Week 4 Results

The efficiency model predicted upsets by Cleveland over Baltimore, Detroit over Chicago, Buffalo over the Jets, Tampa Bay over Carolina, and Kansas City over San Diego.

Overall, the efficiency model correctly predicted winners in 9 out of 12 games. The consensus favorite, as defined by betting lines, was only 3 out of 11 as of Sunday evening. (The difference in total games is due to the GB at MIN game being a pick 'em, i.e. point spread = 0).

Game Predictions Week 4

Game probabilities for week 4 are listed below. The probabilities are based on an efficiency win model explained 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.

Visitor	Home	Vprob	Hprob
BAL	CLE	0.48	0.52
CHI	DET	0.17	0.83
GB	MIN	0.61	0.39
HOU	ATL	0.76	0.24
NYJ	BUF	0.16	0.84
OAK	MIA	0.19	0.81
STL	DAL	0.05	0.95
SEA	SF	0.70	0.30
TB	CAR	0.78	0.22
DEN	IND	0.44	0.56
KC	SD	0.53	0.47
PIT	ARI	0.68	0.32
PHI	NYG	0.70	0.30
NE	CIN	0.86	0.14

Season Win Projections Week 3

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	GWP	Opp GWP	Adj GWP	Tot. Wins
AFC E
NE	0.97	0.17	0.80	14
MIA	0.37	0.58	0.41	5
BUF	0.08	0.94	0.30	4
NYJ	0.23	0.56	0.26	4
AFC N
PIT	0.90	0.22	0.77	13
CIN	0.52	0.38	0.46	7
BAL	0.34	0.43	0.30	6
CLE	0.19	0.55	0.22	4
AFC S
IND	0.91	0.39	0.85	15
JAX	0.63	0.60	0.68	11
TEN	0.61	0.52	0.62	10
HOU	0.54	0.61	0.59	10
AFC W
DEN	0.94	0.31	0.85	13
KC	0.46	0.38	0.40	6
SD	0.20	0.56	0.23	4
OAK	0.23	0.49	0.22	4
NFC E
DAL	0.91	0.28	0.80	14
PHI	0.80	0.51	0.80	12
WAS	0.60	0.50	0.60	10
NYG	0.34	0.70	0.44	6
NFC N
GB	0.59	0.44	0.57	10
MIN	0.49	0.35	0.41	6
DET	0.34	0.50	0.35	6
CHI	0.13	0.52	0.14	2
NFC S
TB	0.85	0.28	0.74	12
CAR	0.47	0.33	0.38	7
ATL	0.26	0.53	0.28	3
NO	0.03	0.79	0.18	2
NFC W
SEA	0.61	0.63	0.68	11
ARI	0.53	0.45	0.51	8
SF	0.40	0.54	0.42	7
STL	0.20	0.57	0.23	3

For now, the projections don't account for future strength of schedule. For example, notice how strong the AFC S appears. Obviously, they have to play each other frequently, so it would be very rare for a division to win so many games. At this point so early in the season, you should pay most attention to the relative ranking of each team rather than the projected win total.

Week 3 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 GWP is also listed, which can be considered strength of schedule. The adjusted GWP (ADJGWP) modifies the generic win probability to reflect the strength of to-date opponents. A full explanation of the methodology can be found here.

TEAM	GWP	Opp GWP	ADJGWP
IND	0.91	0.39	0.85
DEN	0.94	0.31	0.85
NE	0.97	0.17	0.80
PHI	0.80	0.51	0.80
DAL	0.91	0.28	0.80
PIT	0.90	0.22	0.77
TB	0.85	0.28	0.74
JAX	0.63	0.60	0.68
SEA	0.61	0.63	0.68
TEN	0.61	0.52	0.62
WAS	0.60	0.50	0.60
HOU	0.54	0.61	0.59
GB	0.59	0.44	0.57
ARI	0.53	0.45	0.51
CIN	0.52	0.38	0.46
NYG	0.34	0.70	0.44
SF	0.40	0.54	0.42
MIA	0.37	0.58	0.41
MIN	0.49	0.35	0.41
KC	0.46	0.38	0.40
CAR	0.47	0.33	0.38
DET	0.34	0.50	0.35
BAL	0.34	0.43	0.30
BUF	0.08	0.94	0.30
ATL	0.26	0.53	0.28
NYJ	0.23	0.56	0.26
STL	0.20	0.57	0.23
SD	0.20	0.56	0.23
OAK	0.23	0.49	0.22
CLE	0.19	0.55	0.22
NO	0.03	0.79	0.18
CHI	0.13	0.52	0.14

NFL Win Prediction Methodology

Throughout the rest of the 2007 season I intend to publish win probabilities for each game, and season win projections for each team. This post explains the methodology used to calculate these.

Based on a logit regression of every game played for the past 5 seasons, a mathematical model was established to determine the probability each opponent would win a game. The model is based on team efficiency stats which include:

• Offensive pass efficiency, including sack yardage
• Defensive pass efficency, including sack yardage
• Offensive run efficiency
• Defensive run efficiency
• Offensive interception rate
• Defensive interception rate
• Offensive fumble rate
• Penalty rate (penalty yards per play)

Home field is also included in the model. These factors were selected because they are most predictive of future performance, and not necessarily because they explain past performance. Over the past five seasons, the model predicts winners correctly in 69.8% of games (retrospectively). In 2006, the model was correct in 65% of games, well ahead of consensus favorites as determined by betting lines. Last year was particularly difficult year for prognosticators, as consensus favorites only won 57% of the games.

Touchdowns, or red zone performance, or third down success rates are not used in the model because I believe those things are the results of passing and running ability etc. To include them in a model intended for prediction would guarantee it is severely "overfit." In other words, it would capture and explain the unique qualities of past events at the expense of predictive power.

Once the model is established, each game's outcome probability can be calculated. But there are other applications. By calculating the probability a team will win against a notional league-average team at a neutral site, a generic win probability can be determined for each team.

This year the model includes an adjustment for opponent strength. This is especially important earlier in the season when there are fewer data points to establish each team's baseline performance levels. Each opponent's generic win probability is averaged for each team. It is then included back into the win model to refine each prediction. For example, a team with impressive stats against weak teams would not be favored as strongly as a team with similar stats against strong teams.

Another application of the opponent-adjusted generic win percentage is a ranking of each team. Such a ranking is similar to the now ubiquitous "power rankings." A better term for the rankings on this site would be "efficiency rankings."

Lastly, final win totals can be estimated by calculating the probabilities of a team's future games. By using the law of total probability, the probility that each possible final record will occur can be determined. For example, if a team has two games left, one with a 0.7 chance of winning and one with a 0.5 chance of winning, the probability of winning 0, 1, or 2 games can be calculated.

2 wins = 0.5 * 0.7
1 win = 0.5 * (1-0.7) + (1-0.5) * 0.7
0 wins = (1-0.7) * (1-0.5)

The same math can be applied with many more games to go but becomes far more complex. Then once we determine the most likely winning percentage for each team, we can compare those expected values to actual outcomes to determine which teams have been lucky or unlucky.

Lastly, as playoff time approaches, we can go one step further. By applying the same principal of total probability, the outcomes of playoff races can be estimated.

Note: The actual game prediction model and coefficients can be found here.

RB Wins Added 2006

Similar to my efforts to devise a better QB rating, I've applied the same method to estimating the wins contributed by running backs. Although not perfect, it provides a sense of who is helping his team and who is hurting his team, and by how much.

The components of the RB rating are weighted according to how important they are in terms of team wins. The formula is based on a multivariate regression model of team wins. Using data from the past five NFL regular seasons, the regression model estimates team wins based on the efficiency stats of each team including passing, running, turnovers, and penalties.

The rating includes Yards Per Carry (YPC), fumble rate, and an adjusted Yards After Catch per reception (YAC/Att). YAC/Rec is adjusted to reflect the fact that RB receptions constitute 14% of all team pass attempts. Fumble rate is defined as fumbles per carry plus receptions.

Some may ask why I don't include touchdowns in the rating. Touchdowns are the result of yards per carry, reception yds, etc. Including TDs would also skew the rating towards the Alstott-esque "vulture-backs." Also, rushing TDs are often the result of an excellent passing game that frequently gets the ball close to the goal line, and not necessarily the result of good rushing.

The RB rating is computed in terms of how many wins a RB contributes to his team through his level of performance over the course of a full 16-game season, all other things being equal. The equation is:

+WP16 = [(YPC * 0.92) + (YAC/Att * 1.57) - (Fum Rate * 63.2)] - 4.0

(I subtract 4.0 as the linear constant because it's the average score for RBs. An average RB on an average team would produce exactly 8 wins, not 12.)

The resulting ranking of 2006 RBs is below. Keep in mind the list assumes a full 16-game season for each RB.

Player	Team	Rush	YPC	YAC/Att	Fum	+WP16
Norwood	ATL	99	6.4	0.5	0	2.6
Jones-Drew	JAC	166	5.7	0.6	1	1.8
Tomlinson	SDG	348	5.2	0.6	2	1.3
Jones	DAL	267	4.1	1.0	1	1.1
Barber III	DAL	135	4.8	0.4	0	1.1
Westbrook	PHI	240	5.1	0.5	2	1.0
Barber	NYG	327	5.1	0.5	3	1.0
Taylor	JAC	231	5	0.7	3	0.9
Portis	WAS	127	4.1	0.7	0	0.8
Johnson	KAN	416	4.3	0.7	2	0.7
Gore	SFO	312	5.4	0.5	6	0.6
Addai	IND	226	4.8	0.5	2	0.6
Benson	CHI	157	4.1	0.6	0	0.6
Maroney	NWE	175	4.3	0.6	1	0.6
Bell	DEN	157	4.3	0.6	1	0.5
Jacobs	NYG	96	4.4	0.9	2	0.3
Williams	CAR	121	4.1	0.6	1	0.3
Dillon	NWE	199	4.1	0.7	2	0.3
Jackson	STL	346	4.4	0.5	4	0.3
Jones	CHI	296	4.1	0.4	1	0.2
Washington	NYJ	151	4.3	0.6	2	0.2
Dunn	ATL	286	4	0.5	1	0.2
Henry	TEN	270	4.5	0.4	3	0.0
Dayne	HOU	151	4.1	0.4	1	0.0
Jordan	OAK	114	3.8	0.6	1	-0.1
McAllister	NOR	244	4.3	0.4	3	-0.1
Lundy	HOU	124	3.8	0.5	1	-0.1
Betts	WAS	245	4.7	0.5	6	-0.1
Houston	NYJ	113	3.3	0.5	0	-0.3
Morency	GNB	96	4.5	0.5	2	-0.3
Green	GNB	266	4	0.6	4	-0.3
Fargas	OAK	178	3.7	0.4	1	-0.3
Brown	MIA	241	4.2	0.5	4	-0.3
McGahee	BUF	259	3.8	0.7	4	-0.3
Parker	PIT	337	4.4	0.5	7	-0.4
Bush	NOR	155	3.6	0.5	2	-0.5
Morris	SEA	161	3.8	0.3	1	-0.5
Taylor	MIN	303	4	0.4	5	-0.6
Bell	DEN	233	4.4	0.4	5	-0.6
Thomas	BUF	107	3.5	0.4	1	-0.7
Lewis	BAL	314	3.6	0.5	4	-0.8
Foster	CAR	227	4	0.3	4	-0.8
Williams	TAM	225	3.5	0.4	3	-0.9
Jones	DET	181	3.8	0.6	5	-0.9
James	ARI	337	3.4	0.3	3	-0.9
Rhodes	IND	187	3.4	0.4	3	-1.1
Johnson	CIN	341	3.8	0.3	6	-1.1
Droughns	CLE	220	3.4	0.5	5	-1.4
Barlow	NYJ	131	2.8	0.3	1	-1.5
Alexander	SEA	252	3.6	0.3	6	-1.7

QB Wins Added Week 3

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, as well as in the last post. Last year's ratings can be found in the second link.

Here is the list of 2007 QBs and their vital stats through week 3.

Name	Att	PassYds	YAC	Int	Rush	RushYds	SkYds	Fum	+WP16
Brady	88	887	208	1	3	8	19	2	5.57
Romo	88	860	224	2	7	47	38	0	4.60
Manning P	101	873	251	1	1	-2	15	0	4.05
Garcia	65	595	208	0	6	12	22	0	3.38
McNabb	105	805	212	1	9	31	23	1	2.78
Palmer	125	937	208	4	6	9	34	0	2.18
Anderson	98	760	118	4	4	10	36	3	2.12
Garrard	75	630	211	0	21	99	42	2	2.06
Kitna	115	980	188	4	8	31	74	4	1.95
Hasselbeck	97	751	220	2	7	4	31	1	1.59
Harrington	96	760	193	2	4	14	74	0	1.59
Campbell	84	621	148	3	14	80	27	3	1.30
Pennington	43	291	66	0	5	2	39	0	1.06
Green	114	824	185	5	5	9	32	1	1.05
Roethlisberger	77	563	225	1	3	30	23	1	1.04
Favre	125	861	275	2	5	-3	44	1	0.75
Young	67	426	121	2	21	96	18	2	0.38
Manning E	106	755	238	4	2	1	26	2	0.13
Delhomme	86	626	280	1	6	26	46	1	-0.01
McNair	61	401	90	1	4	14	37	4	-0.15
Bulger	109	651	188	3	3	18	49	1	-0.33
Cutler	95	795	367	4	8	15	18	2	-0.63
Boller	51	287	117	1	4	9	7	0	-0.66
Smith	83	461	158	1	8	67	64	2	-0.71
Schaub	83	688	306	3	4	7	41	2	-0.77
Leinart	85	454	173	3	8	33	10	0	-1.08
Rivers	97	675	186	4	7	4	66	4	-1.23
Brees	130	677	241	7	5	23	28	2	-2.55
Huard	90	549	282	3	4	5	42	1	-2.68
Grossman	89	500	144	6	4	9	82	1	-3.37
Clemens	47	295	150	2	3	2	30	1	-3.46
Losman	47	255	128	1	6	51	67	3	-3.70
Jackson	56	329	188	5	7	26	0	0	-4.36
McCown J	68	494	205	5	9	46	55	7	-4.39

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 a 13 and 14 win season (8 + 5.57 = 13.57).

How Bad is Rex Grossman?

We keep hearing how Rex Grossman costs the Bears wins. Is that true, and if so, how many wins?

Sure, Grossman's NFL passer rating is the lowest of all starting QBs. He has 1 TD and 6 INTs in 3 games. Clearly that's not good. In this post, I'll estimate how many wins he would cost his team if he were allowed to continue playing at his present level of performance.

The estimate is based on an improved passer rating formula. The components of the new rating are weighted according to how important they are in terms of team wins. The formula is based on a multivariate regression model of team wins. Using data from the past five NFL regular seasons, the regression model estimates team wins based on the efficiency stats of each team including passing, running, turnovers, and penalties. Regression models can hold all other factors equal, so by only adjusting the factors of interest (QB passing, rushing and turnover performance) we can calculate the effect of QB performance on the estimate of season wins.

Further, the rating excludes receiver Yards After Catch (YAC) and relies only on QB Air Yards. It also includes rushing yards, sack yards, interceptions, and fumbles. All factors are computed on a "per attempt" basis. The resulting formula computes the wins added by a QB's performance per a 16-game season, "+WP16" (apologies to David Berri). The equation is:

+WP16 = [(Total Yds/Total Plays * 1.57) - (Total Turnovers/Total Plays *50.5)] - 4.5

Total yards includes air yards, rushing yards, and sack yards. Total plays includes pass attempts, rushes, and sacks. Turnovers include interceptions and half of all fumbles (lost or not). The equation subtracts 4.5 because that is the average +WP16 score for QBs in 2007 so far. An average QB on an average team would win 8 games, not 12.5.

So for Rex Grossman:

+WP16 = [(283 Yds/102 plays * 1.57) - (6.5 TOs/102 plays * 50.5) - 4.5
= -3.4 wins

So holding all other factors equal, Rex Grossman would cost his team 3.4 losses over the course of a full season. Last year Grossman was in the middle of the pack with +0.3 wins added. He did what the Bears asked of him, which was to break even and allow the defense and special teams to make the difference. This year, not so much.

Improved FG Kicker Ranking

I previously looked at FG kicker performance. My evaluation of each kicker was based on how much better the kicker did than would be expected given how distant his attempts were. However, there were several flaws in the original analyisis, which I've hopefully corrected here.

1. Vandergajt's perfect 2003 season was an outlier that distorts the data greatly. Technically, the regression treated his average miss distance as zero, which made his expected accuracy very low. I decided to exclude this one season in the regression.

2. I realized that including average miss and made distances in calculating expected FG% severely overfits the data. Average miss and made distances are affected directly by missed and made field goals, which is essentially what FG% is. Although those variables help describe the distribution of FG attempt distances, they hurt more than help the model. I excluded them.

3. It was pointed out that many of the top kicker seasons belonged to warm weather and indoor kickers, so the model needs to account for home field environment. I included dummy variables for indoor stadia and warm weather teams.

4. It was also suggested that I should use a non-linear relationship between average attempt distance and FG%. For example, a 50-yd FG attempt is more than twice as difficult as a 25-yd attempt. The best fit turned out to be logarithmic, so I used ln(FG%) as the dependent variable in the regression. In case anyone is curious, the graph below illustrates the average FG% for kicks from various distances.


Below are the results of the regression (n=122). About 8% of the variance in FG kicker seasonal performance can be accounted for by situational variables: average attempt distance, warm weather, and a domed home stadium.

VARIABLE	COEFFICIENT	P-VALUE
Indoor	0.008	0.726
Warm Wx	0.017	0.442
Avg Att Dist	-0.014	0.004
r-squared	0.077

Indoor home stadiums and warm weather kickers do not appear to enjoy a significant advantage throughout a season. Neither variable was close to significance. I got the same results for Indoor and Warm Wx regardless of various combinations of independent and dependent variables. But I left both variables in the final regression model. It's a general rule to keep insignificant variables in a model if their coefficients have the expected sign and they would intuitively help account for factors that are not the primary focus of the model. Although the coefficients may be less than perfectly accurate, they help get you closer to the truth than farther from it.

The table below lists each FG kicker's performance from the 2003-06 seasons. The list is sorted from best to worst in terms of exceeding the expected FG accuracy given each kicker's average attempt distance and home stadium environment.

Click on the table headers to sort.

Year	Player	Team	Avg Yds Att	Act FG%	Exp FG%	Act-Exp
2003	Hanson	Det.	38.1	0.96	0.78	0.18
2005	Rackers	Ariz.	38.1	0.95	0.78	0.17
2004	Hanson	Det.	38.1	0.96	0.79	0.16
2003	Vanderjagt	Ind.	33.8	1.00	0.84	0.16
2005	Nedney	S.F.	38.5	0.93	0.77	0.15
2003	Wilkins	St.L.	35.9	0.93	0.80	0.13
2004	Wilkins	St.L.	35.9	0.93	0.80	0.13
2004	Vinatieri	N.E.	34.9	0.94	0.81	0.13
2006	Kasay	Car.	38.9	0.89	0.77	0.12
2006	Lindell	Buff.	35.9	0.92	0.80	0.12
2003	Janikowski	Oak.	39.0	0.88	0.78	0.10
2005	Wilkins	St.L.	39.1	0.87	0.77	0.10
2006	Stover	Balt.	33.2	0.93	0.83	0.10
2006	Gould	Chi.	36.8	0.89	0.79	0.10
2004	Janikowski	Oak.	36.3	0.89	0.80	0.09
2004	Stover	Balt.	34.8	0.91	0.81	0.09
2006	Elam	Den.	33.3	0.93	0.85	0.09
2003	Graham	Cin.	37.2	0.88	0.79	0.09
2006	Vinatieri	Ind.	36.6	0.89	0.81	0.08
2006	Hanson	Det.	36.3	0.88	0.80	0.08
2006	Kaeding	S.D.	35.8	0.90	0.82	0.08
2003	Longwell	G.B.	36.2	0.89	0.81	0.08
2004	Longwell	G.B.	36.2	0.89	0.81	0.08
2005	Kaeding	S.D.	36.4	0.88	0.80	0.08
2005	Vanderjagt	Ind.	32.8	0.92	0.84	0.08
2003	Anderson	Ten.	36.5	0.87	0.80	0.08
2005	Dawson	Clev.	31.6	0.93	0.86	0.07
2005	Stover	Balt.	35.9	0.88	0.81	0.07
2003	Elam	Den.	36.2	0.87	0.80	0.07
2005	Peterson	Atl.	31.6	0.92	0.85	0.07
2004	Graham	Cin.	37.2	0.87	0.80	0.07
2006	Wilkins	St.L.	36.8	0.87	0.80	0.07
2006	Carney	N.O.	32.4	0.92	0.86	0.06
2006	Nugent	N.Y.J.	33.8	0.89	0.83	0.06
2005	Graham	Cin.	34.0	0.88	0.82	0.05
2005	M. Bryant	T.B.	38.4	0.84	0.79	0.05
2003	Kasay	Car.	36.9	0.84	0.79	0.05
2006	Andersen	Atl.	34.3	0.87	0.82	0.05
2004	Elam	Den.	36.1	0.85	0.81	0.05
2004	Kasay	Car.	36.9	0.84	0.80	0.04
2003	Brien	N.Y.J.	37.3	0.84	0.80	0.04
2003	Stover	Balt.	34.7	0.87	0.83	0.04
2003	K. Brown	Hou.	38.2	0.82	0.78	0.03
2006	Feely	N.Y.G.	34.4	0.85	0.82	0.03
2003	Andersen	K.C.	39.1	0.80	0.77	0.03
2003	Akers	Phil.	36.4	0.83	0.80	0.03
2004	Akers	Phil.	36.4	0.83	0.80	0.03
2006	Scobee	Jax.	39.0	0.81	0.78	0.03
2006	Graham	Cin.	36.9	0.83	0.81	0.03
2004	Reed	Pitt.	34.0	0.85	0.82	0.03
2005	Feely	N.Y.G.	36.4	0.83	0.81	0.02
2005	Lindell	Buff.	35.3	0.83	0.81	0.02
2004	Brien	N.Y.J.	35.9	0.83	0.81	0.02
2005	Mare	Mia.	34.8	0.83	0.81	0.02
2003	P. Dawson	Clev.	33.6	0.86	0.84	0.01
2005	Tynes	K.C.	35.4	0.82	0.81	0.01
2006	Nedney	S.F.	34.3	0.83	0.82	0.01
2006	Brown	Sea.	36.2	0.81	0.80	0.01
2005	Bironas	Ten.	37.4	0.79	0.79	0.01
2005	Reed	Pitt.	35.4	0.83	0.82	0.01
2004	Dawson	Clev.	34.7	0.83	0.82	0.01
2006	Longwell	Minn.	33.6	0.84	0.83	0.01
2005	Vinatieri	N.E.	36.4	0.80	0.80	0.00
2005	Kasay	Car.	38.9	0.77	0.77	-0.01
2003	Cundiff	Dall.	36.0	0.79	0.80	-0.01
2004	Cundiff	Dall.	36.0	0.79	0.80	-0.01
2003	Hall	Wash.	38.8	0.76	0.77	-0.01
2006	Tynes	K.C.	36.9	0.77	0.79	-0.02
2006	K. Brown	Hou.	39.4	0.76	0.78	-0.02
2005	Nugent	N.Y.J.	35.7	0.79	0.80	-0.02
2005	Hanson	Det.	35.7	0.79	0.81	-0.02
2004	Mare	Mia.	39.0	0.75	0.77	-0.02
2004	Hall	Wash.	38.8	0.76	0.78	-0.02
2004	Vanderjagt	Ind.	35.5	0.80	0.82	-0.02
2004	Kaeding	S.D.	35.3	0.80	0.82	-0.02
2004	Anderson	Ten.	37.6	0.77	0.80	-0.02
2004	Lindell	Buff.	29.5	0.86	0.88	-0.03
2005	J. Brown	Sea.	41.3	0.72	0.75	-0.03
2004	J. Brown	Sea.	39.7	0.73	0.76	-0.03
2006	Bironas	Ten.	34.4	0.79	0.82	-0.03
2006	Rackers	Ariz.	37.6	0.76	0.79	-0.03
2005	Gould	Chi.	35.0	0.78	0.81	-0.03
2006	Bryant	T.B.	36.7	0.77	0.81	-0.03
2004	Scobee	Jax.	35.2	0.77	0.81	-0.04
2005	Akers	Phil.	39.6	0.73	0.76	-0.04
2006	Akers	Phil.	34.3	0.78	0.82	-0.04
2003	Mare	Mia.	37.4	0.76	0.80	-0.04
2004	Tynes	K.C.	37.9	0.74	0.78	-0.04
2003	J. Brown	Sea.	39.7	0.73	0.78	-0.04
2003	Carney	N.O.	38.4	0.73	0.78	-0.04
2004	Carney	N.O.	38.4	0.73	0.78	-0.04
2005	Elam	Den.	38.0	0.75	0.79	-0.04
2005	Scobee	Jax.	36.4	0.77	0.81	-0.04
2003	Christie	S.D.	35.9	0.75	0.80	-0.05
2003	Edinger	Chi.	38.4	0.72	0.78	-0.05
2004	Edinger	Chi.	38.4	0.72	0.78	-0.05
2005	Carney	N.O.	33.6	0.78	0.83	-0.05
2005	K. Brown	Hou.	35.6	0.77	0.82	-0.05
2005	Longwell	G.B.	37.7	0.74	0.80	-0.06
2006	Janikowski	Oak.	38.9	0.72	0.78	-0.06
2005	Edinger	Minn.	36.5	0.74	0.80	-0.06
2006	Rayner	G.B.	35.7	0.74	0.80	-0.06
2003	Conway	Clev.	36.8	0.74	0.80	-0.06
2006	Reed	Pitt.	35.6	0.74	0.81	-0.06
2006	Mare	Mia.	37.1	0.72	0.79	-0.07
2006	Dawson	Clev.	36.7	0.72	0.79	-0.07
2003	Elling	Minn.	36.8	0.72	0.79	-0.07
2004	Elling	Minn.	36.8	0.72	0.79	-0.07
2003	Feely	Atl.	38.1	0.70	0.78	-0.07
2004	Feely	Atl.	38.1	0.70	0.78	-0.07
2004	K. Brown	Hou.	37.5	0.71	0.79	-0.08
2006	Gostkowski	N.E.	32.7	0.77	0.85	-0.08
2005	Cortez	Ind.	35.3	0.71	0.81	-0.10
2003	Vinatieri	N.E.	33.0	0.74	0.84	-0.11
2003	Reed	Pitt.	34.4	0.72	0.83	-0.11
2006	Vanderjagt	Dall.	34.0	0.72	0.84	-0.12
2005	Janikowski	Oak.	37.6	0.67	0.78	-0.12
2003	Lindell	Buff.	33.9	0.71	0.83	-0.12
2003	Gramatica	T.B.	37.2	0.62	0.79	-0.17
2004	Gramatica	T.B.	37.2	0.62	0.79	-0.17
2003	Marler	Jax.	35.9	0.61	0.81	-0.20
2004	Gramatica	Ind.	34.6	0.58	0.82	-0.24

One thing that immediately stands out to me is how consistent some kickers are. Notice how many times some kickers' seasons are stacked together in order--Wilkins, Longwell, Akers (twice), Cundiff, Carney, J. Brown, and Edinger. Some kickers are incredibly inconsistent--Janikowski and Vanderjagt in particular.

The bottom line in this analysis is that, accounting for attempt distance and home stadium environment, the standard deviation of adjusted accuracy (Actual - Expected FG%) is 7.7%. A FG kicker one standard deviation above the mean kicks 7.7% more accurately than expected given his attempt distance. The average number of FG attempts for a team is 29, so an extra SD of accuracy would yield an additional 2.33 field goals worth 6.7 points in a season.

A rough estimate of the spread between best and worst FG kicker each year is about 34% of accuracy. That would equate to a difference of 9.9 field goals worth 29.6 points. This makes sense because it represents roughly a 4-standard deviation spread between best and worst.

The kickers who had enough qualifying attempts over the 2003-2006 seasons are ranked below in terms of how far they exceeded their expected FG% given their average attempt distance. Vanderjagt was manually assigned the top score for 2003 for his cumulative ranking. The number of years each kicker qualified is also listed. Take the guys with 1 or 2 years of kicks with a grain of salt.

Rank	Player	Years	Avg Att	Exp FG%	Act FG%	Act-Exp
1	Wilkins	4	36.9	0.79	0.90	0.105
2	Hanson	4	37.1	0.80	0.90	0.101
3	Nedney	2	36.4	0.80	0.88	0.082
4	Stover	4	34.7	0.82	0.90	0.076
5	Rackers	2	37.9	0.78	0.85	0.070
6	Peterson	1	31.6	0.85	0.92	0.069
7	Graham	4	36.3	0.81	0.86	0.058
8	Kasay	4	37.9	0.78	0.83	0.052
9	M. Bryant	1	38.4	0.79	0.84	0.051
10	Kaeding	3	35.8	0.81	0.86	0.045
11	Andersen	2	36.7	0.79	0.84	0.041
12	Elam	4	35.9	0.81	0.85	0.040
13	Gould	2	35.9	0.80	0.83	0.031
14	Brien	2	36.6	0.81	0.84	0.031
15	Vanderjagt*	4	34.1	0.83	0.81	0.030
16	Longwell	4	35.9	0.81	0.84	0.027
17	Anderson	2	37.1	0.80	0.82	0.025
18	Vinatieri	4	35.2	0.82	0.84	0.025
19	Nugent	2	34.8	0.82	0.84	0.022
20	P. Dawson	1	33.6	0.84	0.86	0.015
21	Brown	1	36.2	0.80	0.81	0.008
22	Janikowski	4	38.0	0.78	0.79	0.006
23	Dawson	3	34.3	0.82	0.83	0.003
24	Akers	4	36.7	0.79	0.79	-0.003
25	Lindell	4	33.7	0.83	0.83	-0.003
26	Cundiff	2	36.0	0.80	0.79	-0.008
27	Bironas	2	35.9	0.80	0.79	-0.013
28	Tynes	3	36.7	0.79	0.78	-0.016
29	Scobee	3	36.9	0.80	0.78	-0.017
30	Hall	2	38.8	0.77	0.76	-0.017
31	Carney	4	35.7	0.81	0.79	-0.019
32	Feely	4	36.8	0.80	0.77	-0.024
33	Mare	4	37.1	0.79	0.77	-0.027
34	K. Brown	4	37.7	0.79	0.76<