Developing good quantiatave metrics of defensive skill is really hard. A quick glance a player's stats totals on basketball-reference shows 17 statistics for offense but only 4 for defense (rebounds, blocks, steals, and fouls). This is the case primarily because there aren't many discrete, observable ways to characterize defensive play. However, with optical player-tracking data, we can go beyond the box score to build a better understanding of defensive abilities.

Characterizing defensive skill first requires that we understand defensive intent. For us, this was the most challenging part of defensive analytics.From the data alone, we can't know what the defensive team strategy was, how a player was expected to help or rotate assignments, or what the defender's responsibilities were at any moment. We decided to start with the simplest question about defensive intent: can we identify who is guarding whom? We sought to infer defensive intent by estimating how individual defensive matchups evolve over the course of a possession, and built a statistical model to figure out who's guarding whom.

We started with a very simple premise. A defender's location should be somewhere in the triangle between the offensive player that the defender is guarding, the ball, and the basket (see illustration above). A Hidden Markov Model (HMM) allows us to leverage this basic idea to infer the exact position in this triangle that defenders usually target, as well as the evolution of defensive matchups throughout a possession. For a more technical discussion see our paper in the Annals of Applied Statistics. Below is an animation of our solution from a Clippers/Warriors game next to an animation fo the raw data:

After looking at hundreds of possessions and doing independent validations, we feel that our model does a good job. In particular, we are able to correctly identify double teams and defensive switches. Although there are certainly issues with reducing NBA defense to one-on-one defense, there is still a ton of information that we can glean based on individual matchups. For example, we have used our matchup algorithm to compute,

- Attention drawn: a measure of how much defensive attention a player commands.
- Frequency of switches and double teams
- Counterpoints: an estimate of how many points an individual gives up
- Defensive shot charts: a spatial representation of individual defensive skill
- Better estimates of offensive skill, controlling for defense

In future posts, we'll discuss many of these metrics in more detail.