Patriots and Colts

The Patriots came into Indianapolis and beat the Colts in one of the most hyped mid-season games in NFL history. NE came into the game ranked #1 in efficiency rankings, accounting for strength of schedule. IND came into the game ranked just behind at #2.

This week the Colts will be ranked #1 ahead of the Pats. IND's generic win probability (GWP) -- the probability they would win a game against a league average team at a neutral site-- is 0.92, while NE's is 0.91.

Except for the score, the Colts actually outplayed the Patriots. Given their in-game statistics, it was surprising that NE won the game. One model says IND would have had a 77% chance of winning the game. The 4-point victory by the Patriots came down to one or two critical, high-leverage plays.

Most fans would say, so what? Who cares who was more efficient. The only thing that matters is the score. "You are what your record says you are," says Bill Parcells. That's true, but in-game efficiency stats are very often more indicative of future performance.

Unfortunately for IND, their hopes of an undefeated season are now dashed while NE's are still intact. Updating a previous post, here is NE's probability of finishing the regular season 16-0 accounting for their performance in yesterday's win.

Here are NE's upcoming games and the associated probabilities of winning each one.

Vprob	Visitor	Home	Hprob
0.85	NE	BUF	0.15
0.08	PHI	NE	0.92
0.89	NE	BAL	0.11
0.16	PIT	NE	0.84
0.03	NYJ	NE	0.97
0.02	MIA	NE	0.98
0.82	NE	NYG	0.18

So assuming they don't rest starters or suffer a critical injury, NE's probability of finishing the season 16-0 is now:

0.85 * 0.92 * 0.89 * 0.84 * 0.97 * 0.98 * 0.82 = 0.45.

Advance Game Predictions

Here is a summary of predicted probabilities for the outcomes of NFL games in future weeks.

Week	Visitor	Home	Vprob	Hprob
12	GB	DET	0.68	0.32
12	NYJ	DAL	0.05	0.95
12	IND	ATL	0.88	0.12
12	BUF	JAX	0.30	0.70
12	DEN	CHI	0.70	0.30
12	HOU	CLE	0.44	0.56
12	MIN	NYG	0.29	0.71
12	NO	CAR	0.42	0.58
12	OAK	KC	0.26	0.74
12	SS	STL	0.82	0.18
12	TEN	CIN	0.51	0.49
12	WAS	TB	0.18	0.82
12	SF	ARI	0.17	0.83
12	BAL	SD	0.29	0.71
12	PHI	NE	0.09	0.91
12	MIA	PIT	0.08	0.92
13	GB	DAL	0.16	0.84
13	ATL	STL	0.64	0.36
13	BUF	WAS	0.36	0.64
13	DET	MIN	0.31	0.69
13	HOU	TEN	0.31	0.69
13	JAX	IND	0.12	0.88
13	NYJ	MIA	0.40	0.60
13	SD	KC	0.61	0.39
13	SS	PHI	0.48	0.52
13	SF	CAR	0.19	0.81
13	TB	NO	0.81	0.19
13	CLE	ARI	0.43	0.57
13	DEN	OAK	0.73	0.27
13	NYG	CHI	0.80	0.20
13	CIN	PIT	0.15	0.85
13	NE	BAL	0.92	0.08
14	CHI	WAS	0.15	0.85
14	CAR	JAX	0.22	0.78
14	DAL	DET	0.89	0.11
14	MIA	BUF	0.27	0.73
14	NYG	PHI	0.44	0.56
14	OAK	GB	0.09	0.91
14	PIT	NE	0.20	0.80
14	SD	TEN	0.38	0.62
14	STL	CIN	0.19	0.81
14	TB	HOU	0.76	0.24
14	ARI	SS	0.20	0.80
14	MIN	SF	0.77	0.23
14	CLE	NYJ	0.55	0.45
14	KC	DEN	0.28	0.72
14	IND	BAL	0.90	0.10
14	NO	ATL	0.37	0.63
15	DEN	HOU	0.45	0.55
15	CIN	SF	0.76	0.24
15	ARI	NO	0.44	0.56
15	ATL	TB	0.13	0.87
15	BAL	MIA	0.50	0.50
15	BUF	CLE	0.46	0.54
15	GB	STL	0.81	0.19
15	JAX	PIT	0.23	0.77
15	NYJ	NE	0.03	0.97
15	SS	CAR	0.69	0.31
15	TEN	KC	0.65	0.35
15	IND	OAK	0.96	0.04
15	DET	SD	0.27	0.73
15	PHI	DAL	0.14	0.86
15	WAS	NYG	0.33	0.67
15	CHI	MIN	0.18	0.82
16	PIT	STL	0.90	0.10
16	DAL	CAR	0.88	0.12
16	CLE	CIN	0.37	0.63
16	GB	CHI	0.81	0.19
16	HOU	IND	0.07	0.93
16	KC	DET	0.38	0.62
16	MIA	NE	0.03	0.97
16	NYG	BUF	0.57	0.43
16	OAK	JAX	0.10	0.90
16	PHI	NO	0.63	0.37
16	WAS	MIN	0.47	0.53
16	ATL	ARI	0.44	0.56
16	BAL	SS	0.19	0.81
16	NYJ	TEN	0.19	0.81
16	TB	SF	0.93	0.07
16	DEN	SD	0.37	0.63
17	NE	NYG	0.82	0.18
17	BUF	PHI	0.30	0.70
17	CAR	TB	0.10	0.90
17	CIN	MIA	0.58	0.42
17	DAL	WAS	0.80	0.20
17	DET	GB	0.19	0.81
17	JAX	HOU	0.57	0.43
17	NO	CHI	0.60	0.40
17	PIT	BAL	0.80	0.20
17	SS	ATL	0.65	0.35
17	SF	CLE	0.16	0.84
17	TEN	IND	0.10	0.90
17	MIN	DEN	0.42	0.58
17	SD	OAK	0.76	0.24
17	STL	ARI	0.23	0.77
17	KC	NYJ	0.45	0.55

NFL Prediction Tracking

Here is a great site that tracks the season-long performance of the various NFL prediction models. It also summarizes their weekly predictions. (Thanks to Andy for the link). Model accuracy records from previous years are also available. I will add its link to the right so it can be referred to as the season progresses.

There are many competing statistical models, but it looks like the vast majority don't do very well. Fortunately, it appears the efficiency model used on this site ranks among the very best of the models. So far for 2007, the NFL Stats efficiency model would rank 3rd out of 61. (And if you nitpick, you would notice that the only two models with better records have either attempted predictions for fewer weeks or have possibly cherry-picked games to predict.)

The records for 2006 were strikingly lower. It appears to confirm it was a difficult year to predict with many upsets and with a historically weak average home field advantage. With its 62.56% accuracy rate, the NFL Stats efficiency model would have ranked #1 out of 58 (by a whisker).

Interestingly, there appears to be a lot of churn among the best prediction models. The best models one year aren't usually among the best in other years. This may indicate many of them are benefiting from a significant amount of luck. With so many different models, there are bound to be some that do well not because of predictive insight, but due to randomness. The models with true predictive ability would be the ones that rank near the top from year-to-year.

You can show your support for NFL Stats by sending an email recommending its inclusion in the rankings. [Edit: Never mind. He can't include me unless I predict scores as well.]

Season Win Projections Week 8

Season win totals and division standing projections are listed below. As before, projections are based on each team's opponent-adjusted generic win probability (GWP). The projections account for future opponent strength, and total wins account for current and projected wins. Methodology can be found here.

Team	Rank	Proj GWP	Fut Opp	Proj W
AFC E
NE	1	0.90	0.55	15.2
BUF	19	0.37	0.51	6.3
NYJ	29	0.19	0.57	2.5
MIA	28	0.27	0.54	2.2
AFC N
PIT	5	0.76	0.47	11.9
CLE	20	0.45	0.42	8.1
CIN	15	0.60	0.43	7.4
BAL	16	0.28	0.63	6.6
AFC S
IND	2	0.90	0.52	15.1
JAX	7	0.60	0.52	10.4
TEN	9	0.58	0.52	10.2
HOU	17	0.35	0.55	6.8
AFC W
SD	8	0.61	0.53	9.5
DEN	13	0.61	0.44	8.5
KC	18	0.39	0.52	7.5
OAK	27	0.28	0.52	4.6
NFC E
DAL	3	0.80	0.54	13.2
NYG	11	0.55	0.51	10.4
WAS	12	0.51	0.58	8.6
PHI	10	0.49	0.57	7.4
NFC N
GB	14	0.64	0.43	11.7
DET	22	0.35	0.51	8.2
MIN	23	0.45	0.47	6.0
CHI	30	0.21	0.50	4.7
NFC S
TB	4	0.86	0.40	10.9
CAR	24	0.32	0.55	6.9
NO	25	0.41	0.42	6.7
ATL	26	0.29	0.51	3.6
NFC W
SEA	6	0.80	0.38	11.2
ARI	21	0.47	0.41	7.2
SF	32	0.19	0.44	3.7
STL	31	0.22	0.44	2.0

Game Predictions Week 9

Game probabilities for week 9 NFL games are listed below. The probabilities are based on an efficiency win model explained here and here. The model considers offensive and defensive efficiency stats including running, passing, sacks, turnover rates, and penalty rates. Team stats are adjusted for previous opponent strength. Games in which the model disagrees with consensus favorites are highlighted in red.

Vprob	Visitor	Home	Hprob
0.11	ARI	TB	0.89
0.20	CAR	TEN	0.80
0.51	CIN	BUF	0.49
0.56	DEN	DET	0.44
0.52	GB	KC	0.48
0.69	JAX	NO	0.31
0.65	SD	MIN	0.35
0.23	SF	ATL	0.77
0.71	WAS	NYJ	0.29
0.69	SEA	CLE	0.31
0.54	HOU	OAK	0.46
0.43	NE	IND	0.57
0.65	DAL	PHI	0.35
0.16	BAL	PIT	0.84

Week 8 Efficiency Rankings

NFL team efficiency rankings are listed below in terms of generic winning probability. The GWP is the probability a team would beat the league average team at a neutral site. Each team's opponent's average GWP is also listed, which can be considered to-date strength of schedule. GWP modifies the generic win probability to reflect the strength of past opponents. OGWP is each team's offensive GWP, i.e. it's the team's GWP assuming it had a league-average defense. DGWP is vice-versa. Rankings are based on a logistic regression model applied to data through week 8. A full explanation of the methodology can be found here.

Rank	Team	Last Wk	GWP	Opp GWP	OGWP	DGWP
1	NE	2	0.91	0.46	0.81	0.70
2	IND	1	0.90	0.50	0.76	0.72
3	DAL	4	0.77	0.41	0.69	0.61
4	TB	3	0.76	0.49	0.67	0.60
5	PIT	5	0.71	0.42	0.60	0.61
6	SEA	9	0.65	0.42	0.56	0.55
7	JAX	8	0.61	0.55	0.60	0.54
8	SD	13	0.60	0.45	0.60	0.54
9	TEN	11	0.58	0.51	0.40	0.69
10	PHI	12	0.57	0.39	0.66	0.46
11	NYG	7	0.56	0.41	0.50	0.59
12	WAS	10	0.52	0.51	0.40	0.68
13	DEN	6	0.51	0.57	0.65	0.38
14	GB	15	0.50	0.47	0.54	0.50
15	CIN	14	0.48	0.52	0.64	0.44
16	BAL	24	0.40	0.31	0.38	0.55
17	HOU	18	0.39	0.50	0.46	0.40
18	KC	17	0.39	0.42	0.37	0.57
19	BUF	20	0.38	0.54	0.41	0.55
20	CLE	16	0.37	0.46	0.58	0.37
21	ARI	19	0.37	0.42	0.43	0.49
22	DET	22	0.36	0.41	0.40	0.50
23	MIN	21	0.36	0.44	0.46	0.45
24	CAR	23	0.34	0.46	0.46	0.42
25	NO	28	0.32	0.52	0.48	0.33
26	ATL	26	0.29	0.45	0.45	0.38
27	OAK	25	0.28	0.44	0.29	0.55
28	MIA	29	0.28	0.51	0.49	0.30
29	NYJ	27	0.24	0.49	0.43	0.31
30	CHI	30	0.19	0.49	0.30	0.40
31	STL	32	0.18	0.48	0.31	0.39
32	SF	31	0.14	0.46	0.22	0.42

This week the method of adjusting for opponent strength was improved. Instead of a single iteration of adjustment, the calculations now include as many iterations as required for full convergence. For example, a team that has usually dominated its opponents would have an apparently weaker opponent strength than is the case. Multiple iterations of opponent-strength adjustments corrects for this effect. CLE and BAL appear to be the only teams to be significantly affected.

Patriots or Colts Undefeated?

With the impending showdown between the NFL's top two teams, a lot of the discussion has mentioned the possibility of either the Patriots or Colts going undefeated. Not since the '72 Dolphins went 14-0 in the regular season has an NFL team repeated the feat. There are now 16 games in a regular season, making the achievement even more improbable.

Of course, only one of the two teams could go undefeated this year because they have to play each other. In this post, I'll examine which team is more likely to go 16-0--assuming each wins on Sunday.

The probability that either team would go undefeated is estimated based on a calculation of game-by-game win probabilities. Every permutation of outcomes of wins and losses is computed for each team. The combination that represents only wins and no losses is the probability that the team will be 16-0. The methodology is explained more fully in this post. In short, the probability estimate accounts for all major phases of team efficiency, to-date opponent strength, future opponent strength, and home field advantage in upcoming match-ups.

However, there is one important distinction between teams at this point. Still awaiting their bye, the Patriots and have played, and won, one more game than the Colts. This gives them a distinct advantage when comparing the two teams' chances of winning out. But it is still interesting to know just how possible it is for teams like the Patriots or Colts to do what hasn't been done for three and half decades.

And of course, it all depends on who wins on Sunday.

Both teams have been mercilessly efficient so far in 2007. Below are the efficiency stats for each team (unadjusted for opponent). Also listed is the NFL average (not including NE and IND) for each stat, so we can compare see just how good these two teams are.

Stat	IND	NE	NFL
O Pass	7.57	8.65	6.01
O Run	4.42	4.19	4.05
O Int Rate	0.013	0.011	0.032
O Fum Rate	0.013	0.015	0.027
D Pass	4.79	5.09	6.25
D Run	4.06	4.24	4.05
D Int Rate	0.039	0.042	0.031
Pen Rate	0.21	0.31	0.37

(Pass and run stats are yds per attempt. Fumble rate is fumbles per play. Int rate is in interceptions per attempt. Penalty rate is penalty yards per play.)

NE has the better passing game, but IND has the better running game and defends the pass better. NE gets more interceptions, but IND commits fewer penalties for fewer yards. All things considered, the two teams are about equal. NE has garnered more attention so far because of the fact they've scored more touchdowns, but they've played a considerably weaker schedule.

Below is a table of each team's to-date opponents and their generic win probability (GWP)--the probability a team will beat a notional league-average team at a neutral site. Opponent strengths do account for the beatings handed to them by IND and NE. In other words, NE's strength of schedule isn't penalized due to the pounding their opponents received at the hands of NE themselves. IND's opponents' have been slightly stronger than average with a 0.52 GWP, while NE's opponents' have been below average with a 0.45 GWP.

NE Opp	GWP	IND Opp	GWP
NYJ	0.23	NO	0.32
SD	0.62	TEN	0.58
BUF	0.43	HOU	0.34
CIN	0.50	DEN	0.66
CLE	0.38	TB	0.76
DAL	0.71	bye
MIA	0.23	JAX	0.64
WAS	0.50	CAR	0.33
Avg	0.45		0.52

Although both teams are about equal in (unadjusted) efficiency stats, after adjusting for opponent strength IND comes out on top with a 0.92 GWP compared to a 0.90 GWP for NE. Keep in mind these are estimations, so a difference of 0.02 is essentially a wash. We'll certainly find out more on Sunday.

Given about a 90% chance of winning a game against a league-average opponent at a neutral site, and assuming they win against the Colts, the Patriots would roughly have about a 0.90⁷ = 48% chance of going undefeated. If the Colts win Sunday, they would have about a 0.92⁸ = 51% chance of finishing undefeated.

But NFL games aren't against theoretical league-average opponents, and they aren't (normally) at neutral sites. NE has an slightly easier forthcoming schedule as their future opponents' GWP average is 0.43 while IND's future opponents average a slightly tougher 0.45 GWP.

NE Opp	GWP	IND Opp	GWP
bye		SD	0.62
BUF	0.43	KC	0.44
PHI	0.55	ATL	0.29
BAL	0.34	JAX	0.64
PIT	0.72	BAL	0.34
NYJ	0.23	OAK	0.31
MIA	0.23	HOU	0.34
NYG	0.53	TEN	0.58
Avg	0.43		0.45

NE's upcoming schedule and their associated outcome probabilities are listed below. The series probability that the a team would go undefeated is the product of the probabilities of winning each individual game. Keep in mind this assumes each team wins this Sunday.

Vprob	Visitor	Home	Hprob
0.90	NE	BUF	0.10
0.08	PHI	NE	0.92
0.93	NE	BAL	0.07
0.16	PIT	NE	0.84
0.02	NYJ	NE	0.98
0.02	MIA	NE	0.98
0.85	NE	NYG	0.15

Probability of New England going undefeated =
0.90 * 0.92 * 0.93 * 0.84 * 0.98 * 0.98 * 0.85 = 0.52

IND's upcoming schedule and their associated outcome probabilities are listed below.

Hprob	Visitor	Home	Vprob
0.83	IND	SD	0.17
0.05	KC	IND	0.95
0.95	IND	ATL	0.05
0.10	JAX	IND	0.90
0.94	IND	BAL	0.06
0.95	IND	OAK	0.05
0.03	HOU	IND	0.97
0.08	TEN	IND	0.92

Probability of Indianapolis going undefeated =
0.83 * 0.95 * 0.95 * 0.90 * 0.94 * 0.95 * 0.97 * 0.92 = 0.54

By the end of Sunday's game, one of the teams will see their chances swiftly go to zero.

Note: Republished with a correction to NE's probability.

QB Rating Week 7

The QB Wins Added Per 16 Games stat (+WP16) estimates how many wins a quarterback adds to his team's record over the course of a 16-game season. +WP16 is explained here and here. Last year's ratings can be found in the second link. Here is the list of 2007 QBs and their vital stats through week 7.

Rank	Name	Att	Yds	Air Yds	YAC	Int	Rush	Yds	Sk Yds	Fum	+WP16
1	Brady	229	2125	1248	877	2	8	11	44	3	3.94
2	Manning P	202	1578	1105	473	3	9	-7	31	1	3.78
3	Garrard	148	1141	680	461	0	30	134	73	2	2.58
4	Schaub	197	1581	1043	538	5	14	38	94	7	1.87
5	Palmer	224	1717	1129	588	9	7	11	75	1	1.79
6	Romo	239	1984	1162	822	9	14	81	83	3	1.74
7	Garcia	189	1504	724	780	0	19	40	45	3	1.72
8	Warner	112	883	576	307	3	5	0	30	5	1.64
9	Anderson	184	1496	943	553	8	15	30	63	3	1.48
10	Roethlisberger	166	1303	793	510	5	11	77	119	4	1.15
11	Hasselbeck	233	1705	935	770	6	12	14	80	1	0.83
12	Delhomme	86	624	313	311	1	6	26	46	1	0.81
13	Boller	117	662	402	260	2	7	22	30	1	0.67
14	Pennington	170	1211	757	454	7	15	18	83	0	0.57
15	Smith	84	461	303	158	1	8	67	74	2	0.42
16	Cutler	181	1406	768	638	8	16	74	40	5	0.40
17	McNabb	205	1447	737	710	2	17	56	116	4	0.36
18	Campbell	168	1181	619	562	5	20	93	42	5	0.27
19	Leinart	112	647	374	273	4	11	42	23	0	0.12
20	Manning E	227	1525	819	706	9	9	13	39	3	-0.21
21	McNair	157	922	455	467	2	9	26	37	4	-0.24
22	Young	114	703	414	289	6	32	129	22	3	-0.24
23	Harrington	213	1407	689	718	4	7	14	126	0	-0.25
24	Kitna	187	1480	823	657	6	16	42	152	8	-0.49
25	Favre	247	1715	755	960	6	12	6	73	3	-0.55
26	Huard	215	1470	768	702	7	9	-1	119	2	-0.62
27	Brees	247	1394	754	640	10	11	31	28	2	-0.73
28	Rivers	178	1312	683	629	7	11	2	77	5	-0.75
29	Green	141	987	515	472	7	7	32	53	2	-0.75
30	Griese	163	1203	573	630	6	5	8	77	4	-0.97
31	Lemon	107	643	335	308	4	7	25	51	1	-1.00
32	Culpepper	93	650	317	333	3	13	27	58	2	-1.00
33	Jackson	98	537	264	273	5	11	46	10	0	-1.23
34	Edwards	100	660	331	329	4	3	5	67	1	-1.39
35	Bulger	173	990	591	399	7	4	16	124	3	-1.46
36	Frerotte	85	499	298	201	8	2	3	21	1	-3.04
37	Grossman	89	500	284	216	6	4	9	82	1	-3.12
38	McCown J	68	494	247	247	5	9	46	55	7	-3.80
39	Dilfer	90	463	265	198	5	4	15	100	6	-4.27

I also thought it would be interesting to see how +WP16 compares to the official NFL Passer Rating. Kitna stands out as particularly overrated by the NFL Passer Rating. It appears to be mostly due to his 152 sack yards lost and 8 fumbles, both league-leading stats.

Name	Rank	+WP16	NFL PR Rank	NFL PR
Brady	1	3.94	1	137.9
Manning P	2	3.78	4	103.5
Garrard	3	2.58	5	102.9
Schaub	4	1.87	10	90.5
Palmer	5	1.79	11	89.1
Romo	6	1.74	7	95.6
Garcia	7	1.72	3	106.2
Warner	8	1.64	8	95.2
Anderson	9	1.48	12	88.9
Roethlisberger	10	1.15	6	101.1
Hasselbeck	11	0.83	13	88.7
Delhomme	12	0.81	2	111.8
Boller	13	0.67	26	78.4
Pennington	14	0.57	14	88.6
Smith	15	0.42	33	66.6
Cutler	16	0.40	18	84.2
McNabb	17	0.36	15	88.4
Campbell	18	0.27	25	78.5
Leinart	19	0.12	34	61.9
Manning E	20	-0.21	20	82.9
McNair	21	-0.24	23	80.2
Young	22	-0.24	31	68.0
Harrington	23	-0.25	22	80.9
Kitna	24	-0.49	9	93.9
Favre	25	-0.55	16	87.0
Huard	26	-0.62	24	79.8
Brees	27	-0.73	30	69.1
Rivers	28	-0.75	19	83.8
Green	29	-0.75	28	72.6
Griese	30	-0.97	17	86.0
Lemon	31	-1.00	32	66.8
Culpepper	32	-1.00	21	81.4
Jackson	33	-1.23	37	48.7
Edwards	34	-1.39	29	71.3
Bulger	35	-1.46	35	58.7
Frerotte	36	-3.04	39	44.2
Grossman	37	-3.12	38	45.2
McCown J	38	-3.80	27	75.2
Dilfer	39	-4.27	36	55.0