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

Season Win Projections Week 7

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 now account for future opponent strength. Total wins account for current and projected wins. Methodology can be found here.

Team	Rank	Proj GWP	Fut Opp	Current	Proj
AFC E
NE	2	0.86	0.55	7	14.7
BUF	20	0.40	0.51	2	6.0
NYJ	27	0.26	0.57	1	3.4
MIA	29	0.26	0.54	0	2.3
AFC N
PIT	5	0.73	0.47	4	11.3
CLE	16	0.54	0.42	3	8.4
CIN	14	0.61	0.43	2	8.1
BAL	24	0.24	0.63	4	6.1
AFC S
IND	1	0.89	0.52	6	14.9
JAX	8	0.61	0.52	4	10.1
TEN	11	0.57	0.52	4	9.7
HOU	18	0.38	0.55	4	7.4
AFC W
DEN	6	0.70	0.44	3	10.0
SD	13	0.53	0.53	3	8.3
KC	17	0.43	0.52	4	7.9
OAK	25	0.31	0.52	2	5.1
Team	Rank	Proj GWP	Fut Opp	Current	Proj
NFC E
DAL	4	0.70	0.54	6	12.3
NYG	7	0.64	0.51	5	10.8
WAS	10	0.54	0.58	4	9.4
PHI	12	0.51	0.57	2	7.1
NFC N
GB	15	0.56	0.43	5	10.6
DET	22	0.38	0.51	4	7.8
MIN	21	0.43	0.47	2	6.3
CHI	30	0.26	0.50	3	5.3
NFC S
TB	3	0.82	0.40	4	11.4
CAR	23	0.31	0.55	4	7.1
NO	28	0.36	0.42	2	5.6
ATL	26	0.32	0.51	1	3.8
NFC W
SS	9	0.74	0.38	4	10.6
ARI	19	0.50	0.41	3	7.5
SF	31	0.28	0.44	2	4.8
STL	32	0.26	0.44	0	2.6

Game Predictions Week 8

Game probabilities for week 8 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.

Vprob	Visitor	Home	Hprob
0.68	CLE	STL	0.32
0.57	DET	CHI	0.43
0.92	IND	CAR	0.08
0.82	NYG	MIA	0.18
0.20	OAK	TEN	0.80
0.58	PHI	MIN	0.42
0.57	PIT	CIN	0.43
0.51	BUF	NYJ	0.49
0.29	HOU	SD	0.71
0.27	JAX	TB	0.73
0.49	NO	SF	0.51
0.13	WAS	NE	0.87
0.27	GB	DEN	0.73

Edit: I was just reminded here that the NYG - MIA game is in London this week. I have revised the game probability to reflect this. The result was a swing of 0.06, so MIA's probability of winning went from 0.24 to 0.18. The Giants have benefited from another favorable scheduling aberration recently, when they hosted NO for one of their post-Katrina home games.

Also, if the SD-HOU game is played at an alternate site, the new probabilities would still have SD as the favorites at 0.64 to 0.36.

Week 7 Efficiency Rankings

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 7. A full explanation of the methodology can be found here.

Team	Rank	Last Wk	GWP	Opp GWP	OGWP	DGWP
IND	1	2	0.90	0.52	0.77	0.72
NE	2	1	0.88	0.44	0.79	0.70
TB	3	3	0.76	0.48	0.70	0.57
DAL	4	4	0.73	0.42	0.70	0.61
PIT	5	6	0.70	0.43	0.59	0.62
DEN	6	9	0.65	0.57	0.63	0.51
NYG	7	5	0.65	0.48	0.59	0.60
JAX	8	7	0.63	0.55	0.65	0.49
SEA	9	11	0.63	0.43	0.58	0.53
WAS	10	8	0.61	0.47	0.42	0.71
TEN	11	12	0.58	0.53	0.38	0.70
PHI	12	10	0.58	0.45	0.64	0.46
SD	13	14	0.56	0.51	0.60	0.47
CIN	14	13	0.55	0.56	0.63	0.45
GB	15	15	0.50	0.53	0.49	0.52
CLE	16	17	0.46	0.55	0.53	0.43
KC	17	18	0.45	0.44	0.37	0.58
HOU	18	16	0.42	0.52	0.49	0.44
ARI	19	23	0.41	0.50	0.47	0.49
BUF	20	19	0.41	0.64	0.41	0.52
MIN	21	21	0.40	0.45	0.43	0.46
DET	22	27	0.40	0.52	0.39	0.46
CAR	23	22	0.36	0.39	0.46	0.42
BAL	24	25	0.35	0.33	0.39	0.52
OAK	25	29	0.33	0.45	0.30	0.52
ATL	26	20	0.33	0.47	0.45	0.39
NYJ	27	24	0.32	0.54	0.47	0.33
NO	28	28	0.29	0.62	0.43	0.31
MIA	29	26	0.29	0.55	0.54	0.26
CHI	30	32	0.26	0.54	0.32	0.40
SF	31	30	0.23	0.54	0.24	0.49
STL	32	31	0.22	0.55	0.28	0.43

Behind the Prediction--TB at DET

Detroit is a 2 point favorite at home against Tampa Bay, but the efficiency model estimates that the Buccaneers have a 0.82 probability of upsetting the Lions. In this post I'll break down why the efficiency model favors the Bucs.

Detroit (3-2) is known these days for having a potent passing offense, while Tampa (4-2) is best known for its traditionally tough defense. But their efficiency stats tell a slightly different story.

Below is a table that lists each team's generic win probability (GWP) and their opponents' average GWP, each adjusted for to-date opponent strength. Also listed is each team's offensive and defensive GWP.

Team	GWP	O GWP	D GWP	Opp GWP	Opp O GWP	Opp D GWP
TB	0.82	0.66	0.61	0.49	0.50	0.49
DET	0.36	0.32	0.48	0.49	0.44	0.58

Tampa has been playing at a much higher level in terms of opponent-adjusted efficiency. The two teams have faced roughly equal opponents through week 6, with Tampa having faced average squads and Detroit facing stiffer defenses but weaker offenses.

The next table breaks down each team's (unadjusted) efficiency stats.

Team	O Pass	O Run	O Int Rate	O Fum	D Pass	D Run	D Int Rate	Pen Rate
TB	7.47	3.81	0.007	0.027	5.38	3.77	0.034	0.19
DET	6.06	3.75	0.042	0.060	6.66	3.91	0.049	0.34

The Buccaneers are better in every efficiency stat except defensive interception rate. The biggest advantage the Lions have on Sunday will be their home field. We also see that Tampa Bay is no longer a team reliant on its defense, but is a well-balanced team. Garcia has been very efficient and has thrown only one interception in six games. Tampa actually has the 4th most efficient passing game in the NFL. The Bucs appear to be a well disciplined team too, with one of the lowest penalty rates in the league.

A lot has been made of Martz's aggressive passing attack and the Lions' talent at wide receiver, but their offensive pass efficiency is slightly below average. Tampa Bay actually has a much better passing game so far in 2007.

Tampa has recently lost its starter at running back, but the rushing game has not been the strength of this team. Even if we dialed down their expected rushing efficiency, the Buccaneers would still be clear favorites.

Season Win Projections Week 6

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). But starting this week, the projections now account for future opponent strength. Total wins account for current and projected wins. Methodology can be found here.

Team	Proj GWP	Proj Wins
AFC E
NE	0.87	14.7
BUF	0.39	5.3
NYJ	0.32	4.2
MIA	0.31	3.1
AFC N
PIT	0.70	11.7
CLE	0.59	8.9
CIN	0.65	8.1
BAL	0.30	7.0
AFC S
IND	0.85	14.4
JAX	0.64	11.1
TEN	0.57	9.2
HOU	0.50	9.0
AFC W
DEN	0.68	9.5
SD	0.55	8.5
KC	0.51	8.1
OAK	0.28	5.1
NFC E
DAL	0.73	12.3
NYG	0.72	11.2
WAS	0.63	9.9
PHI	0.63	8.9
NFC N
GB	0.61	11.1
MIN	0.41	6.5
DET	0.31	6.4
CHI	0.24	4.4
NFC S
TB	0.84	12.4
CAR	0.37	7.7
ATL	0.46	5.6
NO	0.35	4.9
NFC W
SS	0.73	10.3
ARI	0.49	7.9
SF	0.26	4.9
STL	0.29	2.9

Future Opponent Strength

Generic Win Probability (GWP) tells us the probability a team will beat a league-average opponent at a neutral site, but teams don't play theoretical average teams. Some teams have harder schedules than others. Some teams have already played their weakest opponents and are probably overrated. Some teams have weathered an onslaught from the NFL's toughest teams and are likely underrated.

The table below lists each team and its GWP adjusted for previous opponents. Also listed is past opponent average GWP and future opponent average GWP. The table is sorted in order of future opponent strength. Teams with higher opponent average GWP will have an uphill climb for the rest of the season.

Team	GWP	Past Opp GWP	Fut Opp GWP
BAL	0.41	0.36	0.61
WAS	0.70	0.51	0.59
NYJ	0.39	0.57	0.58
MIA	0.39	0.53	0.58
JAX	0.70	0.51	0.57
CAR	0.43	0.43	0.57
DET	0.36	0.49	0.57
IND	0.88	0.53	0.56
DAL	0.78	0.44	0.56
HOU	0.56	0.56	0.56
BUF	0.45	0.69	0.56
PHI	0.68	0.51	0.55
NE	0.89	0.49	0.55
OAK	0.33	0.48	0.55
SD	0.60	0.51	0.55
TEN	0.61	0.59	0.54
CHI	0.25	0.56	0.52
MIN	0.43	0.40	0.52
PIT	0.72	0.41	0.51
KC	0.52	0.50	0.51
NYG	0.72	0.57	0.51
ATL	0.45	0.57	0.49
DEN	0.67	0.55	0.49
SF	0.25	0.53	0.49
STL	0.27	0.56	0.48
NO	0.32	0.67	0.46
GB	0.56	0.56	0.45
CIN	0.60	0.61	0.45
ARI	0.44	0.49	0.45
CLE	0.54	0.57	0.45
TB	0.81	0.49	0.44
SEA	0.64	0.49	0.39

Baltimore has the toughest forthcoming schedule. In fact, the Ravens have a stretch when they play SD, NE, IND consecutively. They get a breather against Miami before facing SEA and PIT again. And the AFC North is without its traditional doormat, the Browns, who have already beat Baltimore once.

Although the Ravens are 4-2, they have not performed terribly well against very poor opponents so far this year, including the three worst teams in the worst division in the NFL--the NFC West.

The Ravens' defense will likely keep them in games, but unless there is significant offensive improvement, I expect a significant downturn. There will probably be lots of much-hyped "collapse" stories in the media. Billick will be on the hot seat again and journalists will ask if he has "lost the team." But the reality is this team isn't that good to begin with, and following their bye in week 8 their schedule becomes as brutal as it had been soft.

Game Predictions Week 7

Game probabilities for week 7 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.

Vprob	Visitor	Home	Hprob
0.19	ARI	WAS	0.81
0.54	ATL	NO	0.46
0.38	BAL	BUF	0.62
0.15	MIN	DAL	0.85
0.92	NE	MIA	0.08
0.09	SF	NYG	0.91
0.86	TB	DET	0.14
0.51	TEN	HOU	0.49
0.64	KC	OAK	0.36
0.26	NYJ	CIN	0.74
0.11	CHI	PHI	0.89
0.12	STL	SS	0.88
0.48	PIT	DEN	0.52
0.73	IND	JAX	0.27

Week 6 Efficiency Rankings

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 strength of schedule. The adjusted GWP (Adj GWP) modifies the generic win probability to reflect the strength of to-date 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. To-date average opponent GWP is also listed. Rankings are based on data through week 6. A full explanation of the methodology can be found here.

Team	Rank	Last Wk	GWP	OGWP	DGWP	Opp GWP
NE	1	1	0.89	0.79	0.72	0.49
IND	2	2	0.89	0.80	0.64	0.53
TB	3	8	0.82	0.66	0.61	0.49
DAL	4	4	0.76	0.74	0.59	0.44
NYG	5	3	0.72	0.75	0.68	0.56
PIT	6	10	0.72	0.62	0.63	0.41
JAX	7	6	0.71	0.76	0.50	0.51
WAS	8	5	0.70	0.49	0.83	0.51
DEN	9	11	0.68	0.66	0.54	0.55
PHI	10	9	0.67	0.74	0.60	0.52
SS	11	7	0.66	0.66	0.52	0.49
TEN	12	12	0.61	0.34	0.78	0.59
CIN	13	16	0.60	0.65	0.56	0.62
SD	14	18	0.60	0.67	0.51	0.52
GB	15	15	0.56	0.56	0.64	0.56
HOU	16	14	0.55	0.64	0.52	0.55
CLE	17	26	0.53	0.62	0.40	0.56
KC	18	19	0.52	0.41	0.61	0.50
BUF	19	20	0.46	0.41	0.57	0.69
ATL	20	22	0.44	0.51	0.51	0.57
MIN	21	21	0.43	0.51	0.49	0.40
CAR	22	24	0.41	0.53	0.54	0.42
ARI	23	13	0.41	0.55	0.55	0.49
NYJ	24	27	0.40	0.50	0.36	0.56
BAL	25	23	0.40	0.41	0.66	0.36
MIA	26	17	0.37	0.61	0.34	0.52
DET	27	29	0.36	0.32	0.48	0.49
NO	28	31	0.34	0.49	0.34	0.68
OAK	29	25	0.32	0.28	0.52	0.48
SF	30	28	0.26	0.25	0.50	0.52
STL	31	30	0.25	0.36	0.47	0.55
CHI	32	32	0.25	0.32	0.44	0.55

QB Ranking Week 5

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 5.

Name	Att	Yds	Int	Rush	Yds	Sk Yds	Fum	YAC	+WP16
Manning P	165	1319	2	7	-7	15	0	397	4.2
Brady	158	1383	2	5	6	19	2	534	3.7
Warner	69	580	1	4	0	6	2	199	3.3
Garrard	102	848	0	25	108	59	2	292	3.1
Garcia	113	914	0	11	29	27	1	446	2.2
Schaub	157	1299	4	12	32	63	5	455	2.1
Romo	171	1508	8	12	78	46	1	629	2.0
Palmer	160	1171	6	6	9	42	0	381	1.9
Culpepper	26	193	0	7	28	16	0	92	1.8
Campbell	113	869	3	16	80	27	4	361	1.4
Roethlisberger	131	1013	3	8	57	89	3	393	1.4
Hasselbeck	155	1148	4	10	1	45	1	459	1.2
Anderson	159	1251	8	10	17	62	3	426	1.0
Delhomme	86	626	1	6	26	46	1	313	0.7
Pennington	118	811	5	8	9	50	0	304	0.3
Smith	84	461	1	8	67	74	2	158	0.3
Cutler	152	1158	6	13	33	26	4	529	0.2
Boller	51	287	1	4	9	7	0	136	0.0
Leinart	112	647	4	11	42	23	0	273	0.0
McNabb	136	943	1	13	35	85	4	454	0.0
Favre	210	1527	4	9	-2	54	2	853	-0.1
Harrington	156	1070	3	5	13	91	0	541	-0.2
McNair	157	922	2	9	26	37	4	467	-0.4
Young	100	583	5	29	123	18	2	254	-0.4
Manning E	157	1076	6	9	13	32	2	537	-0.6
Bulger	133	765	4	4	16	67	1	317	-0.6
Rivers	157	1156	6	9	1	77	5	530	-0.8
Green	141	987	7	7	32	53	2	472	-0.9
Kitna	167	1333	6	12	31	136	8	603	-0.9
Huard	149	1029	6	6	2	75	2	497	-1.1
Holcomb	67	427	1	0	0	67	1	212	-1.2
Carr	62	330	2	9	33	35	0	183	-1.6
Edwards	79	507	3	3	5	53	1	272	-2.0
Brees	177	929	9	5	23	28	2	453	-2.0
Clemens	47	295	2	3	2	30	1	150	-2.2
Losman	47	255	1	6	51	67	3	135	-2.7
Griese	77	500	4	3	7	63	2	250	-2.7
Jackson	56	329	5	7	26	0	0	188	-3.1
Grossman	89	500	6	4	9	82	1	216	-3.3
McCown J	68	494	5	9	46	55	7	247	-3.9

The +WP16 stat basically tells us how much a QB is hurting or helping his team. For example, Tom Brady's performance to date would take a team that is completely average in every other way to between an 11 and 12 win season (8 + 3.7 = 11.7).

Luckiest NFL Teams Week 5

Based on opponent-adjusted generic win probability (GWP), the number of expected wins can be estimated for each NFL team. Teams that have won more games than expected can be considered lucky, while teams with fewer wins than expected can be considered unlucky.

The list of teams sorted from luckiest (positive numbers) to unluckiest is posted below. We would expect most teams to be within +/- 1.0 wins. So teams outside that margin can be deemed lucky or unlucky.

Team	Adj GWP	Wins	Expected	Luck
DET	0.25	3	1.3	1.7
CHI	0.16	2	0.8	1.2
CAR	0.36	3	1.8	1.2
BAL	0.37	3	1.9	1.1
GB	0.60	4	3.0	1.0
DAL	0.82	5	4.1	0.9
SF	0.26	2	1.3	0.7
OAK	0.34	2	1.3	0.7
IND	0.90	5	4.5	0.5
PIT	0.70	4	3.5	0.5
NE	0.92	5	4.6	0.4
CLE	0.34	2	1.7	0.3
TEN	0.69	3	2.8	0.2
HOU	0.61	3	3.0	0.0
JAX	0.76	3	3.1	-0.1
ARI	0.62	3	3.1	-0.1
KC	0.43	2	2.2	-0.2
WAS	0.81	3	3.2	-0.2
SD	0.47	2	2.4	-0.4
NYJ	0.28	1	1.4	-0.4
MIN	0.40	1	1.6	-0.6
TB	0.73	3	3.6	-0.6
SEA	0.73	3	3.7	-0.7
NO	0.23	0	0.9	-0.9
ATL	0.40	1	2.0	-1.0
NYG	0.82	3	4.1	-1.1
BUF	0.43	1	2.1	-1.1
STL	0.24	0	1.2	-1.2
CIN	0.60	1	2.4	-1.4
DEN	0.70	2	3.5	-1.5
PHI	0.70	1	2.8	-1.8
MIA	0.47	0	2.4	-2.4

Behind the Prediction--WAS at GB

The Packers are a 3 point favorite at home against the Redskins, but the efficiency model has Washington as the favorites with a 0.62 probability of winning. In this post I'll breakdown why my system favors the Skins.

Although Washington is 3-2 and Green Bay is 4-1, the Redskins are performing significantly better per play. Below is a table that lists each team's generic win probability (GWP) and their opponents' average GWP, each adjusted for to-date oppenent stregnth. Also listed is each team's offensive and defensive GWP.

Team	GWP	Opp GWP	Off GWP	Def GWP	Opp Def	Opp Off
WAS	0.75	0.55	0.60	0.79	0.52	0.58
GB	0.59	0.55	0.63	0.56	0.55	0.53

Washington has been playing at a higher level in terms of opponent-adjusted efficiency. The two teams have faced roughly equal opponents through week 5, with Washington having faced stronger offenses and Green Bay facing stiffer defenses.

The next table breaks down each team's (unadjusted) efficiency stats.

TEAM	O Pass	O Run	O Int Rate	O Fum	D Pass	D Run	D Int Rate	Pen Rate
WAS	7.14	3.83	0.027	0.038	4.52	3.82	0.027	0.35
GB	6.73	3.35	0.019	0.028	6.12	3.99	0.029	0.43

The Redskins' offense is both running and throwing the ball slightly better than Green Bay. Their turnovers are higher, however. The biggest difference is on defense, where the Skins' pass defense is particularly strong, giving up only 4.5 yds per pass attempt.

A lot of attention has been given to Favre and his resurgent offense this year. But, by far, the bigger turnaround story in 2007 is the Redskins pass defense. In 2006 they had the worst pass defense by far, giving up over 6.9 yds per pass (including sack yds). So far in 2007, they have been the league's best.

Green Bay's advantage lies in turnover rates. Favre and the Packers have been measurably better at preventing interceptions than the Redskins. The Packers also have home field advantage.

Running the efficiency stats through the game prediction model, Washington's pass defense trumps Green Bay's Lambeau Feild, giving them a 0.62 probability to win.

The current consensus has Green Bay as a 3 point favorite, which essentially says the teams are equal because home field is generally worth 3 points. As we can see however, the teams are not equal and Washington's pass defense should carry the day given the Packers' tendency to rely on their passing game.

Game Predictions Week 6

Game probabilities for week 6 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. The model now compensates for early-season instability in team efficiency stats to improve confidence levels.

Vprob	VISITOR	HOME	Hprob
0.58	CIN	KC	0.42
0.35	HOU	JAX	0.65
0.52	MIA	CLE	0.48
0.67	MIN	CHI	0.33
0.72	PHI	NYJ	0.28
0.34	STL	BAL	0.66
0.40	TEN	TB	0.60
0.62	WAS	GB	0.38
0.29	CAR	ARI	0.71
0.59	NE	DAL	0.41
0.36	OAK	SD	0.64
0.18	NO	SEA	0.82
0.77	NYG	ATL	0.23

Instability Compensation

To compensate for early-season over-confidence in model predictions, the model now includes a mechanism for extremes in team stat variation.

To explain how the compensation works, consider the recent SD at DEN game. The model had DEN at 0.97 favorites to win, but the Chargers crushed the Broncos. (Some of the following is taken from my comments to the week 5 predictions.) The current model basically says this:

1. Assumes SD's and DEN's to-date efficiency stats represent their true full-season talent,skill, and performance.
2. If a team with season-long stats such as SD's plays at a team with season-long stats such as DEN's, the home team with a stat advantage that enormous would win 97 times out of 100 games.

I think #1 is the problem, but I think #2 is true. I think the overconfidence in the model at this point in the season comes from only a few data points for each statistic so far. Outlier/unrepresentative performances have a large effect on each team's aggregate efficiency stats early in a season. In other words, Denver may have played their best 4 games in terms of team efficiencies already, and from here out their stats will regress to the mean. Until their efficiency stats stabilize, the model would overweight Denver's odds of winning, and vice versa for San Diego.

[Incidentally, this would be true of all statistical models this early in the season. But I think a pure efficiency model might be less susceptable. For example, including 3rd down conversion rates or red zone rates would exaggerate the effect of unrepresentative performances to an even greater degree.]

Ultimately, it's the unstable input variables which may not represent each team's true ultimate efficiency averages. I had already been working on a simple method of Bayesian compensation for early-season unstable team stats. It's similar to what IMDB or other similar sites do with their movie-rating system. IMDB doesn't want one voter to give 5 stars to his favorite Pauly Shore movie, resulting in a perfect 5.00 rating for "Encino Man" until someone else takes time to rate it a zero. So they assign every movie a certain number of baseline votes, so one early voter doesn't move the aggregate too far. Eventually, as the real votes accumulate, the baseline phantom votes are pushed out of the calculation. Throughout the process, the aggregate rating remains stable.

The model's input stats will include a number of "phantom" games at league-average stats for every team. This mitigates the exaggerated confidence levels early in the season. (DEN's stats wouldn't have looked so good, and SD's wouldn't have looked so bad.) The question is, how many pure-average phantom games should be used? We need to look at how quickly each team's stats stabilize. In other words, how many games of data are required before the stats are within an acceptable margin of their final season average?

The answer is more complicated than expected. I plotted each team's 2006 stats by week. The graph for defensive pass efficiency is posted below as an example. The y-axis is yds allowed per attempt and the x-axis is week number. Although hard to read, it's easy to see that the 'funnel' stabilizes shortly before halfway through the season.



Each stat has it's own rate of stabilization. For example, offensive run efficiency stabilizes very quickly, within 4 or 5 games. But defensive pass efficiency doesn't stabilize until about week 8. Turnover rates don't stabilize until week 9.

The compensation is reduced as each week goes by in the early season. Each week, one fewer phantom game is included in the team's averages until the each stat stabilized. For example, by week 5 the compensation for offensive run efficiency has run its course. And by week 8, defensive pass efficiency no longer contains any compensation. At this point in the season, between week 5 and 6, the resulting effect is to mitigate the importance of defensive pass efficiency and turnover rates.

Season Win Projections Week 5

Season win totals and division standing projections are listed below. Projections are based on each team's opponent-adjusted generic win probability (Adj GWP). Total wins account for current and projected wins. Methodology can be found here.

Team	Adj GWP	Current	Proj.
AFC E
NE	0.92	5	15.2
BUF	0.43	1	5.7
MIA	0.47	0	5.2
NYJ	0.28	1	4.1
AFC N
PIT	0.70	4	11.7
CIN	0.60	1	8.2
BAL	0.37	3	7.1
CLE	0.34	2	5.7
AFC S
IND	0.90	5	14.9
JAX	0.76	3	12.2
TEN	0.69	3	11.3
HOU	0.61	3	9.7
AFC W
DEN	0.70	2	9.7
SD	0.47	2	7.2
KC	0.43	2	6.8
OAK	0.34	2	6.0
NFC E
DAL	0.82	5	14.0
WAS	0.81	3	12.7
NYG	0.82	3	12.1
PHI	0.70	1	9.5
NFC N
GB	0.60	4	10.6
MIN	0.40	1	5.8
DET	0.25	3	5.8
CHI	0.16	2	3.8
NFC S
TB	0.73	3	11.0
CAR	0.36	3	7.0
ATL	0.40	1	5.4
NO	0.23	0	2.8
NFC W
SEA	0.73	3	11.0
ARI	0.62	3	9.8
SF	0.26	2	4.9
STL	0.24	0	2.7

Week 5 Efficiency Rankings

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 strength of schedule. The adjusted GWP (Adj GWP) modifies the generic win probability to reflect the strength of to-date opponents. Rankings are based on data through week 5. A full explanation of the methodology can be found here.

Team	Rank	Last Wk	Adj GWP	Opp GWP
NE	1	4	0.92	0.36
IND	2	1	0.90	0.47
NYG	3	8	0.82	0.72
DAL	4	5	0.82	0.34
WAS	5	12	0.81	0.56
JAX	6	7	0.76	0.54
SEA	7	3	0.73	0.53
TB	8	6	0.73	0.33
PHI	9	9	0.70	0.58
PIT	10	11	0.70	0.34
DEN	11	2	0.70	0.58
TEN	12	10	0.69	0.57
ARI	13	13	0.62	0.55
HOU	14	15	0.61	0.55
GB	15	16	0.60	0.54
CIN	16	14	0.60	0.60
MIA	17	18	0.47	0.59
SD	18	29	0.47	0.55
KC	19	17	0.43	0.39
BUF	20	22	0.43	0.67
MIN	21	19	0.40	0.45
ATL	22	25	0.40	0.53
BAL	23	24	0.37	0.41
CAR	24	27	0.36	0.49
OAK	25	21	0.34	0.41
CLE	26	23	0.34	0.55
NYJ	27	28	0.28	0.52
SF	28	30	0.26	0.57
DET	29	20	0.25	0.41
STL	30	31	0.24	0.58
NO	31	26	0.23	0.79
CHI	32	32	0.16	0.55

Opponent Strength

To get a feel for which teams are really doing well, and which have just been beating up on weaker teams, we should look at strength of schedule. One of the interesting applications of accounting for opponent strength using a regression model is that offensive and defensive opponent strength can be analyzed separately. We can see which squads have faced the toughest and easiest opposing units so far this year.

The table below lists each team and their to-date opponents' strength ranked from toughest (1) to weakest (32). The table includes overall opponent strength, opponent offensive strength, and defensive oppoenent strength.

Team	Opp Str	Opp O Str	Opp D Str
NO	1	1	1
BUF	2	2	5
NYG	3	4	2
CIN	4	3	12
JAX	5	5	10
STL	6	8	6
CHI	7	20	4
MIA	8	10	11
SF	9	14	18
PHI	10	21	8
SD	11	24	3
DEN	12	9	21
SEA	13	18	14
HOU	14	6	20
ARI	15	22	9
TEN	16	7	27
OAK	17	16	16
WAS	18	12	19
CLE	19	19	15
IND	20	25	23
MIN	21	23	13
ATL	22	17	24
NYJ	23	11	25
CAR	24	13	26
GB	25	26	17
BAL	26	15	30
DET	27	31	7
PIT	28	29	29
KC	29	32	22
TB	30	28	32
NE	31	27	31
DAL	32	30	28

The defensive units that have faced the toughest offenses so far are NO, BUF, and CIN. Look for those defenses to improve if only because they're not likely to face as difficult a schedule as they have so far. Likewise, the teams that have faced the weakest defenses so far are KC, DET, and DAL. They might appear better than they really are.

The offensive units that have faced the toughest defenses so far are NO, NYG, SD, and CHI. The Giants haven't been too bad on offense so far this year, so perhaps they'll put up some bigger numbers when their schedule eases up. NO has started with the most brutal schedule of all 32 teams. The teams that have faced the weakest offenses so far are TB, NE, BAL, PIT, and TEN. Those defenses might be overrated at this point.

Game Predictions Week 5

Game probabilities for week 5 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.

V Prob	VISITOR	HOME	H Prob
0.85	ARI	STL	0.15
0.13	ATL	TEN	0.87
0.62	CAR	NO	0.38
0.04	CLE	NE	0.96
0.22	DET	WAS	0.78
0.73	JAX	KC	0.27
0.33	MIA	HOU	0.67
0.10	NYJ	NYG	0.90
0.69	SS	PIT	0.31
0.19	TB	IND	0.81
0.49	BAL	SF	0.51
0.03	SD	DEN	0.97
0.09	CHI	GB	0.91
0.90	DAL	BUF	0.10

Season Win Projections Week 4

Season win totals and division standing projections are listed below. Projections are based on each team's opponent-adjusted generic win probability (Adj GWP). Total wins account for current and projected wins. Methodology can be found here.

Team	Adj GWP	Current	Projected
AFC E
NE	0.79	4	13.5
MIA	0.43	0	5.2
BUF	0.32	1	4.8
NYJ	0.26	1	4.1
AFC N
PIT	0.61	3	10.3
CIN	0.55	1	7.6
CLE	0.32	2	5.8
BAL	0.30	2	5.6
AFC S
IND	0.92	4	15.0
JAX	0.70	2	11.1
TEN	0.64	2	10.3
HOU	0.53	2	8.4
AFC W
DEN	0.86	2	12.3
KC	0.44	2	7.3
OAK	0.41	2	6.9
SD	0.23	1	3.8
NFC E
DAL	0.78	4	13.3
WAS	0.61	2	9.9
NYG	0.65	2	9.8
PHI	0.65	1	8.7
NFC N
GB	0.50	4	10.0
DET	0.42	3	8.0
MIN	0.42	1	6.0
CHI	0.14	1	2.6
NFC S
TB	0.75	3	12.0
CAR	0.26	2	5.1
ATL	0.29	1	4.5
NO	0.26	0	3.4
NFC W
SS	0.82	3	12.8
ARI	0.59	2	9.0
SF	0.23	2	4.7
STL	0.18	0	2.1

For now, the projections don't account for future strength of schedule. At this point only 4 games into the season, you should pay more attention to the relative ranking of each team than the projected win total. Further into the season, the projections will account for future opponent strength.

2006 Season Win Projections

Here are the projections from the same timeframe in 2006. Each column indicates the season win projections of a very similar model following weeks 2, 3, and 4. The actual total numbers of wins aren't terribly great, but the relative position of teams within each division is pretty good. I can't emphasize that point enough.

Seven of eight division winners were correctly projected. The only exception was Atlanta in the NFC South, which suffered an epic collapse at the end of the '06 season. The model actually had NO winning the division in week 3, but gave it to ATL by week 4.

Team	Week 2	Week 3	Week 4	Actual
AFC E
06New Engl	9.2	6.6	8.7	12
06Buffalo	5.7	7.0	8.1	7
06NY Jets	7.5	6.9	7.0	10
06Miami	5.6	6.1	5.6	6
AFC N
06Baltimor	9.8	10.6	10.9	13
06Cincinna	10.5	10.9	9.5	8
06Pittsbur	7.4	6.9	6.3	8
06Clevelan	5.4	5.5	4.6	4
AFC S
06Indianap	7.1	9.4	10.4	12
06Jacksonv	10.9	9.5	8.2	8
06Houston	3.8	3.6	4.3	3
06Tennesse	3.9	3.2	2.1	8
AFC W
06San Dieg	12.6	14.2	13.0	14
06Denver	6.0	10.2	10.1	9
06Kansas C	7.2	7.4	9.4	9
06Oakland	5.7	4.4	4.3	2
NFC E
06Philadel	10.4	12.1	13.1	10
06Dallas	10.5	9.7	12.1	9
06NY Giant	11.4	11.5	11.5	8
06Washingt	7.5	9.3	10.9	5
NFC N
06Chicago	11.3	11.3	12.2	13
06Minnesot	8.8	10.2	9.3	6
06Green Ba	6.7	6.0	4.9	8
06Detroit	6.1	5.2	4.4	3
NFC S
06Atlanta	10.3	9.4	11.1	7
06New Orle	9.2	11.1	10.1	10
06Carolina	4.5	4.1	5.8	8
06Tampa Ba	4.4	1.6	1.6	4
NFC W
06Seattle	9.5	10.6	8.6	9
06St. Loui	6.3	6.5	7.8	8
06San Fran	10.7	8.3	6.5	7
06Arizona	7.2	5.0	3.1	5

The biggest misses were the Jets and Redskins. The Jets have returned to mediocrity and were most likely very luckly last year. The model was very wrong about the Redskins, and I have no idea why they took the downturn they did last year.

One more note: Although these predictions were based on a similar model to the current one, the coefficients were derived solely from 2005 season data. 2005 turned out to be uniquely favorable to running offenses and defenses, which skewed the projections. I redid the model using data from 2002-2006 and the results were much better.

Why do the Chargers Stink?

The San Diego Chargers are 1-3 so far in 2007 and are on pace to win between only 3 to 4 games this year according to their efficiency stats. Their sole win has come against perhaps the only team considered more disappointing this year, the Chicago Bears. Media attention focuses on star running back LaDanian Tomlinson and his woes, but what are the real reasons for San Diego's slow start?

By comparing San Diego's stats in 2006 and 2007 through an efficiency model, we can see how the difference in each stat impacts the number of expected wins. The table below lists each efficiency stat in the model for both years. The column "+/-Wins" lists the estimated number of wins lost or gained due to the difference in each stat. Also listed is the Generic Win Probability (GWP) for the Chargers for 2006 and 2007. The GWP is the probability a team would beat the league-average team at a neutral site. The Adjusted GWP accounts for opponent strength.

STAT	SD '06	SD '07	+/-Wins
OPass	6.60	5.54	-1.6
ORun	4.90	3.10	-1.6
OIntRate	0.019	0.043	-1.2
OFumRate	0.016	0.029	-1.0
DPass	5.36	7.39	-3.4
DRun	4.20	3.96	+0.1
DIntRate	0.030	0.031	0.0
PenRate	0.40	0.38	+0.1
GWP	0.77	0.20
Adj GWP	0.77	0.23
Exp. Wins	12.3	3.7	-8.6

First, note that the Chargers were expected to win 12.3 wins last year, 1.7 wins short of their actual total. This indicates they were a solidly talented team, but there was some luck involved in getting to a 14-2 record. This year they are on pace to win 3.7 wins, a difference of 8.6 wins.

LT has seen his yards per rush attempt fall from 5.2 in 2006 to 3.4 in 2007, certainly a significant difference. But San Diego's running game only accounts for 1.6 of the 8.6 win difference between '06 and '07. Their passing game shares and equal amount of blame with a 1.6 win difference.

San Diego's opponents so far have an average GWP of 0.54, slightly above average. But this would only account for 0.03 in their own GWP so far. This equates to only 0.1 wins.

The Chargers' pass defense is the prime culprit, accounting for 3.4 wins of the 8.6 difference in expected wins. Last year their defense gave up only 5.36 yards per pass attempt, but this year they are allowing 7.39 yards per attempt (including sack yards). Although they've faced a ferocious New England passing attack and a resurgent Brett Favre, they've also played against below average QBs Rex Grossman and Damon Huard.

But in total, it's the Charger offense that's responsible for the bulk of their difficulties. Added together, their passing game and running game including turnovers are costing them 5.4 expected wins over the course of a season.

Are the Chargers a 4-win team? Maybe not. But for them to turn their season around, their pass defense needs to improve and not necessarily just their running game.

Week 4 Efficiency Rankings

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 strength of schedule. The adjusted GWP (Adj GWP) modifies the generic win probability to reflect the strength of to-date opponents. Rankings are based on data through week 4. A full explanation of the methodology can be found here.

Team	Rank	Last Wk	GWP	Opp GWP	Adj GWP
IND	1	1	0.92	0.50	0.92
DEN	2	2	0.84	0.53	0.86
SEA	3	9	0.79	0.53	0.82
NE	4	3	0.96	0.28	0.79
DAL	5	5	0.94	0.28	0.78
TB	6	7	0.89	0.31	0.75
JAX	7	8	0.64	0.59	0.70
NYG	8	16	0.52	0.68	0.65
PHI	9	4	0.61	0.54	0.65
TEN	10	10	0.61	0.53	0.64
PIT	11	6	0.76	0.31	0.61
WAS	12	11	0.60	0.51	0.61
ARI	13	14	0.57	0.52	0.59
CIN	14	15	0.47	0.61	0.55
HOU	15	12	0.51	0.53	0.53
GB	16	13	0.54	0.44	0.50
KC	17	20	0.59	0.31	0.44
MIA	18	18	0.39	0.56	0.43
MIN	19	19	0.43	0.49	0.42
DET	20	22	0.50	0.38	0.42
OAK	21	29	0.40	0.51	0.41
BUF	22	24	0.16	0.71	0.32
CLE	23	30	0.32	0.50	0.32
BAL	24	23	0.37	0.41	0.30
ATL	25	25	0.31	0.47	0.29
NO	26	31	0.03	0.81	0.26
CAR	27	21	0.29	0.46	0.26
NYJ	28	26	0.28	0.47	0.26
SD	29	28	0.20	0.54	0.23
SF	30	17	0.18	0.56	0.23
STL	31	27	0.12	0.58	0.18
CHI	32	32	0.09	0.56	0.14

Game Model Coefficients

In the interest of full disclosure, or for those fellow uber-geeks, here is the actual model I'll be using for estimating outcome probabilities for each NFL game.

It is a logit regression model based on the outcomes of all regular season games in 2002-2006. I looked at each game twice, once from the point of view of the home team and from the point of view of the visiting team. I called each team, Team A and Team B. To identify the home team, I used a dummy variable AHome, which was 1 or 0 depending on whether Team A was home or away. The dependent variable is AWon, which is 1 if Team A won or 0 if Team B won. There were 2560 cases (games) considered.

VARIABLE	COEFFICIENT	STD ERROR	T-STAT	SLOPE at mean
const	-0.26	1.36	-0.19
AHOME	0.74	0.09	8.29	0.19
AOPASS	0.45	0.07	6.56	0.11
AORUN	0.27	0.10	2.65	0.07
ADPASS	-0.54	0.09	-5.90	-0.13
ADRUN	-0.21	0.11	-1.87	-0.05
AOINTRATE	-15.90	6.26	-2.54	-3.98
ADINTRATE	17.68	5.16	3.43	4.42
AOFUMRATE	-20.50	7.79	-2.63	-5.12
APENRATE	-1.49	0.72	-2.07	-0.37
BOPASS	-0.45	0.07	-6.54	-0.11
BORUN	-0.27	0.10	-2.64	-0.07
BDPASS	0.53	0.09	5.83	0.13
BDRUN	0.20	0.11	1.79	0.05
BOINTRATE	15.71	6.26	2.51	3.93
BDINTRATE	-18.95	5.16	-3.67	-4.74
BOFUMRATE	21.01	7.79	2.70	5.25
BPENRATE	1.47	0.72	2.04	0.37

Retrodictively, the model predicts 69.5% of the games correctly. But keep in mind there are many evenly matched games and upredictable upsets, so it may be impossible for even the most perfect model to get past 75% or so.

I realize the numbers in the table above are meaningless to most people, but I want to ensure everything I do is out in the open.

Key:
OPASS = (offensive pass yds - sack yds) / pass plays
ORUN = offensive run yds / run plays
DPASS = (defensive pass yds - sack yds) / pass plays
DRUN = defensive run yds / run plays
OINTRATE = offensive interceptions / pass attempts
DINTRATE = defensive interceptions / pass attempts
OFUMRATE = fumbles / offensive plays
PENRATE = team penalty yds / total plays

The t-stat indicates the significance of each variable. For this sample size, a t-stat of approximately 1.8 or greater (or -1.8 or less) indicates a signifcance level of p=0.05 or better.

Below is a graph of the spectrum of game probabilities divided ramdomly into two sets, training cases for the regression, and test validation cases. The graph is of the actual outcome rates vs. the model's predicted probabilities.