Saturday, December 11, 2010

Field Goal Percentage vs Expected

By James Deyerle

Everyone knows that distance matters when it comes to field goals. After all, late in close games the broadcasters will talk about the kicker’s ‘maximum range’ while showing him warming up on the sideline. Everyone can see the red line superimposed on the field and knows that leaving the game in the hands of the kicker for a 56-yard field goal is preposterous, but once you hit that magic number of 55 nothing but the sweet taste of victory is ahead… or at least a new kicker.

Sarcasm aside, distance is largely ignored. A kicker who makes eight of ten 50-yard field goals is clearly more valuable than another who made eight of ten 20-yarders, but they both have a field goal percentage of 80% and scored 24 points. This particular issue has bothered me recently because, as a Cowboys fan, I was tired of hearing about how many potential game-tying or winning field goals David Buehler had missed this season when it was obvious those kicks were longer than normal, not to mention sample size.

That drove me to create a rough formula for predicting the likelihood of a made field goal from a given distance and compare it against how every kicker had actually performed this season. Brian has a chart showing this expected percentage here. Below are my results. For reference, I limited my data to kickers with at least 10 attempts this season; 81% is average for both Raw and Expected Percentage; and data is through Week 13.

BironasTEN2118.12295.5%82.4%2.913.1%95
HansonDET1210.21485.7%72.9%1.812.9%87
PraterDEN1613.81888.9%76.8%2.212.1%90
FeelyARI1513.21693.8%82.5%1.811.3%89
RackersHOU1917.42190.5%82.7%1.67.8%84
KasayCAR1816.42281.8%74.7%1.67.1%78
Scobee*JAC1816.52281.8%75.0%1.56.9%78
Vinatieri*IND1715.91989.5%83.7%1.15.8%76
CarpenterMIA2725.23381.8%76.3%1.85.6%80
Bryant*ATL2422.72788.9%83.9%1.35.0%76
LongwellMIN1312.41492.9%88.6%0.64.3%69
CundiffBAL1918.32286.4%83.2%0.73.2%66
NedneySF1110.71384.6%82.3%0.32.4%59
GouldCHI1918.52382.6%80.3%0.52.3%62
AkersPHI2625.83183.9%83.3%0.20.6%53
TynesNYG1616.01984.2%84.0%0.00.2%51
Kaeding*SD1414.11877.8%78.3%-0.1-0.6%47
Brown*STL2424.22982.8%83.4%-0.2-0.7%45
Nugent*CIN1515.41978.9%80.8%-0.4-1.9%40
MareSEA2121.82584.0%87.1%-0.8-3.1%30
DawsonCLE1818.72378.3%81.5%-0.7-3.2%33
JanikowskiOAK2425.23177.4%81.4%-1.2-4.0%27
Barth*TB1414.71877.8%81.8%-0.7-4.0%32
Crosby**GB1717.92373.9%78.0%-0.9-4.1%30
GostkowskiNE1010.71376.9%82.1%-0.7-5.2%30
LindellBUF1212.91770.6%75.9%-0.9-5.3%28
BuehlerDAL1617.42272.7%78.9%-1.4-6.1%22
Gano*WSH2123.02972.4%79.4%-2.0-7.0%16
Succop*KC1516.42075.0%82.2%-1.4-7.2%19
Folk*NYJ2325.93271.9%80.9%-2.9-9.0%8
HartleyNO1517.12075.0%85.5%-2.1-10.5%8
ReedPIT/SF1820.72572.0%82.8%-2.7-10.8%6

As you can see, some kickers have above average percentages that are boosted by shorter and thus easier kicks, such as Seattle’s Olindo Mare. Others, like the Panthers’ John Kasay, have an average percentage but have been kicking from longer than normal distances. Unfortunately for Dallas fans, Buehler has had a below average performance so far, but ultimately we’re talking about a handful of kicks making all of the difference. The sample sizes are just too small to make a final determination based on two-thirds of a season. On the other hand, the Steelers were justified for cutting ties with Jeff Reed and it’s a very useful retrodictive method of looking at the season. Raw-Exp% could be a simple way of determining who the Pro Bowl kickers should be.

While each individual kick distance isn’t readily available anywhere, you can easily find how many 20, 30, 40, and 50+ yard field goals a kicker attempted back to the 70s. For this reason I compared the true distance results with a midpoint approximation, i.e. all kicks 20-29 yards were considered 25-yard attempts, and within my (albeit small) sample found this to be a reasonable approximation, within +/- 0.5 expected field goals and +/- 2% Expected Percentage.

With this quick and dirty approximation anyone can take a look at past seasons and get a general idea of how a kicker performed, although the further back you go the less accurate the model is as kickers have improved over time. For instance, we can estimate during Vanderjagt’s perfect season in 2003 he made 5.7 field goals over expected for a Raw-Exp% of 15.3%.

Hopefully all the other terms are self-explanatory, but if you need clarification or want to see something else done with the data leave a note in the comments. I plan on updating the results at the end of the season.

Percentile – Determined from the Z-score of 1,000 simulated seasons using the same number of attempts and attempt distances.

* – Indicates the kicker had a blocked field goal. I did not adjust the data but thought it should be noted. Mason Crosby has been unfortunate enough to have two blocked this season.

Bruce D. said...

Interesting.

I wonder how much "luck" is involved.

Like what was raw-exp% of kickers like Bironas last year, or averages for all other seasons?

Do they all usually end up moving towards average over-all(unless they get fired of course)?

James said...

From everything I've read about kickers I'm under the impression there is no discernible difference between them and it's all luck. I can do the midpoint estimation for more seasons/careers until I get the play-by-play, and I'll post the results.

David Hess said...

The FG/XP portion of Football Outsider's special teams ratings do basically what you've done above, except by team instead of by kicker (and they use exact distances instead of 10-yard buckets).
http://footballoutsiders.com/stats/teamst

They have Dallas 30th out of 32 teams, with Buehler costing them 5.1 points compared to an average kicking performance.

James said...

For the record, I used the exact distances for the chart. The buckets was only an idea for seasons in which I don't have all the play by play data parsed.

David Hess said...

Oh, sorry, that's obvious now that I've gone back and re-read the article. My bad.

James said...

Double-checking my work, I forgot to note that Carpenter has had two kicks blocked, and Akers one.

I've also found that the bucket method for past seasons is accurate, given a large enough sample size.