The Best FG Kickers

Note: This analysis has been updated. New post can be found here.

Judging who the best field goal kickers are in the NFL is difficult. The kickers with the best range are often sent out to attempt impossibly long field goal tries. Some kickers benefit from circumstance in some years because their team's drives stall closer to the endzone than others.

Using data from the 2003-2006 regular seasons, obtained at profootballweekly.com, I may have a stumbled on a novel approach to solve the problem. My intent was to follow up on an earlier article that suggested that field goal kickers were severely underpaid relative to their impact on winning. A couple of readers (correctly) pointed out that some kickers' performances appear inflated due to luck, so the "best" kicker one year may really only be an average kicker who got lucky. In attempting to isolate the true talent level from other circumstances, including luck, involved in kicking performance, I developed the following approach.

For each kicker from '03-'06, I computed an expected percentage of FGs made based on three kicker stats:

1. Average FG attempt distance
2. Average FG made distance
3. Average FG missed distance

To compute the expected FG%, I ran a regression of actual FG percentages based on those three variables. The fitted values of the regression model became expected FG%. In simple terms, it's the average FG% that an NFL kicker would be expected to have given his average attempt, made, and miss distances. Essentially, this establishes a level-of-difficulty score, much like in diving, for each kicker's season.

The difference between each kicker's actual FG% and his expected FG% can therefore be considered a true measure of a kicker's performance in a season, accounting for attempt distances. This method does not yet isolate how much of a kicker's performance was due to luck, but it is the first necessary step to do so.

Here are the best kicking performances of the 2003-2006 period, accounting for attempt distances:

Year	Player	Team	Avg Att	Avg Made	Avg Miss	Actual %	Expected %	Act-Exp %
2003	Vanderjagt*	Ind.	33.8	33.8	NA	1.00	0.71	0.287
2004	Hanson	Det.	38.1	37.9	43.0	0.96	0.88	0.077
2003	Hanson	Det.	38.1	37.9	43.0	0.96	0.88	0.077
2006	Kasay	Car.	38.9	36.8	56.0	0.89	0.83	0.063
2005	Kasay	Car.	38.9	35.2	50.8	0.77	0.70	0.062
2005	Rackers	Ariz.	38.1	37.6	48.5	0.95	0.89	0.061
2005	Nedney	S.F.	38.5	38.0	45.5	0.93	0.87	0.058
2003	Janikowski	Oak.	39.0	37.3	51.3	0.88	0.82	0.056
2006	Longwell	Minn.	33.6	30.4	50.0	0.84	0.78	0.055
2003	Graham	Cin.	37.2	35.2	51.3	0.88	0.83	0.055
2003	K. Brown	Hou.	38.2	35.6	49.8	0.82	0.77	0.047
2003	Brien	N.Y.J.	37.3	35.0	49.6	0.84	0.80	0.047
2006	Hanson	Det.	36.3	34.4	50.0	0.88	0.83	0.045
2005	Hanson	Det.	35.7	32.4	48.2	0.79	0.75	0.045
2006	Rackers	Ariz.	37.6	34.0	48.9	0.76	0.71	0.044
2004	Wilkins	St.L.	35.9	35.5	41.7	0.93	0.88	0.044
2003	Wilkins	St.L.	35.9	35.5	41.7	0.93	0.88	0.044
2006	Lindell	Buff.	35.9	35.3	42.5	0.92	0.88	0.043
2006	Stover	Balt.	33.2	33.0	35.5	0.93	0.89	0.040
2006	Vinatieri	Ind.	36.6	35.5	45.3	0.89	0.85	0.039
2004	Vinatieri	N.E.	34.9	34.0	48.5	0.94	0.90	0.038
2006	Graham	Cin.	36.9	34.6	48.4	0.83	0.80	0.038
2003	Longwell	G.B.	36.2	35.0	44.7	0.89	0.85	0.036
2004	Longwell	G.B.	36.2	35.0	44.7	0.89	0.85	0.036
2005	Bironas	Ten.	37.4	34.6	48.3	0.79	0.76	0.033
2004	Janikowski	Oak.	36.3	35.5	43.0	0.89	0.86	0.030
2003	Stover	Balt.	34.7	32.8	47.6	0.87	0.84	0.029
2003	Lindell	Buff.	33.9	29.5	44.4	0.71	0.68	0.027
2004	Stover	Balt.	34.8	34.1	41.7	0.91	0.88	0.027
2006	Elam	Den.	33.3	32.6	43.5	0.93	0.90	0.027
2006	Kaeding	S.D.	35.8	35.2	41.0	0.90	0.87	0.027
2003	Andersen	K.C.	39.1	36.9	47.5	0.80	0.77	0.027
2005	Wilkins	St.L.	39.1	38.4	44.0	0.87	0.84	0.026
2005	Vanderjagt	Ind.	32.8	32.2	39.5	0.92	0.89	0.026
2003	Akers	Phil.	36.4	34.3	46.4	0.83	0.80	0.026
2004	Akers	Phil.	36.4	34.3	46.4	0.83	0.80	0.026
2006	Wilkins	St.L.	36.8	35.5	45.2	0.87	0.84	0.025
2005	Reed	Pitt.	35.4	33.1	46.8	0.83	0.80	0.025
2005	Stover	Balt.	35.9	34.9	43.3	0.88	0.86	0.025
2003	Anderson	Ten.	36.5	35.3	44.8	0.87	0.85	0.024
2006	Gould	Chi.	36.8	36.2	42.0	0.89	0.86	0.024
2004	Graham	Cin.	37.2	36.3	43.0	0.87	0.85	0.023
2005	Dawson	Clev.	31.6	31.3	36.5	0.93	0.91	0.022
2005	Vinatieri	N.E.	36.4	33.9	46.4	0.80	0.78	0.022
2004	Kasay	Car.	36.9	35.3	45.3	0.84	0.82	0.021
2003	Kasay	Car.	36.9	35.3	45.3	0.84	0.82	0.021
2005	Kaeding	S.D.	36.4	35.5	42.7	0.88	0.85	0.020
2006	Carney	N.O.	32.4	32.0	37.5	0.92	0.90	0.020
2005	Peterson	Atl.	31.6	31.0	38.5	0.92	0.90	0.018
2004	Elam	Den.	36.1	34.7	44.0	0.85	0.83	0.018
2003	Feely	Atl.	38.1	34.3	47.1	0.70	0.69	0.018
2004	Feely	Atl.	38.1	34.3	47.1	0.70	0.69	0.018
2004	Gramatica	T.B.	37.2	31.9	45.6	0.62	0.60	0.017
2003	Gramatica	T.B.	37.2	31.9	45.6	0.62	0.60	0.017
2003	Elam	Den.	36.2	35.4	41.5	0.87	0.86	0.014
2003	Christie	S.D.	35.9	32.7	45.4	0.75	0.74	0.014
2005	Graham	Cin.	34.0	32.8	43.0	0.88	0.86	0.011
2006	Feely	N.Y.G.	34.4	32.9	43.0	0.85	0.84	0.010
2005	Akers	Phil.	39.6	36.5	48.0	0.73	0.72	0.010
2006	Nugent	N.Y.J.	33.8	33.2	38.7	0.89	0.88	0.010
2003	Carney	N.O.	38.4	35.3	47.0	0.73	0.72	0.009
2004	Carney	N.O.	38.4	35.3	47.0	0.73	0.72	0.009
2006	Andersen	Atl.	34.3	33.4	40.0	0.87	0.86	0.007
2003	P. Dawson	Clev.	33.6	32.1	43.0	0.86	0.85	0.007
2003	Cundiff	Dall.	36.0	33.7	45.0	0.79	0.79	0.006
2004	Cundiff	Dall.	36.0	33.7	45.0	0.79	0.79	0.006
2005	Gould	Chi.	35.0	32.3	44.7	0.78	0.77	0.006
2006	Bryant	T.B.	36.7	34.2	45.2	0.77	0.77	0.004
2005	Elam	Den.	38.0	35.3	46.0	0.75	0.75	0.003
2004	Vanderjagt	Ind.	35.5	33.4	44.2	0.80	0.80	0.000
2005	Tynes	K.C.	35.4	33.7	43.0	0.82	0.82	-0.001
2005	Nugent	N.Y.J.	35.7	33.5	43.8	0.79	0.79	-0.004
2006	Scobee	Jax.	39.0	37.8	44.2	0.81	0.82	-0.004
2005	Janikowski	Oak.	37.6	33.6	45.6	0.67	0.67	-0.005
2005	Scobee	Jax.	36.4	34.0	44.0	0.77	0.77	-0.005
2003	J. Brown	Sea.	39.7	37.1	46.8	0.73	0.74	-0.006
2004	J. Brown	Sea.	39.7	37.1	46.8	0.73	0.74	-0.006
2004	Tynes	K.C.	37.9	35.2	45.5	0.74	0.75	-0.007
2004	Hall	Wash.	38.8	36.6	45.5	0.76	0.77	-0.008
2003	Hall	Wash.	38.8	36.6	45.5	0.76	0.77	-0.008
2004	Reed	Pitt.	34.0	33.1	38.8	0.85	0.86	-0.011
2004	Scobee	Jax.	35.2	32.9	43.1	0.77	0.79	-0.012
2006	Mare	Mia.	37.1	34.1	45.1	0.72	0.73	-0.012
2003	Elling	Minn.	36.8	33.8	44.4	0.72	0.73	-0.014
2004	Elling	Minn.	36.8	33.8	44.4	0.72	0.73	-0.014
2004	Lindell	Buff.	29.5	28.1	37.8	0.86	0.87	-0.015
2004	Dawson	Clev.	34.7	33.5	40.6	0.83	0.84	-0.016
2006	Nedney	S.F.	34.3	33.2	39.5	0.83	0.85	-0.019
2005	Feely	N.Y.G.	36.4	35.7	40.0	0.83	0.85	-0.020
2006	Brown	Sea.	36.2	34.9	41.8	0.81	0.83	-0.021
2006	Tynes	K.C.	36.9	35.1	43.1	0.77	0.80	-0.024
2006	Bironas	Ten.	34.4	32.5	41.7	0.79	0.81	-0.025
2005	M. Bryant	T.B.	38.4	38.4	38.5	0.84	0.87	-0.026
2005	J. Brown	Sea.	41.3	39.1	46.9	0.72	0.75	-0.027
2003	Mare	Mia.	37.4	35.5	43.1	0.76	0.79	-0.027
2004	Kaeding	S.D.	35.3	34.0	40.6	0.80	0.83	-0.032
2005	Lindell	Buff.	35.3	34.7	38.3	0.83	0.86	-0.032
2006	K. Brown	Hou.	39.4	37.9	44.0	0.76	0.79	-0.034
2004	K. Brown	Hou.	37.5	34.9	43.7	0.71	0.75	-0.039
2004	Brien	N.Y.J.	35.9	35.5	38.2	0.83	0.87	-0.039
2003	Vinatieri	N.E.	33.0	30.4	40.2	0.74	0.78	-0.041
2005	Mare	Mia.	34.8	34.6	35.8	0.83	0.88	-0.045
2006	Janikowski	Oak.	38.9	36.8	44.4	0.72	0.77	-0.045
2003	Conway	Clev.	36.8	34.9	42.0	0.74	0.79	-0.050
2006	Gostkowski	N.E.	32.7	30.9	38.7	0.77	0.82	-0.050
2006	Akers	Phil.	34.3	33.0	39.0	0.78	0.83	-0.051
2005	Carney	N.O.	33.6	32.2	38.4	0.78	0.83	-0.051
2005	K. Brown	Hou.	35.6	34.1	40.6	0.77	0.82	-0.051
2006	Rayner	G.B.	35.7	33.9	40.9	0.74	0.80	-0.056
2004	Anderson	Ten.	37.6	36.7	40.6	0.77	0.83	-0.058
2006	Vanderjagt	Dall.	34.0	31.8	39.6	0.72	0.79	-0.064
2006	Dawson	Clev.	36.7	34.9	41.5	0.72	0.79	-0.067
2005	Cortez	Ind.	35.3	33.3	40.2	0.71	0.79	-0.082
2005	Longwell	G.B.	37.7	36.8	40.4	0.74	0.83	-0.088
2005	Edinger	Minn.	36.5	35.5	39.4	0.74	0.83	-0.096
2004	Edinger	Chi.	38.4	37.7	40.3	0.72	0.83	-0.111
2003	Edinger	Chi.	38.4	37.7	40.3	0.72	0.83	-0.111
2006	Reed	Pitt.	35.6	35.0	37.4	0.74	0.85	-0.113
2004	Mare	Mia.	39.0	39.1	38.8	0.75	0.87	-0.117
2004	Gramatica	Ind.	34.6	31.1	39.5	0.58	0.70	-0.122
2003	Reed	Pitt.	34.4	33.8	36.1	0.72	0.86	-0.141
2003	Marler	Jax.	35.9	33.5	39.5	0.61	0.75	-0.148

Here is a list ranking the kickers from best to worst based on their multi-year performance during the same period. The number of seasons in which each kicker qualified is also listed. (* Vanderjagt's perfect year skews his results strongly. His average miss distance in 2003 was theoretically infinite! Giving him a realistic yet excellent score (+0.10) for '03 would place him between Stover and Nedney.)

Kicker	% Act-Exp	Years
Vanderjagt*	0.062	4
Hanson	0.061	4
Rackers	0.053	2
Kasay	0.042	4
Wilkins	0.035	4
Graham	0.032	4
Stover	0.030	4
Nedney	0.019	2
Peterson	0.018	1
Andersen	0.017	2
Elam	0.016	4
Gould	0.015	2
Vinatieri	0.014	4
Christie	0.014	1
Longwell	0.010	4
Janikowski	0.009	4
P. Dawson	0.007	1
Feely	0.007	4
Cundiff	0.006	2
Lindell	0.006	4
Kaeding	0.005	3
Bironas	0.004	2
Bryant	0.004	1
Brien	0.004	2
Akers	0.003	4
Nugent	0.003	2
Carney	-0.003	4
Scobee	-0.007	3
Hall	-0.008	2
Tynes	-0.010	3
J. Brown	-0.013	3
Elling	-0.014	2
Anderson	-0.017	2
K. Brown	-0.019	4
Dawson	-0.021	3
Brown	-0.021	1
M. Bryant	-0.026	1
Gramatica	-0.029	3
Conway	-0.050	1
Gostkowski	-0.050	1
Mare	-0.050	4
Rayner	-0.056	1
Reed	-0.060	4
Cortez	-0.082	1
Edinger	-0.106	3
Marler	-0.148	1

Acounting for Vanderjagt's perfect year, Jason Hanson comes out on top. But to put things in perspective, a +6% accuracy rate above average equates to about 1.75 extra FGs made per season.

Belichick Cheating Evidence?

One of the more apparent signs that a spy or corrupt official is cheating is that he is living a lifestyle beyond his means.

If Belichick's Patriots exploited unfair advantages in stealing signs from opposing sidelines we would expect to see some sort of evidence that they won games "beyond their means." By means I am referring to the Patriots' passing and running performance on offense and defense.

By successfully exploiting stolen signs, we might expect the Patriots to choose to use that advantage on critical plays--3rd downs in the 4th quarter for example. These critical plays would heavily "leverage" performance on the field to be converted into wins. In other words, the Patriots would win more games than their on field stats would indicate.

This is exactly what we see in the data. Year-in and year-out, Belichick's Patriots have won about 2 more games than expected given their offensive and defensive efficiencies, including turnovers and penalties. No other modern team has even come close to the Patriots in consistently winning more games than their stats indicate. Could those extra wins be due to cheating?


For a comparison of other teams' actual/expected wins charts, see this article. When I first discovered this pattern, I believed it was evidence of Belichick's in-game "genius." He was known for some unconventional tactics, such as going for it on 4th downs more often than his counterparts. (I'd go for it on 4th down too if I knew the play the defense would run.)

In a previous article, I ranked every head coach since 1983 in terms of how many excess wins they had above their expected wins based on team efficiency. Belichick's career, as a whole, was rather average due to his poor results in Cleveland. But by isolating his tenure with New England, his excess wins per season would rank him as the best tactical coach ever, with an extra +2.33 wins per season. The rest of the pack is far behind with the 2nd best coach at +1.83 wins per season. Belichick is a true outlier, at almost 3 standard deviations above the mean.

This is only circumstantial evidence of cheating, but it is evidence. And although hardly damning, we can be sure of one thing about Belichick--he is willing to cheat. If someone has crossed the line by breaking one rule, what makes you think he's not willing to break others?

On some other sites I've read some emotional comments rationalizing the Patriots' cheating. Whether other teams have attempted this or not is not relevant. Patriots fans and Belichick fans must accept the possibility that much of their success has been due to cheating. What I've done here has added weight to that possibility and quantified the potential scope of this scandal. At the very least, we would be justified in continuing to investigate the Patriots' methods.

Note: Some other examples of teams' expected vs. actual wins can be found here. Also, since this post is appearing on many other sites recently, I've posted a response to many of the excellent comments and criticisms over the past several months.

Patriots Sign Stealing

Is there evidence that the New England Patriots benefitted on the field from videotaping their opposition's defensive signals? One indication would be their success in rematch games. If the Patriots have been exploiting signal stealing regularly in past years, we would expect them to have an advantage against teams they play more than once in a season. The Patriots would be expected to score more points in the second game against a given opponent.

Here are the games in which the Patriots played the same opponent twice in a season for the past four years. Each year they play their three division rivals twice, plus they happened to play one of their playoff opponents during the regular season. The points scored by the Patriots in the first meeting and the rematch are listed.

2006	Points Scored
Opponent	1st Game	2nd Game
NYJ	24	14
MIA	20	0
IND	20	34
BUF	19	28
Total	83	76

2005	Points Scored
Opponent	1st Game	2nd Game
BUF	21	35
DEN	20	23
MIA	23	26
NYJ	16	31
Total	80	115

2004	Points Scored
Opponent	1st Game	2nd Game
IND	27	20
BUF	31	29
MIA	24	28
NYJ	13	23
PIT	20	27
Total	115	127

2003	Points Scored
Opponent	1st Game	2nd Game
BUF	0	31
NYJ	23	21
IND	38	17
MIA	19	12
Total	80	81

Only 2005 shows any real difference in points scored between the first and second games against the same opponent. Even so, we'd have to show that the 8.3 point/game difference in 2005 is significantly outside the normal variation between first and second games between all teams during the same period.

This result does not indicate the Patriots were not cheating by videotaping signals, but it does show they did not benefit signifcantly in points scored during rematch games in recent years.

Are Kickers Underpaid?

The place kicker is a unique player because his impact on the game is solitary and direct. A kicker's performance, accounting for field goal distance and attempts, is independent from the performance of the rest of his team. No other position in football is like that, even the punter.

Recently I calculated the weight of each phase of the game in terms of team wins. The results are listed below.

Variable	Importance
O PASS	19%
D PASS	12%
O RUN	7%
D RUN	7%
O INT	9%
D INT	9%
O FUM	5%
D FFUM	5%
PEN	6%
FG/XP	5%
KICK	7%
K RET	1%
PUNT	3%
P RET	4%

The place kicker's performance accounts for at least 5% of the variance in regular season team wins. I say 'at least' because usually the kicker performs kick-offs in addition to field goals and extra points. Accordingly, he should account for 5% of the salary cap as well.

The table below lists all kickers' salary cap charges by year from 2002 to 2006. Also listed in the team salary cap and the total league salary cap for all teams. The final column lists the percentage of the league's salary cap allocated to place kickers.

Year	K Salary	Team Cap	League Cap	K Share
2002	25,062,723	71,100,000	2,275,200,000	1.1%
2003	29,478,799	75,000,000	2,400,000,000	1.2%
2004	36,922,489	85,500,000	2,736,000,000	1.3%
2005	38,873,799	102,000,000	3,264,000,000	1.2%
2006	65,056,804	109,000,000	3,488,000,000	1.9%
Total	$195,394,614	$442,600,000	$14,163,200,000	1.4%

Since 2002, kickers have earned 1.4% of the total salary available in the NFL despite accounting for at least 5% of the variance in team wins. But things are looking up for them, as their share of the total NFL salary in 2006 rose to 1.9%.

The Importance of Field Position

I'm currently reading a copy of KC Joyner's Scientific Football 2007. It's an excellent annual prospectus full of useful stats and analysis, which I highly recommend. KC regularly writes for ESPN Insider. I just read a part of Scientific Football entitled Straight from the Dept of Meaningless Statistics (p.210). KC suggests that average drive starting position is "not meaningful at all." He cites an example comparing the Steelers and Browns in 2006:

"PIT's starting field position was their 26-yd line, which was the worst in the NFL. Cleveland's average starting field position was at their 30-yd line, which was the 2nd best...If the average team has 12-13 drives per game, that would mean each team would have [approximately] 100 drives after 8 games. This means CLE would have a 400-yd advantage in this category.

"Four hundred yards sounds like a lot but let's also put it into prespective. If the Browns had 70 potential field position yards on each of their drives (i.e. they had 70 yds to go for a TD), that would mean they have 7,000 yds to go versus PIT's 7,400. Four hundred yards sounds like a lot until you consider that is in the context of needing to gain 7,000 yards."

At first I began to think about the question this way: 400 out of 7000 yds is about 5%. That's not that much, but as a Ravens fan, I'd gladly accept an extra 5% performance boost to my team's offense. But then I realized that field position is not linear, and percentage would not the best way to conceptualize it.

Think of an offensive drive not in terms of a series of passes and runs, but in terms of a chain of first downs, regardless of how they are achieved. To arrive in scoring position a team needs not just yards, and not just 1st downs, but consecutive first downs. The success rate for achieving a 1st down on each series has been 65% over the past 5 years. So a team's probability of sustaining a scoring drive is 0.65^x, where x is the number of 1st downs needed (which would include the final scoring series as well).

On average, an NFL offense needs 3.7 first downs (including the score itself) to score a touchdown. Therefore, the estimated TD rate would be 0.65^3.7 = 0.20 TDs per drive. (Note: The actual share of drives that resulted in touchdowns over the past five years is very close--19%.)

One way to think of those 4 extra yards is that they would typically require 0.4 more first downs to score. The resulting effect on the probability of scoring is 0.65^4.1 = 0.17. The difference is 0.20-0.17 = 0.03.

A difference of only 3% in the chance of scoring a TD on a typical offensive drive may seem very small, but it has a large impact on points. Given a league average of 12.4 drives per game (according to KC Joyner), the effect on two teams with a 4-yd difference in starting field position would be:

0.17 * 12.4 = 2.1 TDs per game (14.7 points)
0.20 * 12.4 = 2.5 TDs per game (17.4 points)

The result is a 0.4 TD per game advantage to a team with a 4-yd field position edge, the equivalent of 2.8 points per game. But it wouldn't work out exactly that way, because there is obviously no such thing as 0.4 touchdowns. So sometimes a team would end up with an additional TD, sometimes not, but perhaps sometimes 2 additional TDs. In my view, this effect is very meaningful.

Here is perhaps a simpler way to conceptualize it. Instead of saying the team with lesser starting field position needs 0.4 more 1st downs per drive to score, we could say that they need a full additional 1st down in 40% of its drives.

The resulting probabilities of successful TD drives are somewhat simpler to understand. This time I'll say the average # of drives per game is 10, which I believe is closer to the actual number than KC's 12.4 number.

0.65^3.7 = 0.20 probability of TD drive
0.20 * 10 drives/game = 2.1 TD drives/game

0.65^3.7 = 0.20 probability of TD drive
0.65^4.7 = 0.13 probability of TD drive
0.20 * 6 drives/game + 0.13 * 4 drives/game = 1.7 TD drives/game

Again, the difference is 0.4 TDs/game.

But we still need to consider field goals. Drives that stall just shy of the end zone are typically converted into field goals. So the estimated difference in expected points due to touchdowns would be mitigated by the expected consolation of 3 points for the team with the worse starting field position. That is, until we consider that the team with better starting field position would also get into field goal range easier themselves. The effect of field goals is essentially a wash.

This is a league-wide general analysis. I've used a lot of words such as typically, on average, and expected. For individual teams, there are a lot of other variables, the most significant of which is 1st down success rate--65% is only the league average. For example, the 2006 Colts' 1st down success rate was 79%. In contrast, the Buccaneers' success rate last year was only 59%. That's going to have a stronger effect on the probability of scoring than starting field position. But those 4 yds still matter a good deal.

Post Script--I asked KC Joyner about this topic. He pointed out that by "meaningless," he was referring to the statistic of starting field position due to its lack of context, and not field position itself.

How to Beat the Over-Under

Note: A follow-up to the results of the 2007 season can be found here.

Just in time for the beginning of the season, I think we've cracked the code on beating the Vegas over-under lines. Prompted by a recent comment from Tarr, I did some additional analysis. Although this is not a gambling site, I realize a lot of people are interested in it, and many people would at least be interested in how to beat conventional wisdom.

I only had the last two seasons of data available, and although I'd prefer to have more, the results are convincing.

In my past several months of researching NFL win-loss records, I've noted two overwhelming phenomena:

1. The NFL is impossible to predict before the season starts. And,
2. Regression to the mean rules the day.

In practical terms, expert predictions, including the consensus Las Vegas over-under predictions, are bad primarily because they underestimate the annual tendency for bad teams to improve their records and good teams to worsen their records. Expert predictions stink--that's the good news.

The bad news is our own predictions usually stink worse. Sometimes people get lucky and outguess Vegas or the experts, but over time, luck will catch up to you. So the trick is to take advantage of Vegas' flaws by applying the two lessons above, all the while ignoring our own predictions. Here's how:

1. Take the under on teams predicted to finish with 9.5 wins or more.
2. Take the over on teams predicted to finish with 6.5 wins or less.

And here's why:

1. Of the 18 teams predicted to have 9.5 wins or more, 13 finished the season under, and 5 finished over.
2. Of the 15 teams predicted to have 6.5 wins or fewer, 11 finished the season over, and 5 finished under.

Using these two rules, the '9.5 or more' teams would have yielded a net of 13-5=8 winning bets, and the '6.5 wins or fewer' teams would have yielded 11-4=7 winning bets.

I am not a gambler at all, so forgive me if I mess this up. In the last 2 years, if you bet $110 on each game according to these rules, you'd have placed 18+15=33 bets for a total of $3300. For each loss, you'd receive nothing, but for each of the 24 wins, you'd get back $210 ($110 + $100) for a total of $5040. Your net winnings would be $1740. That's a 152% return on your "investment" over two years.

This analysis is based on only two years of data. However, of the 33 observations included, the chance of being correct by chance 24 or more times is p=0.0068. To statisticians, that means it's significant. To gamblers, it means it's a safe bet. But if anyone has over-under data from years prior to 2005, I can include it in the analysis to increase the confidence level.

The lesson here is if you're going to gamble, don't bet on your own dumb guesses. Bet against the dumb guesses of everyone else. Take the over on stupidity.

The table below lists each team's actual wins, pre-season over-under lines, and the error of the over-under predictions. The system's correct predictions are in green and its incorrect guesses are in red.

Year	Team	Wins	Over-Under	O-U Error
2005	IND	14	11.5	-3
2005	PHI	6	11.5	6
2006	IND	12	11.5	-1
2005	NE	10	10.5	1
2006	NE	12	10.5	-2
2006	SS	9	10.5	2
2006	DEN	9	10	1
2005	ATL	8	9.5	2
2005	BAL	6	9.5	4
2005	CAR	11	9.5	-2
2005	MIN	9	9.5	1
2005	NYJ	4	9.5	6
2005	PIT	11	9.5	-2
2006	CAR	8	9.5	2
2006	DAL	9	9.5	1
2006	JAX	8	9.5	2
2006	KC	9	9.5	1
2006	NYG	8	9.5	2
2006	PIT	8	9.5	2
2006	CHI	13	9	-4
2006	CIN	8	9	1
2006	MIA	6	9	3
2006	SD	14	9	-5
2006	WAS	5	9	4
2005	BUF	5	8.5	4
2005	DAL	9	8.5	-1
2005	DEN	13	8.5	-5
2005	DET	5	8.5	4
2005	JAX	12	8.5	-4
2005	KC	10	8.5	-2
2005	SS	13	8.5	-5
2005	STL	6	8.5	3
2006	ARI	5	8.5	4
2006	MIN	6	8.5	3
2006	PHI	10	8.5	-2
2006	TB	4	8.5	5
2005	SD	9	8	-1
2006	ATL	7	8	1
2005	ARI	5	7.5	3
2005	CIN	11	7.5	-4
2005	GB	4	7.5	4
2005	HOU	2	7.5	6
2005	NO	3	7.5	5
2005	OAK	4	7.5	4
2005	WAS	10	7.5	-3
2006	BAL	13	7.5	-6
2006	NO	10	7	-3
2006	STL	8	7	-1
2005	CHI	11	6.5	-5
2005	NYG	11	6.5	-5
2005	TB	11	6.5	-5
2005	TEN	4	6.5	3
2006	BUF	7	6.5	-1
2006	CLE	4	6.5	3
2006	DET	3	6.5	4
2006	GB	8	6	-2
2006	OAK	2	6	4
2005	MIA	9	5.5	-4
2006	HOU	6	5.5	-1
2006	NYJ	10	5.5	-5
2006	TEN	8	5.5	-3
2006	SF	7	5	-2
2005	CLE	6	4.5	-2
2005	SF	4	4.5	1

Pre-Season Predictions Are Worthless

I recently came across online discussions regarding pre-season predictions of win totals for each team in the NFL. In this post I'll show why you shouldn't put much faith in any of the predictions you read before the first snap of the 2007 regular season.

For comparison purposes, I'll use Football Outsiders' predictions and the Vegas over-under lines for the last two NFL seasons as representative statistical and consensus predictions. As it turns out, neither fare very well in their predictions.

I'll judge the accuracy of predictions by mean absolute error (MAE). This is the average of the absolute value of the error. If the MAE is 3.5, it would mean the predictions were off by an average of 3.5 games in either direction. The smaller the MAE, the better the prediction.

For the 2005 and 2006 NFL seasons the accuracies for Football Outsiders and Vegas betting lines are listed in the table below.

Year	FO	Vegas
2005	3.0	3.0
2006	2.3	2.3
Avg	2.6	2.6

Over the past two years, the Football Outsiders predictions are no better than the consensus Vegas lines. They are wrong by an average 2.6 wins for each team. Although the NFL is difficult to predict, 2.6 games is quite a bit in a 16 game season.

How do we judge whether 2.6 games is a good or bad prediction? To judge if predictions are worth anything, we should compare them to obvious knowledge. I compared the FO and Vegas predictions to two sets of obvious predictions. The first is if I mindlessly predicted 8 wins for every team. The second is just using a regression of last year's wins. The resulting comparison of average errors is listed below.

Year	FO	Vegas	8 Wins	Last Year
2005	3.0	3.0	3.0	2.9
2006	2.3	2.3	2.1	2.2
Avg	2.6	2.6	2.5	2.5

The average errors for '05 and '06 was 2.5 games for both the mindless 8-game predictions and last year's records. Both "obvious" methods actually do slightly better than the expert predictions.

Pre-season predictions are completely worthless, at least those of Football Outsiders and Las Vegas. In fact, they're worse than worthless.

One final note--If each division is ranked by their current Vegas over-under lines, the results are virtually identical to last year's final standings. The only exceptions are two ties. If you want to know how to take advantage of bad expert predictions, read this.

Hat Tip: Some data for this analysis came from Football Prediction Network. Original idea stemmed from the Sports Economist via Sabermetric Research.

End note: The regression of season win totals based on previous year wins yielded the following result (n=96): Next Yr Wins = 5.7 + 0.29 * Last Yr Wins.
r-squared=0.12. Significance for Last Yr Wins was p=0.00.

Median Salary and Wins

The last post examined total team salary and estimated its effect on regular season win totals. The data showed there was a connection, and that for every standard deviation above average in team salary ($13 million), a team could expect to win an extra 0.33 wins.

In recent years, I've heard some analysts explain the success of some teams, particularly the Patriots, by noting they are a team of few stars but of great depth. Beyond a couple notable exceptions, their best teams were filled with many above average players and very few big stars. They had very few holes in their starting line-up.

It seemed plausible to me. With less salary cap room taken up by big name stars, there is more to spread around at each position and for reserve players. A team composed like that would have very few weak links and would be less vulnerable to injuries.

To see if there is a connection between team composition and winning, I compared team median salary and regular season wins for 2001-2006 (n=191). A team with a lot of highly paid stars would have a low median salary, and a team with few highly paid stars would have a high median salary. However, I need to account for team total salary, because as a team increases its total salary its median salary would naturally increase without any additional "spreading of the wealth." Also, as I did previously, I normalized the salary variables by year because the salary cap grows annually.

I ran a regression model of regular season wins based on median salary and total team salary. The results are:

VARIABLE	COEFFICIENT	STDERROR	T STAT	P-VALUE
Z Median Salary	0.34	0.23	1.47	0.14
Z Total Salary	0.28	0.18	1.58	0.12
r-squared	0.03

This result supports the notion that an even team composition is advantageous, but it is not quite conclusive. Median salary is marginally significant, as is total salary. For every standard deviation above average in median salary, a team can expect an additional 0.34 wins, holding total salary constant. The team that is most "fair" in spreading the wealth would be about 2 standard deviations above average, so they could expect to win about an extra 0.68 games per year on average.

When I see results like this, that confirm what we'd expect, but with significance levels around 0.1, I suspect that there is almost certainly a connection but because the effect is small we need a larger data set to see higher significance levels.

Also note that the coefficient of total team salary is revised to 0.28 wins per standard deviation (compared to the previous post). This confirms the effects of total and median salary are not independent of one another.

Ultimately, the effects of total salary and median salary are most likely real and measurable, but small. Even the highest spending team can't even guarantee themselves one full additional win for their spending spree. I believe this underscores the importance of revenue sharing and the salary cap. Without those mechanisms to counter-balance free agency, the NFL would be very predictable, and we'd likely be watching the richest teams in the playoffs every year.

Data was obtained from the USA Today NFL salary database.