Punting and Field Goals

by Dean Jens

Field Goals

One of the things I often wondered before discovering The Football Project was how the probability of a kicker making a field goal varied as a function of distance. After eyeballing the distributions for a few kickers for the 2005 season, I figured I could try raising a logistic function to some power. For the first several kickers I tried, I found that that power was statistically indistinguishable from 1, so I set about fitting the probabilities to a simple logistic function, i.e. (1/2)(1+tanh((m-x)/w)).†

I had imagined, in the absence of data, that w might be independent of the kicker, and that kickers could be characterized by m, i.e. how far away they are when their percentages drop. This is not the case; w depends on the kicker, with larger values to kickers who tend to miss easy ones and make longer ones, with lower values to more consistent kickers. Olindo Mare missed a few short ones, so his percentages didn't drop off very quickly. Matt Bryant actually had a slight improvement as distances got longer; this would surely change if more statistics were taken at a normal range of distances. On the other hand, John Kasay had a much higher tendency to hit field goals shorter than 50 than if they were longer than 50; of the 8 he missed, the shortest was 42 (he made 24 shorter than that). Jeff Reed had an even sharper drop around 45 yards, missing nothing shorter than 41 and making nothing longer than 47. While I was unable to fairly characterize the best kicker in terms of a drop-off length, I was able to generate a different metric that adjusts for length. By using my logistic fits, I predicted the percentage of field goals a kicker would make if they kicked from a given distance; I then took the 1006 field goal attempts for the season and calculated the percentage of those 1006 field goals that each kicker would have made. I've only included those kickers who attempted more than 4 kicks; the kickers who were dropped were all notably worse than the ones listed.

kicker	normalized score	percentage	number of kicks
racken001	0.963	0.952	42
nednej001	0.917	0.9	30
wilkij001	0.889	0.871	31
dawsop001	0.889	0.933	30
kaedin001	0.866	0.875	24
kasayj001	0.86	0.805	41
vandem003	0.857	0.889	27
stovem001	0.851	0.882	34
grahas002	0.837	0.879	33
hansoj001	0.836	0.792	24
bryanm001	0.836	0.846	26
bironr001	0.835	0.793	29
feelyj001	0.832	0.833	42
linder001	0.819	0.829	35
mareo001	0.815	0.833	30
hallj006	0.81	0.824	17
elamj001	0.806	0.771	35
tynesl001	0.803	0.818	33
akersd001	0.802	0.727	22
brownj018	0.796	0.697	33
petert005	0.794	0.885	26
reedj005	0.785	0.844	32
nugenm001	0.773	0.786	28
vinata001	0.773	0.786	28
carnej001	0.762	0.781	32
longwr001	0.751	0.741	27
gouldr001	0.749	0.786	28
brownk008	0.745	0.765	34
scobej001	0.743	0.75	32
edingp001	0.736	0.735	34
janiks001	0.704	0.667	30
franct001	0.686	0.778	9
cortej002	0.671	0.706	17
novakn001	0.608	0.8	10
cundib001	0.541	0.556	9

This obviously does not adjust for wind, and the linemen on both the kicking and defending sides will have some influence on these statistics, but this at least tells which unit is doing better than which other with the confounding variable of distance removed. The average length for a field goal attempt was 36.3 yards; the average for Nick Novak was 33.7, while for Josh Brown it was 41.2. Accordingly the "scores" for these kickers find themselves lower and higher, respectively, than the raw percentage. The scores and the actual percentages have a corelation of 0.8. The means and variances are very similar, though the variance of the raw percentages is a little bit smaller; while the difference isn't statistically significant*, it is what would be expected from coaches deciding to attempt longer field goals with better kickers, and punting or going for the first down with worse kickers. Perhaps looking at all fourth down plays from around the thirty yard line would be a good step for further research.

† This isn't a least-squares fit; I try to maximize the sum of the logarithm of the fitted probability of the actual outcome: for kicks that the kicker makes, P is the fitted probability that the kicker would make the kick, while for those the kicker missed (or were blocked or whatever), it is the fitted probability that the kicker would miss the kick.

* It would be significant at the 25% confidence level on a two-tailed test; arguably a one-tailed test could be used here, but even that isn't going to pass a common significance test. When a team prepares to punt, the punter's statistics are often cited, typically the average length of his punts and the number of times he has left teams behind their own 20 yard line. These seem like kind of strange statistics to me; if I were to take the line of scrimmage and the end position of the ball and plot one against the other, what I would likely expect to see, as a first approximation, would be a 45 degree line† up to a point, and then a horizontal line from there on out. Behind a certain point on the field, a punter would be expected to net a certain length; ahead of that, he would be expected to average a certain level of field position. Grabbing every punt the Packers made that year, I found that the break-point from a least squares fit was very near midfield. Accordingly, it seems to me we ought to characterize the net length of punts from one's own half of the field, and the average final field position for punts from the fifty yard line and beyond.

Punting

Taking the data from The Football Project for 2005, I calculated these statistics for each player who punted. Every player who punted more than twice had at least one punt from each half of the field, so the figures for them are well defined. Remember, the "length" is only calculated for those punts from the punter's own end of the field; the "depth", the name of which is probably more poetically than logically motivated, is the average ensuing field position of the receiving team after punts from the fifty and beyond. I use results net of the return, though using results before the return leaves a lot of what follows more or less unchanged. The players are ordered by length-depth/4, due to the fact that about 4/5 of punts originated from the punting team's side of the fifty.

punter	length	depth	number of punts
moormb001	41.51	13.85	74
jonesd018	41.04	13.35	88
johnsd022	39.78	10.5	42
bergem001	39.69	10.88	75
sauert001	39.38	11.05	83
grahab001	38.84	9.82	75
scifrm001	39.76	14	74
bakerj001	39.55	14.18	88
hentrc001	39.48	14.22	79
mcbrim001	39.16	13.09	85
bidwej001	39.45	15.68	97
hansoc001	38.72	14.52	92
koenem001	38.8	14.84	78
feaglj001	38.02	13.35	78
frostd001	38.21	14.71	91
grooma001	38.89	17.67	12
playes001	36.95	10.5	76
colqud001	37.8	14.14	66
harrin002	36.05	9.71	89
landes001	38.41	20	34
edingp001	35	7	2
maynab001	37.78	18.48	106
leea003	36.44	13.11	110
barkeb001	36.7	14.27	51
gardoc001	36.48	13.95	86
aragul001	37.08	16.4	18
lechls001	36.18	13.08	84
smithh009	35.28	11.08	59
larsok002	36.47	17.73	66
stanlc002	34.81	11.5	79
benned001	34.57	11	8
millej012	36.46	19.1	88
kluwec001	35.21	14.43	75
richak003	34.81	13.17	81
rouent001	34.96	14	76
murphn001	33.5	15	7
sandeb002	33.37	15.4	64
hodger001	32.31	13.92	44
flinnr001	31	23	6
brownj018	NA	11.5	2
cundib001	NA	20	1
dawsop001	NA	6.5	2
ellina001	NA	2	1
gouldr001	NA	24	1
kasayj001	NA	20	1
mareo001	NA	27	1
nugenm001	NA	17	1
roethb001	NA	10.5	2
vinata001	NA	4	1
wilkij001	NA	20	1

Number one is Brian Moorman, of the Buffalo Bills; second is Donnie Jones. They are the only two punters to average more than 40 net yards from their own end of the field; of punters who punted more than twice, the two who left the ball inside the ten yard line when they punted from midfield or closer were Ben Graham, who had pretty good length as well, and Nick Harris, whose length was more mediocre.

Adding the length and depth for each player with more than two punts, I get a surprisingly narrow distribution. It is centered around 51.4 or 51.5 — 50.5 would be ideal for the use of these statistics — and has a standard deviation of only 3.5 yards. Most punters, then, seem to punt for distance behind their own 49 or so, and for field position beyond there. If I exclude Ryan Flinn, who had six punts (the fewest among those with more than two) for the worst result in both statistics (among those with more than two punts), the correlation between length and depth is 0 to two decimals.* Accordingly, a punter with better length will tend to be affected by the endzone further into his own territory, while a punter who is particularly good at pinning the opposing team against its goal line is more likely to still be punting for length a bit beyond the fifty; there is no unambiguous connection, independent of one's measure of "skill", between a punter's "breakpoint" and the skill of the punter.

It won't come as a great surprise that the length as I measure it and the average length of all punts has a correlation greater than 0.9. It might not be a big surprise either that the percentage of punts to end up inside the twenty has a correlation of -0.4 with "depth", but, interestingly, either length measurement has a correlation of 0.4 with the inside-the-twenty statistic. From a linear regression standpoint, it looks as though the inside-the-twenty statistic is including some length information; 1/3 of the variance can be explained from the two numbers in my table. The median punt to end up inside the 20 starts from 2 yards behind midfield, but 20% come from behind the punter's own 40; some of what is being recorded in that figure is not any deftness in terms of avoiding the touchback or letting one's teammates get downfield, but is simply the ability to kick to the red zone from farther away. This is a nice skill, of course, but it is fully incorporated into the length statistic; the frequency of leaving a punt inside the twenty is a hybrid of skills, and is not the best measure for any of them.

† There is some attempt here to keep the statistics simple. In fact, this line is slightly flatter than 45 degrees because the endpoint is bounded both above and below; punts from behind midfield give a slope of 0.95 that is statistically distinct from 1 at the 5% confidence level.

* This actually is less true without the return; punters who punt the ball farther before the return also tend to punt it closer to the endzone, but not dramatically so. The distribution of punters' depth+length is similar to the results with the return, with several yards simply moved from depth to length.