## Wednesday, January 14, 2009

### 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.

kickernormalized scorepercentagenumber of kicks
racken0010.9630.95242
nednej0010.9170.930
wilkij0010.8890.87131
dawsop0010.8890.93330
kaedin0010.8660.87524
kasayj0010.860.80541
vandem0030.8570.88927
stovem0010.8510.88234
grahas0020.8370.87933
hansoj0010.8360.79224
bryanm0010.8360.84626
bironr0010.8350.79329
feelyj0010.8320.83342
linder0010.8190.82935
mareo0010.8150.83330
hallj0060.810.82417
elamj0010.8060.77135
tynesl0010.8030.81833
akersd0010.8020.72722
brownj0180.7960.69733
petert0050.7940.88526
reedj0050.7850.84432
nugenm0010.7730.78628
vinata0010.7730.78628
carnej0010.7620.78132
longwr0010.7510.74127
gouldr0010.7490.78628
brownk0080.7450.76534
scobej0010.7430.7532
edingp0010.7360.73534
janiks0010.7040.66730
franct0010.6860.7789
cortej0020.6710.70617
novakn0010.6080.810
cundib0010.5410.5569

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.

punterlengthdepthnumber of punts
moormb00141.5113.8574
jonesd01841.0413.3588
johnsd02239.7810.542
bergem00139.6910.8875
sauert00139.3811.0583
grahab00138.849.8275
scifrm00139.761474
bakerj00139.5514.1888
hentrc00139.4814.2279
mcbrim00139.1613.0985
bidwej00139.4515.6897
hansoc00138.7214.5292
koenem00138.814.8478
feaglj00138.0213.3578
frostd00138.2114.7191
grooma00138.8917.6712
playes00136.9510.576
colqud00137.814.1466
harrin00236.059.7189
landes00138.412034
edingp0013572
maynab00137.7818.48106
leea00336.4413.11110
barkeb00136.714.2751
gardoc00136.4813.9586
aragul00137.0816.418
lechls00136.1813.0884
smithh00935.2811.0859
larsok00236.4717.7366
stanlc00234.8111.579
benned00134.57118
millej01236.4619.188
kluwec00135.2114.4375
richak00334.8113.1781
rouent00134.961476
murphn00133.5157
sandeb00233.3715.464
hodger00132.3113.9244
flinnr00131236
brownj018NA11.52
cundib001NA201
dawsop001NA6.52
ellina001NA21
gouldr001NA241
kasayj001NA201
mareo001NA271
nugenm001NA171
roethb001NA10.52
vinata001NA41
wilkij001NA201

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.

#### 1 comment:

Fred Noll said...

Question: Is the Punt length taken with the line of scrimmage as the starting point or does it start from the yard line where the player kicked the ball.