Back in 2012, on the heels of my PhD in nonparametric Bayesian density estimation, I developed a methodology that constructs a nonparametric Bayesian density and teases out a nice spatio-temporal decomposition of movement on a space of interest. Pointing this at NBA SportVu data, the decomposition kindly identified player tendency in specific types of offenses and defenses. In 2013, I constructed a 12 page report for an Eastern Conference NBA team; detailing the rate of movement for three point shooters with respect to their offensive flow.
Now, five years later since model construction, being on the edge of journal submission, I have pointed this model at defensive tendencies of teams with respect to the Pick-And-Roll offense of an opponent. In this article, there will be no math, but rather an intuitive glance at the process. If you are interested in the article, feel free to shoot me a message at firstname.lastname@example.org or @squared2020 on Twitter.
To give an example of the process, let’s consider a single play from a Cavaliers’ playoff game against the Indiana Pacers. In this play, the Pacers run a pick-and-roll on the left wing between Indiana’s Myles Turner and Jeff Teague. With a Cavaliers double team on Teague, Turner frees himself by rolling towards the free throw line.
The Cavaliers have a series of options on their rotation defense. With Tristan Thompson and Kyrie Irving doubling Teague, the Cavaliers must do one of three things: Pick up Turner at the free throw line from the baseline, Pick up Turner at the free throw line from the wing, or Hold and let Turner go free.
The Cavaliers opt to hold by planting Kevin Love in the middle of the box. LeBron James abandons C.J. Miles to guard an empty short corner. The result is that Turner take an uncontested shot attempt [Thompson recovers from behind Turner, with no effect on the shot] from the free throw line, resulting in two points.
Modeling as a Density
Now, we can model this action as a spatio-temporal density of actions. The simplest method is to perform a kernel density estimator. However doing this, we don’t much knowledge other than the Kullback-Leibler divergence of differing plays; which does not yield enough signal-to-noise for player motion.
Instead, we look at empirical orthogonal functions (EOF), and perform a density estimation over the components. What makes this special? The EOF breakdown yields correlations between spaces over time. The resulting transitional density estimates give a signature to each defensive play. Furthermore, the EOF differences yield quantifiable data for player movement. For instance, we can look at the transition of LeBron James and show that his movement is low, yielding little-to-no-change in the EOF coefficients. How does this translate to edge on the court?
- Cavaliers hold on Myles Turner; accepting a lower probability mid-range field goal attempt.
- If Kevin Love rotates, LeBron James’ movement is slow to recover a pull from Thaddeus Young across the key.
- This will most likely result in an assist to Young for two points.
This helps identify the speed of movement of players on the court. In a later play, the team jumps the shooter and this does indeed result in a Thaddeus Young basket; again due to late off-ball rotation.
Reconstructing the EOF distribution, we get a KDE-like transition of defensive movement.
We can also use the spatio-temporal breakdown to classify team defense types; as well as compare different teams’ ability to cover the pick-and-roll. This requires knowledge of two items: hypothesis testing and the Karhunen-Loeve Transform for empirical orthogonal functions.
Keep an eye out for the academic paper!