Field goal kicking—like putting in 3D with oblong balls


Andrew Gelman (the author of most posts on this blog, but not this one), recently published a Stan case study on golf putting that uses a bit of geometry to build a regression-type model based on angles and force.

Field-goal kicking

In American football, there’s also a play called a “field goal.” In the American football version, a kicker (often a player migrating from the sport everyone else in the world calls “football”) tries to kick an oblong-ish “ball” between 10 and 70 meters between a pair of vertical posts and above a post at a certain height. If you’re not from the U.S. or other metrically-challenged country still using (British) imperial measures, it’ll help to know that a meter is roughly 1.1 yards.

Sounds kind of like putting, only in 3D and with no penalty for kicking too hard or far and wind effects instead of terrain features. This modeling problem came to my attention from the following blog post:

Unlike Gelman’s golf-putting example, Long’s model combines a kick-by-kick accuracy model with a career-trajectory model for kickers, another popular contemporary sports statistics adjustment. Long used brms, a Bayesian non-linear multilevel modeling package built on top of Stan, to fit his model of field-goal-kicking accuracy. (For what it’s worth, more people use brms and rstanarm now than use Stan directly in R, at least judging from CRAN downloads through RStudio.)

Model expansion

The focus of Gelman’s case study is model expansion—start with a simple model, look at the residuals (errors), figure out what’s going wrong, then refine the model. Like Gelman, Long starts with a logistic regression model for distance; unlike Gelman, he expands the model with career trajectories and situational effects (like “icing” the kicker) rather than geometry. An interesting exercise would be to do what Gelman did and replace Long’s logistic model of distance with one based on geometry. I’m pretty sure this could be done with brms by transforming the data, but someone would need to verify that.

Similarly, Gelman’s model still has plenty of room for expansion if anyone wants to deal with the condition of the greens (how they’re cut, moisture, etc.), topography, putter career trajectories, situational effects, etc. My father was a scratch golfer in his heyday on local public courses, but he said he’d never be able to sink a single putt if the greens were maintained the way they were for PGA tournaments. He likes to quote Lee Trevino, who said pro greens were like putting on the hood of a car; Trevino’s quotes are legendary. My dad’s own favorite golf quote is “drive for show, putt for dough”—he was obsessive about his short game—his own career was ended by knee and rotator cuff surgery—hockey wasn’t good to his body, either, despite playing in a “non-contact” league as an adult.

It would be fun to try to expand both Long’s and Gelman’s models further. This would also be a natural discussion for the Stan forums, which have a different readership than this blog. I like Gelman’s and Long’s post because they’re of the hello-world variety and thus easy to understand. Of course, neither’s ready to go into production for bookmaking yet. It’d be great to see references to some state-of-the-art modeling of these things.

Other field goals

Field goals in basketball (shots into the basket from the floor as opposed to free throws) would be another good target for a model like Gelman’s or Long’s. Like the American football case and unlike golf, there’s a defense. Free throws wouldn’t be a good target as they’re all from the same distance (give or take a bit based on where they position themeselves side to side).

Are there things like field goals in rugby or Australian-rules football? I love that the actual name of the sport has “rules” in the title—it’s the kind of pedantry near and dear to this semanticist’s heart.


I thought twice about writing about American football. I boycott contact sports like football and ice hockey due to their intentionally violent nature. I’ve not watched American football in over a decade.

For me, this is personal now. I have a good friend of my age (mid-50s) who’s a former hockey player who was recently diagnosed with CTE. He can no longer function independently and has been given 1–2 years to live. His condition resulted from multiple concussions that started in school and continued through college hockey into adult hockey. He had a full hockey scholarship and would’ve been a pro (the second best player after him on our state-champion high-school team in Michigan played for the NY Rangers). My friend’s pro hopes ended when an opponent broke both his knees with a stick during a fight in a college game. He continued playing semi-pro hockey as an adult and accumulating concussions. Hockey was the first sport I boycotted, well over 30 years ago when my friend and my father were still playing, because it was clear to me the players were trying to hurt each other.

I’m now worried about baseball. I saw too many catchers and umpires rocked by foul tips to the face mask this season. I feel less bad watching baseball because at least nobody’s trying to hurt the catchers or umpires as part of the sport. The intent is what originally drove me out of watching hockey and football before the prevalence of CTE among former athletes was widely known. I simply have no interest in watching people trying to hurt each other. Nevertheless, it’s disturbing to watch an umpire get led off the field who can no longer see straight or walk on his own or see a catcher don the gear again after multiple concussions. As we know, that doesn’t end well.