Nylon Calculus: Looking for an NBA Defensive Player of the Year

A few weeks ago, the NBA announced the addition of a new feature on its website of stats — box scores detailing individual defensive matchups. We, the Nylon Nerds, were intrigued by this new source of information — our collective interest was piqued. Very piqued. We’ve already found a variety of uses for the matchup data — Senthil highlighted Ben Simmons’ defensive versatility, Ian identified the league’s best LeBron-stoppers, and PR charted height advantages by team. I’ve been feeling a bit left out of the fun — so, for my contribution, I’ll be using matchup stats to help decide who should win the Defensive Player of the Year Award.

The candidates

Recently, DPOY has gone to a player who is the anchor of an elite defense. According to Basketball-Reference, 14 of the last 15 DPOYs have played for a team with a top-five defensive rating. There have been a lot of centers honored with the prize during that stretch — Ben Wallace, Marcus Camby, Kevin Garnett, Dwight Howard, Tyson Chandler, Marc Gasol, Joakim Noah, Draymond Green — but the defensive linchpin doesn’t necessarily need to be a rim protector. Perimeter players occasionally win DPOY, too. Beyond position, then, a more useful indicator of a worthy DPOY candidate is that his team’s defensive rating improves when he is on the court. We can find a pool of potential DPOYs in the lower right-hand corner of this chart:

A quick aside about Andre Roberson: His individual defensive rating is a full eight points below Oklahoma City’s overall rating — a bigger differential than any other player on the chart. It’s impressive, but he played less than half a season. So he’s out.

There are another eight players whose teams allow less than 100 points per 100 possessions while they are on the court – -each one a member of a top-five defensive team (Boston, Utah, Philadelphia, San Antonio, or Toronto). Four of these players — Royce O’Neale, DeJounte Murray, Marcus Smart, and Fred VanVleet — have not been regular starters this year, so they’re out of contention, too. Aron Baynes and Robert Covington will probably be overshadowed by their starier teammates and are unlikely to garner serious consideration for DPOY. That leaves just two legit possibilities — Utah’s Rudy Gobert and Philadelphia’s Joel Embiid.

So, which player saved his team more points this season — Embiid or Gobert? We can use matchup stats to find out.

Matchup stats

The NBA’s matchup data is provided by Second Spectrum using an algorithm that estimates which offensive player each defender was guarding on each possession. Matchup assignments are defined by who-guarded-who for the MAJORITY of a defensive possession.

Consider, for example, the following hypothetical sequence. Gobert begins a defensive possession by guarding Steven Adams for the first ten seconds. Then, he switches onto Russell Westbrook after a pick-and-roll by the Thunder and continues to guard him for the next three seconds. Finally, Westbrook ends the possession by shooting a jumper over a long-armed contest by Gobert. In this case, the matchup assigned to Gobert would be Adams, not Russ.

This ‘majority of the possession’ approach creates scenarios where a defensive player is credited (or blamed) for a shot contested by one of his teammates. It’s a more holistic philosophy for assigning defensive responsibility; one that represents a departure from the familiar defended and contested field goal stats that have been available on the NBA’s website, which just assign defensive responsibility to whoever was closest at the time of the shot.

For any defender, we can calculate a scoring rate for each of his matchups — as the number of points scored over the number of possessions played in defense. This matchup-specific scoring rate can be compared to the season-long scoring rate for the same offensive player, to create a quantity we could call POINTS SAVED per 100 possessions.

Role comparison

When you start to calculate Points Saved for different defenders in this way, you immediately notice that there is a big wrench in the works — shot distance. The average shot distance (and, thus, the scoring rate) for an offensive player in a specific matchup may vary greatly from his season-average shot distance (and scoring rate). This confounding is likely exacerbated for cross-position matchups. That is, centers tend to give up scoring rates way above season averages when matched up with guards. In part, the discrepancy reflects how difficult it is for a 7-footer to keep up with the best ball-handlers in the world; but, it also reflects that big men will be assigned a disproportionate number of matchups when the offensive player is near the basket — including instances when the offensive player is taking a shot near the basket. When calculating Points Saved, it’s hard to account for the impact of shot distance directly, because the matchup data is aggregated by game and matchup-specific shot distances are not recorded.

The implication is that — if we want to make valid comparisons between two defenders using Points Saved based on matchup stats — we need to be sure that the two players have the same defensive role. So, is Gobert vs. Embiid an apples-to-apples comparison?

Both are 7-foot centers that patrol the paint and protect the rim. In terms of shot distance, the two players are responsible for defending field goals attempted from the same general range. Of the shots that Embiid defended this year, 46 percent were attempted within six feet; the equivalent proportion for Gobert was a very similar 47 percent.

Sorting the matchup data by the position of the offensive player, we find that the two centers also have a comparable array of individual opponents. Based on the NBA’s designations, 60 percent of Embiid’s defensive possessions were spent covering centers, 17 percent on forward/centers, 15 percent on forwards, 2 percent on guard/forwards, and 7 percent on guards. That’s almost an exact match to Gobert’s breakdown of 58, 19, 16, 1, and 6 percent by matchup position.

My colleague, Positive Residual (@presidual), has created these beautiful alluvial diagrams to chart defensive matchups for individual games. You can see, for example, how similar the defensive assignments were for Embiid and Gobert in two games against Detroit this year.

Each player spent most of his time guarding the Pistons starting center Andre Drummond (41 possessions each, which represented 62 percent of all defensive possessions for Embiid and 59 percent for Gobert) with the remainder of their efforts dedicated to back-up bigs Boban Marjanovic and Eric Moreland. There were also some sporadic matchups for each of the DPOY candidates against more perimeter-oriented players, like Tobias Harris and Ish Smith.

All in all, I believe the matchup stats can provide a meaningful comparison between Embiid and Gobert, because they have such similar defensive roles. Again, this would NOT work for comparing one of these two with Smart or Roberson or any other perimeter defender you’re considering for DPOY.

Points saved

The general idea, here, is that we’re going to compare matchup-specific scoring rates to season-average scoring rates for the same offensive player to calculate a Points Saved rate (per 100 possessions). Then, we can take the weighted average of the Points Saved per 100 possessions for every individual matchup across every game of the entire season to decide who was a better individual defender.

Using all available matchups (3824 defensive possessions for Embiid and 3384 for Gobert), we estimate that Gobert saves an average of 0.4 points per 100 opponent possessions relative to his matchup’s season-average scoring rate. That may not sound like much, but it’s actually better than Embiid who gave up an extra 1.5 points per 100 opponent possessions ABOVE his matchup’s season-average scoring rate. Of course, we anticipated that these big guys would be penalized for their defensive positioning, so we shouldn’t be surprised to see such “meh” numbers, here. The algorithm has assigned them to matchups with all sorts of offensive players who — just based on their proximity to the basket — scored at higher-than-average rates.

One way to mitigate confounding by shot distance is to focus on Points Saved in matchups exclusively with other centers (i.e., centers + forward/centers). Ignoring matchups with guards and forwards reduces the number of defensive possessions included in the calculation to 2933 (77 percent of the total) for Embiid and 2586 (76 percent) for Gobert. Against his fellow centers, Gobert saves an average of 3.0 points per 100 opponent possessions relative to his matchup’s season-average scoring rate. Embiid, too, is now “in the black”, here, saving 0.4 points per 100 possessions in this subset of matchups.

Another way to chop up the data is to consider only those offensive players for which Embiid or Gobert was the “primary defender”, i.e., those players who were guarded by Embiid or Gobert on more than 50 percent of the possessions in any given game. This group of matchups — which overlaps with the centers — included 2195 (57 percent) defensive possessions for Embiid and 2184 (65 percent) for Gobert. As the primary defender, Gobert saves an average of 2.3 points per 100 possessions and Embiid saves 0.7.

Finally, we can compare the list of offensive players for which Embiid was the primary defender (in at least one game) to the list of offensive players for which Gobert was the primary defender to find the overlapping group of players who were covered by both DPOY candidates during the course of the season. There is a set of 26 big men (mostly centers) for whom we can make direct comparisons in the scoring rates allowed by Embiid and Gobert. This group accounts for 1680 defensive possessions (44 percent of the total) for Embiid and 1542 (46 percent) for Gobert.

For example, one of Gobert’s stingiest matchups listed in the table came against Phoenix center Alex Len. Gobert guarded Len for 127 possessions during three games against the Suns, surrendering just 12 total points (9 points per 100 Phoenix possessions). That’s a big reduction below Len’s season average scoring rate of 20 points per 100 team possessions. Len’s stifling included this block (one of five that Gobert tallied against the Suns on Oct. 25):

By comparison, Embiid didn’t fare as well against Len, individually. He gave up 6 points over the course of 31 Phoenix possessions when he was matched up with Len — which was right around Len’s average scoring rate.

Overall, Gobert allowed the lower scoring rate of the pair in 14 of the 26 matchups, Embiid was better in 11, and there was one tie. Comparing weighted averages across these 26 matchups, once again, Gobert comes out on top. He saved an average of 1.4 points per 100 possessions in these matchups compared to 0.5 points saved by Embiid. So, there it is, Rudy Gobert is your 2018 Defensive Player of the Year.

I’m being a little tongue-in-cheek, here. I don’t really believe that matchup data should be the sole criteria in deciding DPOY. This approach has a bunch of limitations. First, it doesn’t account for Gobert’s lack of availability during his periods of injury this season, because it’s a per-100 rate stat. But, that’s a pretty trivial thing to fix — if you multiplied Points Saved per 100 by the number of possessions each player has played defensively over the course of the season, you’d still come to the conclusion that Gobert had the larger impact as an individual defender.

Next: LeBron's defense, 76ers, and Raptors playoff rotation

What’s more damning is — by definition — this approach focuses on individual matchups and it ignores all the subtleties of team defense. Perhaps you’ve had this experience at the gym — when a teammate absolves himself of all responsibility for a loss by saying “my guy didn’t score a single bucket on me!”, meanwhile my dude didn’t play any help D and his guy scored six times in transition. It’s obvious that, just because a player’s matchup didn’t score doesn’t mean he’s necessarily playing great defense.

But, when the team defensive ratings, the advanced stats, AND the matchup data are all in agreement with each other — there’s no need to equivocate — it’s gotta be Gobert.