Basketball, in some sense, is fundamentally a shooting game. Shooting isn’t the only important action that takes place on a basketball court, obviously. But if no one kept track of who was taking shots and making buckets, we’d have, at best, an extremely fuzzy impression of which players were actually any good, even if we had access to all their other statistics.

But believe it or not, this had long been the situation when it came to measuring player defense. There are individual defensive statistics such as rebounds and steals, of course. But there’s no direct measure of *shooting* defense (other than blocks, which account for a relatively small fraction of missed shots). If an opponent gets hot against your team and shoots 53 for 91 en route to scoring 130 points, we know your team defended poorly in the aggregate, but we don’t know which players to blame.

That is, until a few years ago, when the NBA started publishing data on opponents’ shooting. Last regular season, for example, NBA Defensive Player of the Year Rudy Gobert defended a league-high 1,426 shots, according to motion tracking data by Second Spectrum, which identifies the nearest defender on every field goal attempt. Opponents made only 45 percent of those field goal attempts, well below the roughly 49 percent that Second Spectrum estimates “should” have gone in against average defense for a given distance to the basket.

We’ve been obsessed with this opponents’ shooting data for a while, in part because it sometimes seemed to track closely with players who had stronger or weaker defensive reputations than you would infer from other advanced statistics such as Real Plus-Minus. Boston’s Kyrie Irving was regarded as a slightly above-average defender by RPM last year, for instance. But his opponents’ shooting data suggests he’s a big liability instead. On the other hand, Toronto’s Serge Ibaka was an excellent defender based on opponents’ shooting, whereas RPM regards him as just average.

So this year, we decided to evaluate the opponents’ shooting data in a more comprehensive way and incorporate it into our projection system, CARMELO. Just as CARMELO is a goofy backronym (Career-Arc Regression Model Estimator with Local Optimization) that honors one of our favorite players, Carmelo Anthony, we decided to give our new defensive rating a player-centric name, this time in honor of the Golden State Warriors’ Draymond Green, who has long been one of the best players in basketball by opponent shooting. So our new rating is called DRAYMOND, which stands for….

**D**efensive

**R**ating

**A**ccounting for

**Y**ielding

**M**inimal

**O**penness by

**N**earest

**D**efender

🙄

All right, so the acronym may or may not catch on. But it does get at one essential discovery we made in playing around with the opponents’ shooting data: the idea of *minimizing openness*. The main goal of shooting defense, especially in today’s spacing-centric, ball-movement-forward offensive era, is really to minimize the chance of an open shot.

So when I cited Gobert’s numbers earlier in this article, for instance, the most impressive part was not that opponents shot poorly against him, although that helped the Jazz, of course. Rather, it was that he was the nearest defender on so many shots: about 26 shots per 100 possessions that he was on the floor last year as compared with a league average of about 17 shots defended per 100 possessions. By contrast, Oklahoma City’s Russell Westbrook — whom DRAYMOND regards as being vastly overrated by other defensive metrics — was the nearest defender on only 12 shots per 100 possessions. Some of this has to do with Westbrook’s and Gobert’s respective positions — centers naturally defend more shots than guards do, a factor that DRAYMOND corrects for (see below). But even accounting for that, it’s clear that some players are much more impactful defenders than others.

I’m sure you’re curious to see some data, but first, an explanation of how DRAYMOND is calculated. We’ll keep it pretty brief.

As I mentioned above, what we’re really interested in is how much value a defender provides relative to an open shot. That is to say, we generally don’t want to punish a player for happening to be the nearest defender according to the Second Spectrum data. Some defense is generally better than none; if Player X hadn’t defended the shot, it’s possible that no one else would have.

Through trial and error, we found that DRAYMOND performs best if you assume that shooting percentages on open shots are about 8 percentage points higher than against average defense. For instance, if a certain type of above-the-break 3-pointer is made 34 percent of the time against average defense, we’d expect it to go in about 42 percent of the time if it was truly open.

This allows us to calculate an initial score that we call RAW_DRAYMOND. For example, if a player faced 100 2-point shots and allowed 46 of them to go in when you’d expect 56 percent of them to be converted if wide open, that player prevented …

(.56-.46) x 100 x 2 = 20

… about 20 points from being scored with his defense. (Obviously, this player could have provided additional value based on his defense against 3-point shots. Indeed, since 3-point shots are worth more than 2-pointers — hashtag #math — players who are effective at defending threes are especially rewarded by DRAYMOND.)

However, there are several adjustments we need to make in getting from RAW_DRAYMOND to regular DRAYMOND:

- Since DRAYMOND is based on both regular-season and playoff data, we adjust for the fact that defenders face slightly tougher shooters on average in the playoffs.
- We divide RAW_DRAYMOND by the number of possessions that the player was on the floor, so that DRAYMOND (like RPM and most other NBA stats) is a rate statistic rather than a counting statistic.
- We adjust the number of shots defended based on a player’s position. The average point guard and shooting guard defends about 15 shots per 100 possessions, the average small forward defends about 16 shots, the average power forward 19 shots, and the average center 22 shots. This somewhat equalizes defensive value over the five positions. Even so, bigs are generally the most valuable defenders in basketball according to DRAYMOND, as they are under most other advanced statistics.
- Finally, we subtract the value of league-average shooting defense per possession from each player’s score. Thus, like RPM and Box Plus/Minus (BPM), the statistics that CARMELO has traditionally used to make its projections, DRAYMOND is a plus-minus statistic measured per 100 possessions, where a score of 0 represents average defense.

Among players who have played at least 10,000 possessions over the past six seasons (the NBA’s opponents’ shooting data goes back to 2013-14), the top defender according to DRAYMOND is … Draymond Green, who has provided the Warriors with +3.2 points per 100 possessions of defensive value based on his scoring defense alone, not counting all of the other ways (e.g., steals) that he produces defensive value. Green is followed on the list by a fairly star-studded cast of defenders: Joel Embiid, Kristaps Porzingis (!), Rudy Gobert, Tim Duncan, Andre Roberson and Anthony Davis. Meanwhile, the worst-rated defender over the past six seasons according to DRAYMOND is Rajon Rondo.

##### The best defender according to DRAYMOND is Draymond

NBA players by DRAYMOND* defensive ratings, based on opponents’ shooting data in the regular season and playoffs, with a minimum of 10,000 possessions played since 2013-14

And here’s the data for last season (2018-19), with a minimum of 2,000 possessions defended. The Jazz’s Derrick Favors was the top defender, followed by the Knicks’ Mitchell Robinson, while the Cavaliers’ Collin Sexton was the worst defender in the league.

##### The best DRAYMOND defenders of 2018-19

NBA players by DRAYMOND* defensive ratings, based on opponents’ shooting data in the regular season and playoffs, with a minimum of 2,000 possessions played in 2018-19

You can download a complete set of DRAYMOND data dating back to 2013-14 at this link.

But does DRAYMOND measure something that’s actually meaningful? To test this — and I have to apologize because there are a lot of similarly named statistics here with confusing acronyms — we regressed DRAYMOND and defensive BPM
against five-year defensive Regularized Adjusted Plus-Minus (RAPM). What the hell does that mean? BPM is based on conventional box score statistics — most importantly rebounds, blocks and steals for the purposes of measuring defense. DRAYMOND is based on opponents’ shooting. RAPM, meanwhile, measures how much better or worse a team plays when a player is on or off the floor. In the long run, RAPM is basically
the “right” way to measure player value, since it can account for all the direct and indirect contributions a player makes that may or may not have a corresponding statistic attached to them. In the short run and even the medium run, however (remember all that misleading data people cited about how the Warriors were so good without Kevin Durant?), RAPM can be *extremely* noisy. So RAPM is great if you’re looking back over a five-year sample, as we’re doing here, but on-court/off-court statistics need to be treated with extreme caution over small samples.

In any event, what we found is that BPM and DRAYMOND basically do equally well in predicting long-term RAPM. What that means is that the *opponents’ shooting data is basically as powerful as all box score defensive statistics combined* in predicting how much value a player’s defense truly has over the long run.

We also found, however, that BPM and DRAYMOND are largely *not* redundant with one another. Blocks, steals and rebounds, which BPM captures, are certainly valuable things, and DRAYMOND does not purport to measure those. But they are also not especially good proxies for shooting defense. There are some players such as Green and Gobert who are even better defenders than you’d gather from their box score stats, even though those stats are pretty good. But there are others like Trevor Ariza, who gets lots of steals but has been rated poorly by DRAYMOND in recent seasons. That doesn’t mean that Ariza is a *poor* defender, just that you need to take the good (steals) with the bad (allows opponents to convert field goals at a high rate) when evaluating him.

Let’s conclude with a list of players who are most affected, positively or negatively, by the incorporation of DRAYMOND. The table below compares our old CARMELO defensive ratings, which were based on a mix of two-thirds RPM and one-third BPM, to our new version, which still uses these statistics but also uses DRAYMOND. Here are the old and new defensive ratings for everyone with at least 10,000 possessions played since 2013-14.

##### Which players’ defense had been underrated or overrated?

Change in CARMELO defensive ratings since 2013-14 after incorporating DRAYMOND*, for players with a minimum of 10,000 possessions

These are some pretty interesting lists. Porzingis, Embiid, Klay Thompson and Kevin Durant are among the players whose defense had been most underrated by BPM and RPM. There’s also new Boston Celtics point guard Kemba Walker and, in something of a surprise, former Celtics point guard Isaiah Thomas, who still rates as a pretty terrible defender, just not *quite* as terrible as before when you incorporate his DRAYMOND data. The most overrated defenders include players such as Westbrook, Rondo, Ariza, Otto Porter Jr. and Nikola Jokic.

Cases such as Thompson and Westbrook are interesting because the conventional wisdom has been way off from where the advanced metrics have them. RPM and BPM say that Westbrook is the *much* better defensive player, when a lot of NBA general managers might prefer Thompson or at least would regard it as close. But Thompson is a good defender according to DRAYMOND, whereas Westbrook is a wretched one, which closes at least some of the gap. Undoubtedly, there are even better ways to use opponents’ shooting data than what we’ve established with DRAYMOND, but the data ought to be a central part of the conversation about player defense going forward.

*Check out our **NBA player ratings**.*

Between the playoffs and regular season combined.

Between the playoffs and regular season combined.

A more advanced version of DRAYMOND might identify which player was *supposed* to have defended a shot (e.g., Westbrook was originally assigned to Damian Lillard) and compare it against which player was actually the nearest defender (e.g., Stephen Adams picked up the shot after Lillard blew by Westbrook). But that requires more detailed data than is currently available publicly, so we’re sticking with the simpler version for the time being.

Between the playoffs and regular season combined.

A more advanced version of DRAYMOND might identify which player was *supposed* to have defended a shot (e.g., Westbrook was originally assigned to Damian Lillard) and compare it against which player was actually the nearest defender (e.g., Stephen Adams picked up the shot after Lillard blew by Westbrook). But that requires more detailed data than is currently available publicly, so we’re sticking with the simpler version for the time being.

By regressing against five-year Regularized Adjusted Plus-Minus (RAPM); see the discussion later in this article for more detail.

Between the playoffs and regular season combined.

A more advanced version of DRAYMOND might identify which player was *supposed* to have defended a shot (e.g., Westbrook was originally assigned to Damian Lillard) and compare it against which player was actually the nearest defender (e.g., Stephen Adams picked up the shot after Lillard blew by Westbrook). But that requires more detailed data than is currently available publicly, so we’re sticking with the simpler version for the time being.

By regressing against five-year Regularized Adjusted Plus-Minus (RAPM); see the discussion later in this article for more detail.

The adjustment works by multiplying the number of shots faced by 17 then dividing it by the number of shots faced on average at the position. For instance, for a power forward, the number of shots defended is multiplied by 17/19ths.

Between the playoffs and regular season combined.

*supposed* to have defended a shot (e.g., Westbrook was originally assigned to Damian Lillard) and compare it against which player was actually the nearest defender (e.g., Stephen Adams picked up the shot after Lillard blew by Westbrook). But that requires more detailed data than is currently available publicly, so we’re sticking with the simpler version for the time being.

By regressing against five-year Regularized Adjusted Plus-Minus (RAPM); see the discussion later in this article for more detail.

The adjustment works by multiplying the number of shots faced by 17 then dividing it by the number of shots faced on average at the position. For instance, for a power forward, the number of shots defended is multiplied by 17/19ths.

Specifically, the raw version of BPM, without the adjustment for team performance.

Between the playoffs and regular season combined.

*supposed* to have defended a shot (e.g., Westbrook was originally assigned to Damian Lillard) and compare it against which player was actually the nearest defender (e.g., Stephen Adams picked up the shot after Lillard blew by Westbrook). But that requires more detailed data than is currently available publicly, so we’re sticking with the simpler version for the time being.

The adjustment works by multiplying the number of shots faced by 17 then dividing it by the number of shots faced on average at the position. For instance, for a power forward, the number of shots defended is multiplied by 17/19ths.

Specifically, the raw version of BPM, without the adjustment for team performance.

I have a couple of technical objections to RAPM, based on the question of whether a player should essentially be punished for his teammates performing well while he’s off the floor, but I’ll spare you those for now.

Between the playoffs and regular season combined.

*supposed* to have defended a shot (e.g., Westbrook was originally assigned to Damian Lillard) and compare it against which player was actually the nearest defender (e.g., Stephen Adams picked up the shot after Lillard blew by Westbrook). But that requires more detailed data than is currently available publicly, so we’re sticking with the simpler version for the time being.

Specifically, the raw version of BPM, without the adjustment for team performance.

I have a couple of technical objections to RAPM, based on the question of whether a player should essentially be punished for his teammates performing well while he’s off the floor, but I’ll spare you those for now.

As a technical aside, RPM is essentially a combination of BPM and one-year RAPM. That is, it leans fairly heavily on box score statistics because RAPM is quite noisy over the short run. Therefore, DRAYMOND is picking up information that isn’t well-measured by either RPM or BPM.