I leave the baseball analysis to my brothers at baseball-reference.com, but I know enough to be dangerous. There’s a stat called BABIP, which stands for Batting Average on Balls In Play. A “ball in play” is simply any at bat that doesn’t end in a home run or a strikeout. The thinking goes that luck and randomness is mostly responsible for the variance in BABIP allowed by pitchers to opposing batters. Pitchers can control the number of strikeouts they throw and control whether they allow home runs or not, but they can’t really control their BABIP.

Therefore, if a pitcher has a high BABIP, sort of like an NFL team with a lot of turnovers, he’s probably been unlucky. And good things may be coming around the corner. A high BABIP means a pitcher probably has an ERA higher than he “should” and that his ERA will go down in the future. In fact, you can easily recalculate a pitcher’s ERA by replacing the actual BABIP he has allowed with the league average BABIP. And that ERA will be a better predictor of future ERA than the actual ERA. At least, I think. Forgive me if my baseball analysis is not perfect.

Are you still awake? It’s Monday, and I’ve brought not only baseball into the equation, but obscure baseball statistics. Let’s get to the point of the post by starting with a hypothesis:

Assume that it is within a quarterback’s control as to whether he throws a completed pass on any given pass attempt. However, if he throws an incomplete pass, then he has no control over whether or not that pass is intercepted.

Essentially, we’re saying that all incomplete passes are “passes in play.” Therefore, a quarterback’s average of “Picks On Passes In Play” — the number of interceptions per incomplete pass he throws — is out of his control. This is just a hypotheses; how would we go about proving or disproving this theory?

Let’s look at an example. In 2010, Eli Manning led the NFL with 25 interceptions, throwing an interception on 4.6% of his pass attempts, and on 12.5% of his incomplete passes. That same year, his draft classmate Ben Roethlisberger had just five interceptions on 389 attempts. Roethlisberger averaged only 1.3 interceptions per 100 passes, and threw an interception on just 3.4% of his incomplete passes.

Eli actually had a higher completion percentage than Roethlisberger. Maybe that’s a sign that completion percentage and interception rate aren’t strongly related, or maybe it’s a sign that interception rates on incomplete passes are random. In 2010, 7.5% of all incomplete passes were intercepted. If 7.5% of all of Eli Manning’s incomplete passes were intercepted, he would have thrown 15 interceptions in 2010 instead of 25, and therefore would have an estimated interception rate of 2.8% based on a league average POPIP ratio. For Big Ben, if 7.5% of his incomplete passes had been picked off, he would have thrown 11.2 interceptions instead of just five; that would give him an estimated INT rate of 2.9%.

Okay, so what does any of this mean? Manning had an actual INT rate of 4.6% but an estimated rate of 2.8%, while Roethlisberger was at 1.3% and 2.9%, respectively. Obviously this doesn’t impact what’s already happened. But just like how BABIP can help predict future INT, POPIP could help predict future INT rate — well, at least that’s the theory.

As it turns out, in 2011, Manning and Roethlisberger both had actual INT rates of 2.7%. That gives us two pieces of evidence that estimated INT rate based on POPIP is a better predictor of future INT rate than actual INT rate. But those are just two pieces of evidence.

Since 1970, there have been 813 quarterbacks to play for the same team in consecutive years, and throw at least 224 passes in Year N and at least 100 passes in Year N+1. Why those cutoffs? 224 passes in the current minimum number of attempts needed to qualify for passing crowns in rate statistics; meanwhile, I don’t want to lose out on including quarterbacks who were benched early the next year because they were bad. But we can play around with several cutoffs.

I went through and gave a win to the actual INT rate if the player’s interception rate in Year N+1 was closer to his actual INT rate from Year N than his estimated INT rate. On the other hand, if the player’s estimated INT rate in Year N was closer to the actual INT rate in Year N+1 than the actual INT rate, I gave a win to the estimated INT metric.

The results? 335 times, the actual interception rate proved to be the better predictor, while 478 times the estimated interception rate closer to the future rate. So 59% of the time, using estimated INT rates based on POPIP proved to be helpful.

If we make the quarterbacks throw 224+ times in both years, we’re left with 693 pairs of quarterback seasons. The estimated INT rate was a better predictor in 403, or 58%, of those pairs.

If we go back to only 1978 instead of 1970, the estimated interception rate was better 58% of the time out of 595 pairs. If we change the cutoff to 1990, the estimated interception rate was better 58% of the time on 385 pairs.

If we bump the attempts threshold to 350 in both Year N and Year N+1, since 1990, the estimated interception rate was the better predictor on 157 of 253 pairs, or 62% of the time. If we limit it to just the past ten years, we have 122 pairs of quarterbacks — and the estimated INT rate was better on 63% of those pairs. Change the cutoffs to 400 attempts both years and look at only quarterbacks over the last five years, and 60% of the time on 57 pairs the estimated interception rate was better.

I think you get the point. Estimated interception rate isn’t perfect — there are so many fluky interceptions that no one could come very close to predicting future interception rate — but I feel pretty confident in telling you that estimated interception rate is better at predicting future INT rate than actual INT rate. In that vein, it is similar to how Pythagorean winning percentage is a better predictor of future winning percentage than actual winning percentage.

We can also use POPIP to find quarterback outliers. We can calculate how many interceptions a quarterback was estimated to throw for his career along with how many he actually threw. The difference there might be pretty informative. The table below lists all quarterbacks since 1970 with at least 50 interceptions; as always, quarterback who played prior to 1970 are included but only their stats since 1970 are reflected in the table below. The table is currently sorted based on the quarterbacks who came in under their estimated number of interceptions the most. Let me use Donovan McNabb as an example.

The first row reads: McNabb for his career has 5,374 attempts and 2,204 incomplete passes. His career INT rate is 2.2%, and has thrown an interception on 5.3% of his incompletions. Based on league average POPIP, we would have expected him to throw an interception on 3.2% of his passes. For his career, he has 117 interceptions and we would estimate that he would have thrown 171.1 interceptions. As a result, McNabb has thrown 54.1 fewer interceptions than we would have estimated (this is what the table is sorted by). He has thrown one fewer interception per 100 passes than we would have projected.

Rk	Name	Att	INC	INT RT	INT/INC	EST INT RT	INT	EST INT	INT DIFF	INT RT DIF
1	Donovan McNabb	5374	2204	2.2%	5.3%	3.2%	117	171.1	-54.1	-1%
2	Roman Gabriel	2267	1050	3.3%	7%	5.1%	74	116.2	-42.2	-1.9%
3	Joe Montana	5391	1982	2.6%	7%	3.3%	139	178.1	-39.1	-0.7%
4	Neil O'Donnell	3229	1364	2.1%	5%	3.3%	68	105.5	-37.5	-1.2%
5	Mark Brunell	4640	1879	2.3%	5.7%	3.1%	108	144.7	-36.7	-0.8%
6	John Elway	7250	3127	3.1%	7.2%	3.6%	226	261.8	-35.8	-0.5%
7	Tom Brady	5321	1924	2.2%	6%	2.8%	115	149.5	-34.5	-0.6%
8	Neil Lomax	3153	1336	2.9%	6.7%	3.9%	90	123.8	-33.8	-1.1%
9	Ken Anderson	4475	1821	3.6%	8.8%	4.3%	160	193.2	-33.2	-0.7%
10	Dan Marino	8358	3391	3%	7.4%	3.4%	252	284	-32	-0.4%
11	Doug Williams	2507	1267	3.7%	7.3%	5%	93	125	-32	-1.3%
12	Ken O'Brien	3602	1492	2.7%	6.6%	3.6%	98	129.6	-31.6	-0.9%
13	Ron Jaworski	4117	1930	4%	8.5%	4.7%	164	195.5	-31.5	-0.8%
14	Phil Simms	4647	2071	3.4%	7.6%	4%	157	187.9	-30.9	-0.7%
15	Jim Hart	4183	2010	4.5%	9.3%	5.2%	187	217.9	-30.9	-0.7%
16	Bernie Kosar	3365	1371	2.6%	6.3%	3.5%	87	117.6	-30.6	-0.9%
17	Roger Staubach	2911	1249	3.7%	8.6%	4.7%	107	137.1	-30.1	-1%
18	Rich Gannon	4206	1673	2.5%	6.2%	3.2%	104	132.7	-28.7	-0.7%
19	Jeff Garcia	3676	1412	2.3%	5.9%	3%	83	110.2	-27.2	-0.7%
20	Fran Tarkenton	3445	1389	3.8%	9.5%	4.5%	132	154.4	-22.4	-0.7%
21	Joe Theismann	3602	1558	3.8%	8.9%	4.4%	138	158.9	-20.9	-0.6%
22	Steve McNair	4544	1811	2.6%	6.6%	3.1%	119	139.5	-20.5	-0.5%
23	Randall Cunningham	4289	1860	3.1%	7.2%	3.6%	134	154.3	-20.3	-0.5%
24	Bill Kenney	2430	1100	3.5%	7.8%	4.3%	86	104.5	-18.5	-0.8%
25	Bert Jones	2551	1121	4%	9%	4.7%	101	119.1	-18.1	-0.7%
26	Kerry Collins	6261	2774	3.1%	7.1%	3.4%	196	212.9	-16.9	-0.3%
27	Jeff George	3967	1669	2.8%	6.8%	3.3%	113	129.5	-16.5	-0.4%
28	Drew Bledsoe	6717	2878	3.1%	7.2%	3.3%	206	220	-14	-0.2%
29	Jason Campbell	2131	835	2.3%	6%	3%	50	64	-14	-0.7%
30	Joe Ferguson	4519	2150	4.6%	9.7%	4.9%	209	223	-14	-0.3%
31	Michael Vick	2538	1116	2.8%	6.5%	3.4%	72	85.7	-13.7	-0.5%
32	Greg Landry	2092	919	4.1%	9.4%	4.8%	86	99.6	-13.6	-0.6%
33	David Garrard	2281	875	2.4%	6.2%	2.9%	54	67.1	-13.1	-0.6%
34	Steve Bartkowski	3456	1524	4.2%	9.4%	4.5%	144	156.9	-12.9	-0.4%
35	Billy Kilmer	2028	940	4.5%	9.8%	5.2%	92	104.7	-12.7	-0.6%
36	Jim Zorn	3149	1480	4.5%	9.5%	4.9%	141	153.6	-12.6	-0.4%
37	Kyle Orton	2204	920	2.6%	6.2%	3.1%	57	69.4	-12.4	-0.6%
38	Steve Young	4149	1482	2.6%	7.2%	2.9%	107	119.4	-12.4	-0.3%
39	Jim Harbaugh	3918	1613	3%	7.3%	3.3%	117	128.3	-11.3	-0.3%
40	Jay Schroeder	2808	1382	3.8%	7.8%	4.2%	108	118.4	-10.4	-0.4%
41	Doug Flutie	2151	974	3.2%	7%	3.6%	68	78.3	-10.3	-0.5%
42	Tony Banks	2356	1078	3.1%	6.8%	3.5%	73	82.8	-9.8	-0.4%
43	Bobby Douglass	1030	591	5.4%	9.5%	6.3%	56	65.3	-9.3	-0.9%
44	Aaron Brooks	2963	1290	3.1%	7.1%	3.4%	92	101.3	-9.3	-0.3%
45	Jeff Blake	3241	1414	3.1%	7%	3.3%	99	108	-9	-0.3%
46	Tony Eason	1564	653	3.3%	7.8%	3.8%	51	59.9	-8.9	-0.6%
47	Pat Haden	1363	632	4.4%	9.5%	5%	60	67.6	-7.6	-0.6%
48	Mike Pagel	1509	753	4.2%	8.4%	4.7%	63	70.6	-7.6	-0.5%
49	Mike Livingston	1590	762	4.8%	10.1%	5.3%	77	84.2	-7.2	-0.5%
50	Mark Rypien	2613	1147	3.4%	7.7%	3.6%	88	95.1	-7.1	-0.3%
51	Gary Danielson	1932	827	4%	9.4%	4.4%	78	84.9	-6.9	-0.4%
52	Jim McMahon	2573	1081	3.5%	8.3%	3.8%	90	96.6	-6.6	-0.3%
53	Philip Rivers	3037	1107	2.6%	7%	2.8%	78	84.5	-6.5	-0.2%
54	Brad Johnson	4326	1658	2.8%	7.4%	3%	122	128.4	-6.4	-0.1%
55	Jeff Hostetler	2338	981	3%	7.2%	3.3%	71	77.1	-6.1	-0.3%
56	Brian Sipe	3439	1495	4.3%	10%	4.5%	149	155	-6	-0.2%
57	Chris Miller	2892	1312	3.5%	7.8%	3.7%	102	108	-6	-0.2%
58	Matt Hasselbeck	4797	1906	3%	7.5%	3.1%	142	147.9	-5.9	-0.1%
59	Alex Smith	1959	822	3%	7.1%	3.2%	58	63.2	-5.2	-0.3%
60	Craig Morton	3201	1453	4.7%	10.4%	4.9%	151	156.2	-5.2	-0.2%
61	Bubby Brister	2212	1005	3.5%	7.8%	3.7%	78	82.8	-4.8	-0.2%
62	Don Majkowski	1905	849	3.5%	7.9%	3.8%	67	71.5	-4.5	-0.2%
63	Matt Schaub	2279	813	2.5%	7.1%	2.7%	58	61.9	-3.9	-0.2%
64	Archie Manning	3642	1631	4.8%	10.6%	4.8%	173	176.4	-3.4	-0.1%
65	Dan Pastorini	3055	1499	5.3%	10.7%	5.4%	161	164	-3	-0.1%
66	Boomer Esiason	5205	2236	3.5%	8.2%	3.6%	184	186.8	-2.8	-0.1%
67	Troy Aikman	4715	1817	3%	7.8%	3%	141	143.3	-2.3	0%
68	Joey Harrington	2538	1114	3.3%	7.6%	3.4%	85	87.2	-2.2	-0.1%
69	Len Dawson	1344	564	4.5%	10.8%	4.7%	61	62.8	-1.8	-0.1%
70	Stan Humphries	2516	1085	3.3%	7.7%	3.4%	84	85.3	-1.3	-0.1%
71	Billy Joe Tolliver	1707	816	3.7%	7.8%	3.8%	64	65.1	-1.1	-0.1%
72	Trent Green	3740	1474	3%	7.7%	3.1%	114	115	-1	0%
73	Chad Pennington	2471	839	2.6%	7.6%	2.6%	64	64.9	-0.9	0%
74	Warren Moon	6823	2835	3.4%	8.2%	3.4%	233	233.8	-0.8	0%
75	Steve Beuerlein	3328	1434	3.4%	7.8%	3.4%	112	112.7	-0.7	0%
76	Marc Bulger	3171	1202	2.9%	7.7%	2.9%	93	93.4	-0.4	0%
77	Gus Frerotte	3106	1407	3.4%	7.5%	3.4%	106	106.3	-0.3	0%
78	James Harris	1113	521	5.2%	11.1%	5.2%	58	58.3	-0.3	0%
79	David Carr	2264	913	3.1%	7.8%	3.1%	71	71.1	-0.1	0%
80	David Whitehurst	980	476	5.2%	10.7%	5.2%	51	50.8	0.2	0%
81	Tommy Kramer	3651	1639	4.3%	9.6%	4.3%	158	157.7	0.3	0%
82	Scott Brunner	1046	534	5.2%	10.1%	5.1%	54	53.4	0.6	0.1%
83	Charley Johnson	1345	638	5.3%	11.1%	5.2%	71	70.4	0.6	0%
84	Daryle Lamonica	981	490	5.6%	11.2%	5.5%	55	54.3	0.7	0.1%
85	Steve Walsh	1317	604	3.8%	8.3%	3.7%	50	48.7	1.3	0.1%
86	John Brodie	1069	470	5.1%	11.5%	4.9%	54	52.6	1.4	0.1%
87	Tony Romo	2592	920	2.8%	7.8%	2.7%	72	70.4	1.6	0.1%
88	Eric Hipple	1546	716	4.5%	9.8%	4.4%	70	68.3	1.7	0.1%
89	Peyton Manning	7210	2528	2.7%	7.8%	2.7%	198	196.2	1.8	0%
90	Dave M. Brown	1634	742	3.5%	7.8%	3.4%	58	56.2	1.8	0.1%
91	Kyle Boller	1519	658	3.6%	8.2%	3.4%	54	51.8	2.2	0.1%
92	Jack Trudeau	1644	771	4.2%	8.9%	4.1%	69	66.6	2.4	0.1%
93	Scott Mitchell	2346	1045	3.5%	7.8%	3.3%	81	78.5	2.5	0.1%
94	Derek Anderson	1436	680	3.8%	8.1%	3.7%	55	52.5	2.5	0.2%
95	Drew Brees	5479	1866	2.7%	7.8%	2.6%	146	143.1	2.9	0.1%
96	David Woodley	1300	613	4.8%	10.3%	4.6%	63	60.1	2.9	0.2%
97	Rick Mirer	2043	955	3.7%	8%	3.6%	76	72.9	3.1	0.2%
98	Mark Sanchez	1414	632	3.6%	8.1%	3.4%	51	47.6	3.4	0.2%
99	Erik Kramer	2299	982	3.4%	8%	3.3%	79	75.3	3.7	0.2%
100	Elvis Grbac	2445	999	3.3%	8.1%	3.2%	81	77.2	3.8	0.2%
101	Jim Everett	4923	2082	3.6%	8.4%	3.5%	175	171	4	0.1%
102	Eli Manning	3921	1630	3.3%	7.9%	3.2%	129	124.9	4.1	0.1%
103	Kordell Stewart	2358	1042	3.6%	8.1%	3.4%	84	79.8	4.2	0.2%
104	Steve DeBerg	5024	2150	4.1%	9.5%	4%	204	199.6	4.4	0.1%
105	Gary Huff	788	396	6.3%	12.6%	5.6%	50	44.4	5.6	0.7%
106	Rex Grossman	1562	699	3.8%	8.6%	3.4%	60	53.7	6.3	0.4%
107	John Hadl	2175	1051	5.7%	11.7%	5.4%	123	116.6	6.4	0.3%
108	Ben Roethlisberger	3313	1223	3%	8.2%	2.8%	100	93.5	6.5	0.2%
109	Steve Ramsey	921	465	6.3%	12.5%	5.5%	58	50.9	7.1	0.8%
110	Gary Hogeboom	1325	582	4.5%	10.3%	4%	60	52.6	7.4	0.6%
111	Mark Malone	1648	809	4.9%	10%	4.4%	81	73.1	7.9	0.5%
112	Vince Young	1304	549	3.9%	9.3%	3.3%	51	42.9	8.1	0.6%
113	Bob Griese	2491	1038	4.9%	11.8%	4.6%	122	113.9	8.1	0.3%
114	Terry Bradshaw	3901	1876	5.4%	11.2%	5.2%	210	201.8	8.2	0.2%
115	Dave Krieg	5311	2206	3.7%	9%	3.6%	199	190.8	8.2	0.2%
116	Mike Phipps	1799	913	6%	11.8%	5.5%	108	99.5	8.5	0.5%
117	Jake Delhomme	2932	1191	3.4%	8.5%	3.1%	101	92.2	8.8	0.3%
118	Bob Avellini	1110	550	6.2%	12.5%	5.4%	69	60.1	8.9	0.8%
119	Dave Wilson	1039	488	5.3%	11.3%	4.4%	55	45.3	9.7	0.9%
120	Vince Evans	1390	686	5.3%	10.8%	4.6%	74	64.2	9.8	0.7%
121	Jay Fiedler	1717	709	3.8%	9.3%	3.3%	66	56	10	0.6%
122	Dan Fouts	5604	2307	4.3%	10.5%	4.1%	242	231.4	10.6	0.2%
123	Randy Wright	1119	517	5.1%	11%	4.1%	57	46.1	10.9	1%
124	Marc Wilson	2081	996	4.9%	10.2%	4.4%	102	90.7	11.3	0.5%
125	Jay Cutler	2521	980	3.4%	8.8%	3%	86	74.6	11.4	0.5%
126	Jim Plunkett	3701	1758	5.3%	11.3%	5%	198	186	12	0.3%
127	Ryan Fitzpatrick	1744	712	3.7%	9.1%	3%	65	53	12	0.7%
128	Rodney Peete	2346	1002	3.9%	9.2%	3.4%	92	79.3	12.7	0.5%
129	Tim Couch	1714	689	3.9%	9.7%	3.2%	67	54.2	12.8	0.7%
130	Chris Chandler	4005	1677	3.6%	8.7%	3.3%	146	133.1	12.9	0.3%
131	Tommy Maddox	1200	514	4.5%	10.5%	3.4%	54	40.6	13.4	1.1%
132	Wade Wilson	2428	1037	4.2%	9.8%	3.6%	102	88.6	13.4	0.6%
133	Daunte Culpepper	3199	1183	3.3%	9%	2.9%	106	92.5	13.5	0.4%
134	Carson Palmer	3545	1322	3.3%	8.8%	2.9%	116	102.3	13.7	0.4%
135	Mike Tomczak	2337	1089	4.5%	9.7%	3.9%	106	90.7	15.3	0.7%
136	Bobby Hebert	3121	1282	4%	9.7%	3.5%	124	108.6	15.4	0.5%
137	Jake Plummer	4350	1866	3.7%	8.6%	3.3%	161	144.4	16.6	0.4%
138	Danny White	2950	1189	4.5%	11.1%	3.9%	132	115.1	16.9	0.6%
139	Jim Kelly	4779	1905	3.7%	9.2%	3.3%	175	158.1	16.9	0.4%
140	Brian Griese	2796	1044	3.5%	9.5%	2.9%	99	81.8	17.2	0.6%
141	Norm Snead	1360	588	6%	13.9%	4.7%	82	64.5	17.5	1.3%
142	Kurt Warner	4070	1404	3.1%	9.1%	2.7%	128	109.4	18.6	0.5%
143	Dennis Shaw	924	435	7.4%	15.6%	5.2%	68	48.5	19.5	2.1%
144	Vince Ferragamo	1615	713	5.6%	12.8%	4.4%	91	71.4	19.6	1.2%
145	Trent Dilfer	3172	1413	4.1%	9.1%	3.4%	129	107.8	21.2	0.7%
146	Joe Namath	1719	859	6.7%	13.5%	5.5%	116	94.3	21.7	1.3%
147	Richard Todd	2967	1357	5.4%	11.9%	4.7%	161	138.2	22.8	0.8%
148	Jon Kitna	4442	1765	3.7%	9.3%	3.1%	165	138.5	26.5	0.6%
149	Vinny Testaverde	6701	2914	4%	9.2%	3.5%	267	233.8	33.2	0.5%
150	Steve Grogan	3593	1714	5.8%	12.1%	4.8%	208	173.8	34.2	1%
151	Brett Favre	10169	3869	3.3%	8.7%	3%	336	300.2	35.8	0.4%
152	Lynn Dickey	3125	1378	5.7%	13%	4.5%	179	140.1	38.9	1.2%
153	Ken Stabler	3793	1523	5.9%	14.6%	4.3%	222	162.1	59.9	1.6%

It’s tempting to attribute much of the spread between actual and estimated interceptions to luck. No doubt, luck plays a big part, and is perhaps the biggest single factor. I don’t know if there is a lot of talent involved in keeping your POPIP low; both Peyton Manning and Drew Brees have almost exactly hit their estimated interception numbers. Greats like Brett Favre and Kurt Warner came in with a bit more interceptions than expected, while Donovan McNabb, Bernie Kosar and Ken O’Brien were great at having a low POPIP average. And, of course, we should need to guard against circular logic such as ‘Keeping your POPIP low is a skill because some of the best quarterbacks kept it low, and those quarterbacks are some of the best quarterbacks because they didn’t throw many interceptions.’

But just like we can look at the relationship between sack rate and interception rate to see a quarterback’s style of play rather than just consider stats as good and bad, we can do the same here. Commenter Red astutely pointed out that McNabb had a low interception rate even though he was inaccurate, and he did seem to throw a lot of bad passes towards his receivers’ feet and not by defenders’ hands. I don’t really think of Warner and Favre as similar quarterbacks, but both did seem to throw a fair share of interceptions.

Ken Stabler is the one that really throws me. His INT/INC rate is off the charts, even for his era. Let me know your thoughts in the comments. I’ll close with a cool chart, showing the INT/ATT and INT/INC rates for every year since the merger.