Aikman	21.94	18.01	180	105	110.7	-5.7
215	Ken Anderson	21.31	19.29	178	93	99.5	-6.5
216	Ron Jaworski	19.06	17.32	151	77.5	84.0	-6.5
217	Rich Gannon	24.12	19.47	139	80	86.8	-6.8
218	Bart Starr	22.99	16.68	167	106	113.8	-7.8

If you want to make the case for Peyton Manning and Tom Brady (in either order) being the two greatest quarterbacks to ever play the game, this is a good place to start. According to Pythagoras, they are the two biggest overachievers in NFL history. In a league where records in close games regress heavily toward the mean from one season to the next, Manning and Brady have consistently defied the odds and won games they had no business winning, year in and year out. The presence of Dan Marino at #3 runs counter to the popular narrative of the Dolphins great coming up small in big moments; despite often being saddled with mediocre teammates, Miami won significantly more games than it should have with Marino under center. Conversely, John Elway’s reputation as a winner has long exceeded his statistical output, but in this case the numbers agree with conventional wisdom. Elway’s Broncos won 10 more games than expected, and I’d say it’s fair to give most of the credit to Elway himself.

Dan Pastorini is a fascinating case, at least to me. By any statistical measure, Pastorini is one of the worst long term starters in NFL history. Yet he also ended up as one of the most prolific Pythagorean overachievers in history! How did this happen? I don’t have an answer, but I do have a theory. Despite Pastorini’s poor play, the Oilers’ staff noticed that the team was winning an inordinate percentage of close games when he started. Given that us humans are loathe to accept the vagaries of random chance, someone in Houston probably concluded that Pastorini must be clutch and/or have winnersauce flowing through his veins. And since winnersauce is such a rare quality, the Oilers kept starting him even though he played like Christian Ponder.

Take a gander at the biggest underachievers, it surely must be a bunch of scrubs. Instead we find… Hall-of-Famers, MVP’s, and Pro-Bowlers? I was beyond shocked to see Bart Starr dead last, and nearly as surprised to see Aikman, Bradshaw, and Young down there with him. Besides having a bust in Canton, these guys have something else in common – they all played on dominant teams. The tendency of dominant teams is to win big and lose close, the perfect recipe for tricking Pythagoras into thinking the team isn’t winning as many games as it should. I feel safe in concluding that’s the reason for these all-time greats to appear so low on this list. Really bad quarterbacks like Randy Wright, Blaine Gabbert (thus continuing our streak of mentioning Justin Blackmon or someone on the ugly 2012 Jaguars), and Dennis Shaw don’t get much of a chance to underperform: those three are the only ones on here with less than 10 Pythagorean wins.

Now I’ll turn the floor over to the FP readership. Does this study reveal anything significant, or is it mostly statistical noise? If you believe the former, which QB’s stand out to you and why?

Tagged as: Adam Steele, Guest Posts, Pythagorean

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