Guest Post: Introducing Equivalency Rating

by Chase Stuart on September 19, 2014

Just above these words, it says “posted by Chase.” And it was literally posted by Chase, but the words below the line belong to Bryan Frye, a longtime reader and commenter who has agreed to write this guest post for us. And I thank him for it. Bryan lives in Yorktown, Virginia, and operates his own great site at http://www.thegridfe.com/, where he focuses on NFL stats and history.

In August, I introduced a concept on my site to better adjust the NFL’s passer rating for the league passing environment. I love Pro Football Reference’s use of the Advanced Passing Index for passer rating (Rate+), but it still bothered me that the internal math of the NFL’s formula remained the same.

The NFL’s official passer rating formula is based on four variables: completion percentage, yards per attempt, touchdown percentage, and interception rate. Each of those variables are then used to determine four different variables, as seen below:

A = (Cmp% – .3) * 5
B = (Y/A – 3) * .25
C = TD% * 20
D = 2.375 – Int% * 25

Passer rating is then calculated as follows, provided that each variable is capped at 2.375 and has a floor of zero:

(A + B + C + D)/(0.06)

For each component, a score of 1 represents the ideal average passer. Because the formula is based on a league average completion rate of 50%, modern passers significantly exceed that; pre-modern passers rarely reached it. Similarly, the NFL’s model is based on a 5.5% interception rate and a 5% touchdown rate. Thanks to a Greg Cook injury (and Bill Walsh’s genius reaction to it), those numbers have also changed significantly. Last year, the league interception and touchdown rates were 2.8% and 4.4%, respectively.

One of the two greatest quarterbacks of the first half of the 20th century.

On the other hand, when Sid Luckman set the league on fire in 1943, the NFL as a whole had much higher interception and touchdown rates – 10.1% and 7.0%, to be exact. What this all means is that post-West Coast Offense passers benefit from better completion and interception rates, while pre-AFL passers suffer from inferior stats in those areas. It also means that modern quarterbacks are actually hurt by their significantly lower touchdown rates, whereas the old-school guys get a rating boost from all the scoring they did.

To account for that, I came up with a “floating” formula that changes as league averages change. I called it the “Equivalency Rating” because it sort of describes the basic idea of the stat and because I really couldn’t think of a better name for it. Under the floating model, the league average rating for any given year is always 66.67, just as the NFL intended when passer rating was introduced in 1973.

To give an example, I’ll use the floating formula to account for the averages of two disparate seasons: 1950 and 2007.

1950 averages: 46.9% completions, 6.76 YPA, 5.2% TDs, and 7.8% Ints

A = (Cmp% – .269) * 5
B = (Y/A – 2.76) * .25
C = TD% * 19.38
D = 2.375 – Int% * 17.54

Remember, the idea is the league average passer should score a 1 in each category. So for completion percentage, we need a number that, when multiplied by 5, gives us 1. That means the league-average completion percentage will always be 20% higher than the number we will put in that equation. For yards per attempt, you need to subtract 4 from the league-average ratio, and put that number into variable B. For touchdown percentage, we simply need to divide 1 by the league-average rate, and for interception percentage, we need to divide 1.375 by the league-average metric. Here is the formula for the 2007 season:

2007: 61.2% completions, 6.85 YPA, 4.2% TDs, and 3.1% Ints

A = (Cmp% – .412) * 5
B = (Y/A – 2.85) * .25
C = TD% * 23.81
D = 2.375 – Int% * 43.83

I did this for every year since 1932, and came up with the following top 100 Passing Equivalency Ratings. Read the table thus: In 1943, Sid Luckman of the Bears completed 110 of 202 passes for 2194 yards, 28 touchdowns, and 12 interceptions. This comes out to an NFL rating of 107.5 and a PER of 117.5.

Rk	Quarterback	Year	Tm	Cmp	Att	Yds	TD	Int	NFL Rat	PER
1	Sid Luckman	1943	CHI	110	202	2194	28	12	107.5	117.5
2	Sammy Baugh	1945	WAS	128	182	1669	11	4	109.9	116.4
3	Aaron Rodgers	2011	GNB	343	502	4643	45	6	122.5	113.9
4	Roger Staubach	1971	DAL	126	211	1882	15	4	104.8	110.8
5	Peyton Manning	2004	IND	336	497	4557	49	10	121.1	110.7
6	Nick Foles	2013	PHI	203	317	2891	27	2	119.2	110.6
7	Tom Brady	2007	NE	398	578	4806	50	8	117.2	109.6
8	Milt Plum	1960	CLE	151	250	2297	21	5	110.4	109.4
9	Otto Graham	1946	CLE	95	174	1834	17	5	112.1	109.4
10	Otto Graham	1953	CLE	167	258	2722	11	9	99.7	108.7
11	Joe Montana	1989	SF	271	386	3521	26	8	112.4	108.6
12	Sammy Baugh	1940	WAS	111	177	1367	12	10	85.6	107.9
13	Steve Young	1994	SF	324	461	3969	35	10	112.8	107.7
14	Ken Stabler	1976	OAK	194	291	2737	27	17	103.4	105.7
15	Bart Starr	1966	GNB	156	251	2257	14	3	105	105.4
16	Bert Jones	1976	BAC	207	343	3104	24	9	102.5	105.3
17	Len Dawson	1962	DLT	189	310	2759	29	17	98.3	105.3
18	Len Dawson	1966	KC	159	284	2527	26	10	101.7	105.3
19	Otto Graham	1947	CLE	163	269	2753	25	11	109.2	104.8
20	Kurt Warner	1999	STL	325	499	4353	41	13	109.2	104.7
21	Steve Young	1992	SF	268	402	3465	25	7	107	104.5
22	Len Dawson	1968	KC	131	224	2109	17	9	98.6	104.1
23	Dan Marino	1984	MIA	362	564	5084	48	17	108.9	103.6
24	Peyton Manning	2013	DEN	450	659	5477	55	10	115.1	102.7
25	Tom Brady	2010	NE	324	492	3900	36	4	111	102.6
26	Otto Graham	1955	CLE	98	185	1721	15	8	94	102.5
27	Ken Stabler	1974	OAK	178	310	2469	26	12	94.9	102.3
28	Cecil Isbell	1942	GNB	146	268	2021	24	14	87	101.8
29	Ken Anderson	1974	CIN	213	328	2667	18	10	95.7	100.4
30	Charlie Conerly	1959	NYG	113	194	1706	14	4	102.7	100.3
31	Steve Young	1997	SF	241	356	3029	19	6	104.7	100.2
32	Otto Graham	1949	CLE	161	285	2785	19	10	97.5	100.1
33	Josh McCown	2013	CHI	149	224	1829	13	1	109	99.9
34	Randall Cunningham	1998	MIN	259	425	3704	34	10	106	99.5
35	Daunte Culpepper	2004	MIN	379	548	4717	39	11	110.9	99.4
36	Brian Griese	2000	DEN	216	336	2688	19	4	102.9	99.1
37	Frankie Albert	1948	SF	154	264	1990	29	10	102.9	99
38	Cecil Isbell	1941	GNB	117	206	1479	15	11	81.4	98.9
39	George Blanda	1961	HOO	187	362	3330	36	22	91.3	98.5
40	Y.A. Tittle	1963	NYG	221	367	3145	36	14	104.8	98.2
41	Brett Favre	2009	MIN	363	531	4202	33	7	107.2	98.1
42	Dave Krieg	1994	DET	131	212	1629	14	3	101.7	98.1
43	Roger Staubach	1973	DAL	179	286	2428	23	15	94.6	98.1
44	Drew Brees	2009	NOR	363	514	4388	34	11	109.6	98
45	Drew Brees	2011	NOR	468	657	5476	46	14	110.6	97.5
46	Y.A. Tittle	1953	SF	149	259	2121	20	16	84.1	97.5
47	Joe Montana	1984	SF	279	432	3630	28	10	102.9	97.4
48	Bob Griese	1971	MIA	145	263	2089	19	9	90.9	97.3
49	Tommy Thompson	1948	PHI	141	246	1965	25	11	98.4	97.2
50	Steve Young	1991	SF	180	279	2517	17	8	101.8	97
51	Chad Pennington	2002	NYJ	275	399	3120	22	6	104.2	97
52	Sammy Baugh	1942	WAS	132	225	1524	16	11	82.5	97
53	John Brodie	1970	SF	223	378	2941	24	10	93.8	96.8
54	Babe Parilli	1962	BOS	140	253	1988	18	8	91.5	96.5
55	Trent Green	2000	STL	145	240	2063	16	5	101.8	96.4
56	Aaron Rodgers	2012	GNB	371	552	4295	39	8	108	96.3
57	Vinny Testaverde	1998	NYJ	259	421	3256	29	7	101.6	96.3
58	Ken Anderson	1981	CIN	300	479	3754	29	10	98.4	96.2
59	Bob Griese	1977	MIA	180	307	2252	22	13	87.8	96.1
60	Ken Anderson	1975	CIN	228	377	3169	21	11	93.9	95.9
61	Fran Tarkenton	1973	MIN	169	274	2113	15	7	93.2	95.8
62	Joe Montana	1987	SF	266	398	3054	31	13	102.1	95.8
63	Norm Van Brocklin	1953	LARM	156	286	2393	19	14	84.1	95.7
64	Peyton Manning	2005	IND	305	453	3747	28	10	104.1	95.7
65	Norm Van Brocklin	1950	LARM	127	233	2061	18	14	85.1	95.3
66	Sammy Baugh	1947	WAS	210	354	2938	25	15	92	94
67	Arnie Herber	1936	GNB	77	173	1239	11	13	58.9	93.5
68	Tommy Thompson	1949	PHI	116	214	1727	16	11	84.4	93.4
69	Sid Luckman	1945	CHI	117	217	1727	14	10	82.5	92.7
70	Tobin Rote	1952	GNB	82	157	1268	13	8	85.6	92.4
71	Bob Waterfield	1951	LARM	88	176	1566	13	10	81.8	90.8
72	Sammy Baugh	1949	WAS	145	255	1903	18	14	81.2	90.6
73	Johnny Unitas	1957	BAC	172	301	2550	24	17	88	90.1
74	Norm Van Brocklin	1951	LARM	100	194	1725	13	11	80.8	89.8
75	Johnny Unitas	1958	BAC	136	263	2007	19	7	90	89.7
76	Johnny Unitas	1959	BAC	193	367	2899	32	14	92	89.7
77	Bobby Thomason	1953	PHI	162	304	2462	21	20	75.8	89.2
78	Sammy Baugh	1943	WAS	133	239	1754	23	19	78	89.2
79	Y.A. Tittle	1948	BAC	161	289	2522	16	9	90.3	89
80	Bob Waterfield	1945	LARM	89	171	1609	14	17	72.4	88.9
81	Otto Graham	1951	CLE	147	265	2205	17	16	79.2	88.7
82	Eddie LeBaron	1957	WAS	99	167	1508	11	10	86.1	88.5
83	Ed Brown	1956	CHI	96	168	1667	11	12	83.1	88.4
84	Bobby Thomason	1955	PHI	88	171	1337	10	7	80	87.7
85	Johnny Lujack	1949	CHI	162	312	2658	23	22	76	87.1
86	Frankie Albert	1949	SF	129	260	1862	27	16	82.2	86.7
87	Sid Luckman	1946	CHI	110	229	1826	17	16	71	86.2
88	Milt Plum	1959	CLE	156	266	1992	14	8	87.2	85.3
89	Charlie Conerly	1948	NYG	162	299	2175	22	13	84	84.7
90	Otto Graham	1948	CLE	173	333	2713	25	15	85.6	84.1
91	Adrian Burk	1954	PHI	123	231	1740	23	17	80.4	83.4
92	Bob Waterfield	1946	LARM	127	251	1747	17	17	67.6	82.6
93	Bob Waterfield	1950	LARM	122	213	1540	11	13	71.7	82.4
94	Jim Hardy	1948	LARM	112	211	1390	14	7	82.1	82.3
95	Sammy Baugh	1948	WAS	185	315	2599	22	23	78.3	82.3
96	Tommy Thompson	1947	PHI	106	201	1680	16	15	76.3	82.1
97	Y.A. Tittle	1957	SF	176	279	2157	13	15	80	81.9
98	Norm Van Brocklin	1952	LARM	113	205	1736	14	17	71.5	81.6
99	George Ratterman	1949	BUF	146	252	1777	14	13	76.8	81.4
100	Bobby Thomason	1951	GNB	125	221	1306	11	9	73.5	80.9

As you can see, the older fellows look a lot better in proper context. I’ve already talked way too much, so here are a few quick takeaways:

Bill Walsh was a pretty good coach, mentoring players who make up 10% of this list (not to mention his influence on later passers).
San Francisco really has had an embarrassment of riches at the quarterback position, as Chase noted in the methodology post of his latest GQBOAT series. Hall of Famers Y.A. Tittle, Joe Montana, and Steve Young account for nine seasons. Frankie Albert and John Brodie add three more.
Tittle makes the list for three different teams; Bobby Thomason is the only other player to represent more than one team.
Because this doesn’t incorporate important sack data, Peyton Manning doesn’t look as good as you may have expected.
Otto Graham and Sammy Baugh lead with seven appearance each. All four of Graham’s AAFC seasons make the cut, to the surprise of no one.
Steve Young makes the most appearances of any “modern” passer, with four.
We all know Milt Plum’s 1960 was one for the ages, but his play the prior year was pretty good too.
Arnie Herber’s magical 1936 season has the biggest gap between NFL passer rating and Equivalency Rating; he rates 34.6 points higher in the latter.
Drew Brees’ 2011 sees the biggest decline, dropping 13.1 points.

There’s more to come about the Equivalency Rating, including ways to incorporate rushing and total offense/defense numbers. But for today, we’ll stick to the basic methodology: please let us know your thoughts in the comments.

Tagged as: Bryan Frye, Guest Posts

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