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Department of Defense

A new Sloan Conference paper might be the key to unlocking our understanding of defensive basketball

Back in March 2014 at Staples Center, Stephen Curry and the Warriors were playing the Clippers. After David Lee missed a layup, Blake Griffin swatted at the rebound, but the ball flung back toward the top of the arc and into the hands of Curry. Naturally, he looked to shoot. As he gathered the ball and began his shooting motion, Chris Paul recovered his defensive position and took that option away. Curry dribbled forward and looked for a pull-up jumper inside the arc. He found one, but Paul remained on his hip and Curry’s shot missed.

In the box score, this was marked down as a rare, forgettable missed field goal for Curry. Who cares? Nowhere in the box score does it mention that Paul chased Curry off the arc while also maintaining decent enough defensive position to contest Curry’s failed pull-up a few dribbles later.

Anecdotally, Paul is considered one of the best defenders in the NBA. But we don’t have any charts or advanced metrics to prove that conventional wisdom. In fact, while the statistics we use to judge offensive play have never been more thorough and complex, defensive analytics are still overly reliant on age-old tallies like steals and blocks.

But thanks to the player-tracking revolution, that’s about to change.

Later this week, my colleagues Alexander Franks and Andrew Miller, who are both PhD students at Harvard,1 will present a research paper at the MIT Sloan Sports Analytics Conference in Boston. In conjunction with professor Luke Bornn of Harvard’s Statistics Department and myself, Franks and Miller have been researching defensive analytics in the NBA for almost two years. You can read the full paper here, but here’s the elevator pitch: We are confident that we’ve developed methods that will enable analysts to more richly characterize defensive performance in the NBA.

Measuring defense is a challenging endeavor, and the behaviors of truly great defenders don’t fit nicely into the cells of spreadsheets. Highlight culture rewards individual offensive achievement, while the defenders in those clips are largely reduced to the same status as officials. If they do their jobs, people don’t even notice they’re there. (Unless we’re talking about Brandon Knight.) As a result, defensive reputations remain murky, and with a few exceptions — Zach Lowe’s wonderful article about the Raptors from two years ago, Ethan Sherwood Strauss’s look at the making of the Warriors defense — meaningful defensive analyses are rare.

In the summer of 2013, the NBA installed player-tracking systems in all 29 of its arenas. Every seemingly mundane action on the court would now be catalogued — from distance run to dribbles taken. But the massive new data set offered something else much juicier: the chance to finally analyze every second of defense played in every arena in the NBA.

Franks and Miller began with a simple goal: to build a model that estimated defensive assignments at any given point in an NBA game. According to Ryan Warkins, the assistant vice-president of Stats LLC, and the guy in charge of managing SportVU, the NBA’s player-tracking system, “By assigning matchups and responsibilities, you can begin to measure the impact individual defenders are having throughout the game.” In short, the matchup model is the first key step in teasing out defensive intelligence from player-tracking data.

Despite the ambitions of Franks and Miller, the statistical modeling and computation were complex, methods did not publicly exist, and the 80-gigabyte player-tracking database loomed as an unwieldy pain in the ass. Still, they were determined to make it work, and spent thousands of hours coding and recoding matchup models.

It took more than a year, but their findings are now ready to see the light of day — in two key venues. First, for the academic statisticians, a peer-reviewed article describing the approach in painfully wonky detail is set to appear in the Annals of Applied Statistics. Franks and Miller will also introduce how the model enabled the creation of a broad new ensemble of defensive metrics when they present the work at the Sloan Conference this Friday in Boston.

Their method snaked its way through every millisecond of the 2013-14 NBA player-tracking data set, and estimated who was guarding whom and when they were doing so. Then it quantified the performances of individual defenders for the season, in exciting new ways.

Houston Rockets v San Antonio SpursD. Clarke Evans/NBAE via Getty Images

On Christmas Day 2013, the Rockets were in San Antonio playing the Spurs. With less than five minutes left, Tony Parker dished the ball to Kawhi Leonard, who was open beyond the right wing. James Harden, the man assigned to defend Leonard, was entangled in a Tim Duncan screen — way out of position. As Leonard gathered the ball to shoot, Harden frantically tried to close him out, bursting out of the paint toward the arc and flailing desperately at Leonard’s jumper. But it wasn’t a jumper — it was a pump fake. Harden’s last-gasp leap took him right out of the play. Leonard took a dribble forward and calmly drained a wide-open 2-point jumper.

Here’s what that play looks like as player-tracking data, with the matchup model in place. The blue lines represent the matchup model’s estimate of who is guarding whom and when. As you can see, the model suggests that Harden was responsible for Leonard as he knocked down his jumper.

Here’s what Paul’s Staples Center closeout on Curry looked like.

Those unassuming little blue lines unlock new avenues, allowing us to quantify and understand individual defensive performances in the NBA. As Franks told me over email, “With detailed knowledge of moment-by-moment defensive matchups, we can fit complex regression models which describe how individual defenders impact opponents’ shot frequency and shot efficiency in different areas of the court.”

Among the many new defensive metrics that Franks and Miller will present at Sloan this week, two stand out:

1. Defensive Shot Charts: Depictions of how a defender’s opponents shoot and score against him.

2. Counterpoints: Estimates of how many points an individual defender allows, per 100 possessions.

According to Franks and Miller, Chris Paul is the best perimeter defender in the NBA. They have empirical evidence that the Clippers point guard suppresses and disrupts shot activity as much or more than any other guard in the league.

Below is Paul’s defensive shot chart for the 2013-14 season. Think of it as the inverse of a conventional shot chart: It reflects the shooting behavior of players when Paul was defending them. The sizes of the symbols on the chart correspond to shot frequency; the color of the symbols represents shot efficiency.


Paul’s chart is peppered with tiny blue dots. This indicates two things: He suppressed the expected shot activity of his nightly assignments and reduced their shot efficiency.

It’s also important to note that the model accounts for baseline activity and effectiveness of the players he was defending. As a result, these defensive shot charts are an aggregate depiction of whether a defender’s assignments shot more or less frequently, and whether they shot more or less accurately than we would expect. If a defender drew a perfectly average response, in both frequency and effectiveness, his chart would be full of medium-size yellow hexagons. But as you can see, Paul’s chart is full of tiny, mostly blue symbols — dots, really. This means that, whether he was guarding Stephen Curry or Rajon Rondo, on average, Paul reduced his opponents’ field goal attempts and field goal percentage.

Those tiny hexagons all over the court mean that players rarely shot when Paul was the on-ball defender. The fact that they’re tiny blue hexagons means that when they did shoot, they were really ineffective. Results from the Franks-Miller study reveal that among all perimeter defenders, Paul’s matchups exhibited some of the biggest decreases in both shot frequency and shot efficiency.

The same could not be said of James Harden.


Relative to Paul, Harden’s hexagons are bigger, more orange, and more red. This means that his defensive assignments became more active and more effective shooters when Harden was the defender.2 All of that red above the break illustrates that a lot of NBA wings got good looks from that area when Harden was marking them.

Compare this with Kawhi Leonard, whose assignments hardly ever got those looks, and when they did, they were more likely to miss.


These defensive shot charts do a good job of showing the relevance of individual defenders. Players like Paul and Leonard reduce the effectiveness of whoever they’re guarding. Guys like Harden heighten it.

The Franks-Miller method also helps us understand differences in interior defenders. Below, you see the 2013-14 defensive shot charts of three of the NBA’s most prominent rim protectors.


As you can see, all of these guys turned the paint blue, meaning opponents suddenly shot at below expected efficiency when facing them. However, while Roy Hibbert and Tim Duncan each faced a lot of shots in the paint, Dwight Howard deterred opponents from even attempting close-range field goals. Abandon all hope, ye who enter the paint against Superman.

Now, were these differences in interior defense symptomatic of individual skill, or were they reflections of the varying defensive principles among teams? Did the Spurs and Pacers intentionally “funnel” shooters toward their behemoth basket protectors in ways that the Rockets did not? Of course, schemes and teammates matter — Rudy Gobert makes Trey Burke a better defender, just like Hibbert made Paul George a better defender. But that caveat doesn’t negate some of the new ways we’re able to quantify defensive performance.

Another important stat to come out of Franks and Miller’s work: Contest Rate. Last season, NBA players attempted more than 200,000 shots. We can now see which frontcourt players contested shots the most often when they were on the floor and who contested shots the least often.

Highest Contest Rates Among Frontcourt players, 2013-14

  1. Roy Hibbert: 41.9 percent
  2. Robin Lopez: 40.1 percent
  3. Ian Mahinmi: 39.3 percent
  4. Joakim Noah: 37.3 percent
  5. Timofey Mozgov: 37.2 percent

Hibbert not only contested almost 42 percent of shots, but his backup, Ian Mahinmi, was third. Which brings us back to that idea of the Pacers funneling shooters toward their centers. It’s an idea bolstered by David West’s placement on the next list:

Lowest Contest Rates Among Frontcourt players, 2013-14

  1. David West: 23.4 percent
  2. Mike Scott: 23.9 percent
  3. Josh McRoberts: 25.1 percent
  4. Blake Griffin: 25.3 percent
  5. Jeremy Evans: 25.6 percent

Contest Rate is one thing; tallying up Points Against is another.

This stat gives us another sensible summary of a defensive player’s performance. We look at all matchups for a defensive player when shots occur (0.5 to 0 seconds before release) and compute the “attempts against” and “points against” values. To do this, we look at all of the possessions played by a defender (in which a shot is attempted) and count how many times he was defending the shooter at the moment of the shot, and how many points were scored, per 100 possessions.

No player in Franks-Miller is as stingy as CP3, who allowed 11 points per 100 possessions while dealing with ferocious NBA matchups — Damian Lillard, Steph Curry, Tony Parker, et al. — on a nightly basis. Paul’s matchups ended up shooting about 80 percent as much as expected, while Harden’s matchups ended up shooting about 114 percent as much as expected.3

Points Against (Backcourt Defenders), 2013-14

  1. Chris Paul: 10.8
  2. Norris Cole: 11.1
  3. Nick Calathes: 12.0
  4. C.J. Watson: 12.0
  5. Greivis Vasquez: 12.3

We talk a lot about how player tracking is poised to revolutionize basketball analytics. But up until now, what we really mean is offensive basketball analytics. Offense is sexy and fun, and it’s generally easier to model, measure, and quantify.

The antiquated nature of defensive stats affects everything from sports bar spats to free-agent contract negotiations. As basketball races headlong into its own version of the big data era, this has to change. Unfortunately, with the exception of a few outside groups, a vast majority of progress in this area is occurring behind the locked doors of practice facilities because of league rules. And while some teams may be cracking the codes of defensive analytics, they sure as hell aren’t sharing their findings with the public.

This research may not change basketball forever, but it represents an important publicly readable step in the evaluation of defensive play in the NBA. There are still many challenges in understanding defensive performance; with no prior knowledge about a team’s principles and rotations, it’s very difficult to know what a defender is supposed to do. But until Gregg Popovich and Tom Thibodeau start publishing their defensive playbooks, we’re just going to have to make educated guesses. Regardless, while there will probably always be an analytical bias that leans toward offense, this work is evidence that the integration of statistical modeling, computation, and player tracking offers an unprecedented opportunity to improve our understanding of defensive play.

The NBA is experiencing a boom in popularity, and millions of fans are obsessed with learning about the game and studying everything there is to know about their favorite players. Unfortunately, even if you examine all of the stats, it’s hard to appreciate greatness on both ends of the floor; hopefully this new research will start to change that. 

Filed Under: NBA, Chris Paul, Steph Curry, Roy Hibbert, Kawhi Leonard, James Harden, Sloan Conference, Kirk Goldsberry

Kirk Goldsberry is a professor and Grantland staff writer.

Archive @ kirkgoldsberry