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	-0.029
35	J. Brown	3	40.2	0.76	0.73	-0.032
36	Bryant	1	36.7	0.81	0.77	-0.035
37	Reed	4	34.9	0.82	0.78	-0.037
38	Christie	1	35.9	0.80	0.75	-0.052
39	Edinger	3	37.8	0.78	0.73	-0.056
40	Rayner	1	35.7	0.80	0.74	-0.062
41	Conway	1	36.8	0.80	0.74	-0.062
42	Elling	2	36.8	0.79	0.72	-0.073
43	Gostkowski	1	32.7	0.85	0.77	-0.084
44	Cortez	1	35.3	0.81	0.71	-0.103
45	Gramatica	3	36.3	0.80	0.60	-0.195
46	Marler	1	35.9	0.81	0.61	-0.203