I’ve been on a major QB kick lately, and there’s no reason to stop now. Today, I want to look at a method that might tease out a quarterback’s “true talent” better than if we simply use his raw stats from the season.

Three years ago, our colleague Jason Lisk had a post on the old PFR Blog about which rate stats stay consistent when a QB changes teams. Basically, he grabbed QBs who were still in their primes and changed teams, looking at how their key rate stats correlated from one year to the next. Here’s what Jason found:

[…]I looked at the correlation coefficient for our group of 48 passers, for the year N advanced passing score compared to the year N+1 advanced passing score in each category. This should tell us whether the passers who were good in a performance area (or bad) tended to be the ones who remained good in that performance area the following season, even with the uncertainty of team changes (some positive, some negative for the quarterback).

Sack Percentage:  0.31
Completion Percentage: 0.25
Yards Per Attempt:  0.20
Touchdown Percentage: 0.12
Interception Percentage: 0.10

What do those correlations mean, exactly? Well, take sack percentage as an example. In general, a correlation of 0.31 means you can expect 31% of a QB’s difference from the mean to be repeated next year when he changes teams. In other words, you have to regress the QB’s sack rate 69% towards the mean to get the true rate that “belongs” to him. If the average sack rate is 6.1%, and a QB has a rate of 4.0% (like, say, Drew Brees this year), his “true” sack rate is probably something like 5.4% — 31% of the distance between .061 and .040.

The same concept applies to the other stats listed above. Tony Romo’s observed 66.7% completion percentage is really more like 62.5% after regressing to the mean, and so forth. Do that for every QB who had a reasonable number of attempts this year, and you get these rate stats:

Player	Tm	G	GS	Att	A-Sk%	A-Cmp%	A-YPA	A-TD%	A-INT%	R-Sk%	R-Cmp%	R-YPA	R-TD%	R-INT%
Matthew Stafford	DET	14	14	629	4.3	59.5	6.8	2.7	2.4	5.5	60.7	7.0	4.0	2.6
Drew Brees	NOR	14	14	574	4.0	62.0	7.6	6.3	3.1	5.4	61.4	7.2	4.5	2.7
Tony Romo	DAL	14	14	568	5.3	66.7	7.5	3.9	2.8	5.9	62.5	7.2	4.2	2.7
Andrew Luck	IND	14	13	564	6.2	54.6	7.1	3.5	3.2	6.1	59.5	7.1	4.1	2.7
Carson Palmer	OAK	14	14	562	4.4	60.9	7.1	3.9	2.5	5.6	61.1	7.1	4.2	2.6
Tom Brady	NWE	14	14	560	3.9	63.4	7.6	5.4	1.1	5.4	61.7	7.2	4.4	2.5
Matt Ryan	ATL	14	14	539	4.4	68.5	7.8	5.0	2.6	5.6	63.0	7.2	4.3	2.7
Peyton Manning	DEN	14	14	511	3.9	67.9	7.9	6.1	2.0	5.4	62.8	7.2	4.4	2.6
Brandon Weeden	CLE	14	14	498	5.0	57.2	6.6	2.8	3.4	5.7	60.2	7.0	4.0	2.7
Philip Rivers	SDG	14	14	488	8.1	64.3	6.7	4.5	3.1	6.7	62.0	7.0	4.2	2.7
Joe Flacco	BAL	14	14	487	6.5	59.1	7.1	4.1	2.1	6.2	60.7	7.1	4.2	2.6
Eli Manning	NYG	14	14	487	3.0	60.4	7.4	4.1	3.1	5.1	61.0	7.1	4.2	2.7
Sam Bradford	STL	14	14	482	6.8	60.2	6.8	3.7	2.3	6.3	60.9	7.0	4.2	2.6
Matt Schaub	HOU	14	13	476	4.0	64.7	7.5	4.6	2.1	5.5	62.0	7.2	4.3	2.6
Aaron Rodgers	GNB	14	14	474	8.7	66.7	7.6	6.8	1.7	6.9	62.5	7.2	4.5	2.6
Andy Dalton	CIN	14	14	472	7.5	62.5	7.0	5.5	3.0	6.5	61.5	7.1	4.4	2.7
Josh Freeman	TAM	14	14	469	4.3	54.8	7.4	5.3	2.6	5.5	59.6	7.1	4.3	2.7
Ryan Fitzpatrick	BUF	14	13	444	5.9	61.7	6.6	5.0	3.4	6.0	61.3	7.0	4.3	2.7
Christian Ponder	MIN	14	14	425	6.6	63.1	5.9	3.3	2.8	6.2	61.6	6.9	4.1	2.7
Ryan Tannehill	MIA	14	14	424	5.8	58.7	6.9	2.4	2.8	6.0	60.5	7.0	4.0	2.7
Cam Newton	CAR	14	14	423	7.2	58.2	8.2	4.3	2.4	6.4	60.4	7.3	4.2	2.6
Mark Sanchez	NYJ	14	14	418	7.3	54.8	6.4	3.1	4.1	6.5	59.6	6.9	4.1	2.8
Ben Roethlisberger	PIT	11	11	398	5.7	64.1	7.3	5.5	1.5	6.0	61.9	7.1	4.4	2.6
Jay Cutler	CHI	13	13	377	8.5	59.7	7.0	4.5	3.7	6.8	60.8	7.1	4.2	2.8
Russell Wilson	SEA	14	14	353	6.9	62.9	7.6	5.9	2.5	6.3	61.6	7.2	4.4	2.7
Robert Griffin III	WAS	13	13	351	7.4	66.4	8.3	5.1	1.1	6.5	62.5	7.3	4.3	2.5
Michael Vick	PHI	9	9	316	7.9	58.5	6.9	3.5	2.8	6.6	60.5	7.0	4.1	2.7
Blaine Gabbert	JAX	10	10	278	7.3	58.3	6.0	3.2	2.2	6.5	60.4	6.9	4.1	2.6
Matt Cassel	KAN	9	8	277	6.4	58.1	6.5	2.2	4.3	6.2	60.4	7.0	4.0	2.8
Jake Locker	TEN	9	9	269	5.6	57.6	7.0	3.3	3.3	5.9	60.3	7.1	4.1	2.7
Matt Hasselbeck	TEN	8	5	221	6.0	62.4	6.2	3.2	2.3	6.1	61.5	6.9	4.1	2.6
Nick Foles	PHI	6	5	217	6.5	59.4	6.2	2.3	1.8	6.2	60.7	6.9	4.0	2.6
Alex Smith	SFO	9	9	217	10.0	70.0	8.0	6.0	2.3	7.3	63.4	7.3	4.4	2.6
Chad Henne	JAX	8	4	216	8.5	51.9	6.7	3.7	2.3	6.8	58.8	7.0	4.2	2.6
John Skelton	ARI	7	6	201	6.9	54.2	5.6	1.0	4.5	6.4	59.4	6.8	3.8	2.8
Kevin Kolb	ARI	6	5	183	12.9	59.6	6.4	4.4	1.6	8.2	60.8	6.9	4.2	2.6
Brady Quinn	KAN	8	6	159	9.1	59.7	5.8	1.3	3.8	7.0	60.8	6.8	3.9	2.8
Colin Kaepernick	SFO	11	5	154	8.3	65.6	8.4	4.5	1.3	6.8	62.3	7.3	4.3	2.5
Ryan Lindley	ARI	6	3	141	6.6	51.1	4.3	0.0	4.3	6.3	58.6	6.5	3.7	2.8

(“A-” before a stat means the actual observed rate; “R-” means the regressed rate.)

Now we just need to reconstruct the player’s raw passing line as though he posted those rate stats instead of his actual rates. Cmp%, YPA, TD%, and INT% are easy (just multiply by attempts), and Sack% can be derived via simple algebra:

Sacks_new = (-reg_sk% * Attempts) / (reg_sk% – 1)

(Sack yards can be assumed by multiplying raw sack yards per sack by the new sack total.)

Finally, we plug the new totals into the Adjusted Net Yards Per Attempt formula, and we have a QB stat that is sort of like baseball’s Fielding Independent Pitching (FIP), which also seeks to reduce the noise and teammate interactions in a pitcher’s ERA by reducing his performance to only those elements he has control over — strikeouts, walks, and home runs.

Here are the 2012 leaders in QB-FIP (along with their regressed totals):

Rk	Player	Age	Tm	G	GS	Cmp	Att	Yds	TD	Int	Sk	SkYds	QB-FIP
1	Peyton Manning	36	DEN	14	14	321	511	3697	23	13	29	191	6.22
2	Tom Brady	35	NWE	14	14	346	560	4027	24	14	32	214	6.20
3	Robert Griffin III	22	WAS	13	13	219	351	2568	15	9	24	166	6.15
4	Colin Kaepernick	25	SFO	11	5	96	154	1130	7	4	11	76	6.11
5	Ben Roethlisberger	30	PIT	11	11	246	398	2836	17	10	25	141	6.11
6	Matt Ryan	27	ATL	14	14	339	539	3893	23	14	32	225	6.11
7	Eli Manning	31	NYG	14	14	297	487	3476	20	13	26	165	6.09
8	Drew Brees	33	NOR	14	14	352	574	4118	26	16	33	237	6.08
9	Josh Freeman	24	TAM	14	14	279	469	3350	20	12	27	181	6.08
10	Aaron Rodgers	29	GNB	14	14	296	474	3402	21	12	35	197	6.06
11	Cam Newton	23	CAR	14	14	256	423	3086	18	11	29	203	6.05
12	Russell Wilson	24	SEA	14	14	217	353	2539	16	9	24	148	6.05
13	Alex Smith	28	SFO	9	9	138	217	1575	10	6	17	97	6.04
14	Matt Schaub	31	HOU	14	13	295	476	3407	20	12	27	228	6.01
15	Tony Romo	32	DAL	14	14	355	568	4071	24	15	35	255	5.97
16	Andy Dalton	25	CIN	14	14	290	472	3336	21	13	33	176	5.94
17	Joe Flacco	27	BAL	14	14	295	487	3453	20	13	32	209	5.93
18	Carson Palmer	33	OAK	14	14	343	562	3980	23	15	33	254	5.92
19	Ryan Fitzpatrick	30	BUF	14	13	272	444	3101	19	12	29	151	5.89
20	Andrew Luck	23	IND	14	13	336	564	3990	23	15	37	230	5.89
21	Matthew Stafford	24	DET	14	14	382	629	4413	25	17	37	256	5.88
22	Jake Locker	24	TEN	9	9	162	269	1900	11	7	17	108	5.88
23	Michael Vick	32	PHI	9	9	191	316	2223	13	8	22	124	5.84
24	Sam Bradford	25	STL	14	14	294	482	3380	20	13	32	216	5.82
25	Brandon Weeden	29	CLE	14	14	300	498	3477	20	14	30	198	5.80
26	Ryan Tannehill	24	MIA	14	14	257	424	2987	17	11	27	205	5.78
27	Chad Henne	27	JAX	8	4	127	216	1511	9	6	16	94	5.78
28	Philip Rivers	31	SDG	14	14	302	488	3422	21	13	35	221	5.77
29	Matt Cassel	30	KAN	9	8	167	277	1928	11	8	18	97	5.75
30	Jay Cutler	29	CHI	13	13	229	377	2661	16	10	28	187	5.74
31	Christian Ponder	24	MIN	14	14	262	425	2912	17	11	28	164	5.70
32	Nick Foles	23	PHI	6	5	132	217	1500	9	6	14	102	5.70
33	Matt Hasselbeck	37	TEN	8	5	136	221	1525	9	6	14	105	5.70
34	Mark Sanchez	26	NYJ	14	14	249	418	2903	17	12	29	178	5.68
35	Blaine Gabbert	23	JAX	10	10	168	278	1907	11	7	19	138	5.61
36	Kevin Kolb	28	ARI	6	5	111	183	1270	8	5	16	96	5.61
37	Brady Quinn	28	KAN	8	6	97	159	1086	6	4	12	70	5.50
38	John Skelton	24	ARI	7	6	119	201	1365	8	6	14	89	5.46
39	Ryan Lindley	23	ARI	6	3	83	141	921	5	4	9	72	5.15
	Lg Average												5.92