Another Shot at Measuring Individual Defense

How do defenders end opponents’ possessions, or decrease or increase their value, thereby preventing the opposing team from scoring?

As we all know, measuring the individual defensive impact of a basketball player is difficult. This holds true, even though we now literally track every movement of every player on the court at every moment of every game. The only viable and trustworthy way to assess individual defense still appears to be combining the infamous eye test with a bunch of different statistics from basic boxscore stats (such as blocks and steals) to plus/minus or on-off court numbers and SportVU’s tracking data (such as the defended field goal percentage at the rim).

The holy grail(s) of sports analytics, however, are comprehensive metrics which try to depict a player’s impact in one single number. Despite the many intricacies, there have been several enlightening endeavors to determine this number in the realm of individual basketball defense. Nevertheless, I decided to take another (probably rather dilettantish) shot at it. My motive was to create a metric that is based solely on publicly available data, mathematically simple, and easily replicable, but extensive in scope and detailed in its components.

Despite many flaws (most of which I’ll try to discuss below), the metric can hopefully contribute to the existing cornucopia of basketball statistics. In principle, single-number metrics should never be used as end-all rankings, especially defensively. They can serve as solid (but noisy) proxies, at best. The jumping-off point of this undertaking is a straightforward question: How many points does a player’s individual defensive effort prevent? To measure these “Opponent Points Averted” (OPA), two issues need to be addressed: What is the value of an offensive possession? And how do defenders end opponents’ possessions, or decrease or increase their value, thereby preventing the opposing team from scoring?

The first question is rather easy to answer. During the 2016-17 regular season, NBA teams scored an average of 1.088 points per possession. Thus, presumably, this was the average value of any single offensive possession. Consequently, ending an offensive possession averted 1.088 points an opponent – on average – would have otherwise scored. The second question calls for a more extensive answer. Defenses can (1) end their opponent’s possession, (2) decrease or (3) increase its value in many different ways.

1) Ending an offensive possession

The most obvious way to end an opponent’s offensive possession is to just take the ball from an opposing player. Steals, therefore, are assumed to avert the league average points per possession (1.088 points for the 2016-17 regular season). Likewise, blocks seem to end possessions in a similar manner. The difference, however, is that a blocked shot does not automatically take the ball away from the opposing team. It can lead to either the end of the opponent’s possession or, as was particularly discussed with respect to Hassan Whiteside’s defensive impact during the 2014-15 and 2015-16 seasons, an offensive rebound (inbounds or out of bounds). Even though the latter outcome doesn’t end an offensive possession, it still decreases its value (i.e. its expected efficiency), particularly by reducing the time remaining on the shot clock.

As shooting efficiency drops significantly in late shot clock situations (the average possession during the 2016-17 regular season ended with about 9 seconds left, per, a defender is still credited with reducing the value of the offensive possession by the difference of the league average effective field goal percentages “early” (15-22 seconds left; 55.6 eFG%) and “late” in the shot clock (0-7 seconds left; 44.6 eFG%) in case his block is rebounded by the opposing offense. (Note that the distinction between blocked shots rebounded by the defender’s own team an those rebounded by an opponent is not yet implemented in the preliminary OPA data presented below. It will be accounted for in a prospective updated version.)

A more frequent way to end an offensive possession is to grab a defensive rebound. As Russell Westbrook’s triple double heroics became probably the most discussed topic of the past NBA season, the actual value of a defensive rebound was the focus of several insightful analyses. While much of the discussion revolved around the offensive impact of Westbrook’s rebounding, the defensive value of collecting a missed shot appears to be easier to assess. Even though the circumstances of a defensive board don’t matter from a team perspective, an individual defender should only be credited with ending the offensive possession if he manages to grab a contested defensive rebound.

Crediting a player grabbing an uncontested rebound – in many cases benefiting from his teammates efforts to box out (or from coincidentally being in the right place) – with the value of an entire opponent’s possession ended, would overvalue his defensive contribution. Obviously, there still is some value to collecting uncontested defensive rebounds, and a future version of OPA will account for it. For the moment, it seems more accurate to ignore them.

The last two plays considered to end a (potential) offensive possession, thereby averting the respective amount of points, are loose balls recovered and offensive fouls drawn.

2) Decreasing the value of an offensive possession

The obvious effort a defensive player can (and is supposed to) make in order to decrease the value (i.e. the efficiency) of an offensive possession is to contest shots by staying close to his opponent, fighting over screens, rotating, closing out on shooters or challenging them at the rim. It is difficult to assess the quality and effect of those contests. During the 2016-17 regular season, field goal percentages – contrary to what the casual observer might expect – were lower on what the NBA and SportVU call “open” and “wide open” looks (i.e. shot attempts with no defender within 3.5ft of the shooter) than on “tightly” or “very tightly” contested attempts. The reason is simple: Shot attempts closer to the basket, which are generally higher percentage looks, tend to be more tightly contested, whereas players almost never attempt contested shots from distance. Over the entire NBA season, less than 6 percent of all field goal attempts were “contested” three-point shots, and only 20 percent were “uncontested” two-point attempts. Nearly 75 percent of all field goal attempts were either contested twos or uncontested looks from beyond the arc. As a result, despite the lower overall FG%, the league average 2P%, 3P% and eFG% increased significantly without a defender within 3.5 ft of the shooter.

Therefore, it seems appropriate to assume that there is an inherent value in simply being up in a shooter’s space. To account for this effect, a defender (defined by SportVU as) contesting a shot is credited with lowering the value of the opponent’s possession by the difference in league average eFG% between contested and uncontested field goal attempts. During the 2016-17 regular season, this difference amounted to 4.47 percent. Hence, every shot contest by a defender is assumed to avert 0.047 * 1.088 = 0.051 opponent points.

Nevertheless, opponents may take advantage of weak defenders by attacking them time after time and taking shot after shot, despite the (allegedly) weak defenders “contest”. There obviously are differences in the quality of players’ efforts to rotate, close out, jump, extend their arms and contest shots. Therefore, the Defended FG% Difference (the impact a defender’s tracked contests have on shooters’ field goal percentages compared to their average shooting efficiency) also matters. A defender “averts” points by contesting shots (by virtue of his mere presence near a shooter) and by contesting in a way that decreases opponents’ shooting efficiency. If he contests in a way that increases opponents’ field goal percentage, however, he “allows” points (e.g. because of height disadvantage, failing to extend his arms, not being close enough to shooters, or just coincidentally being near a shooter without even trying to defend).

It has to be stated that the validity of SportVU’s data on shot contests and “Defended FG% Difference” is somewhat questionable. Nevertheless, it is the only publicly available estimate of defenders’ effect on the success of opposing shooters. The most reliable data on challenged shots are SportVU’s rim protection stats. Including only the latter, though, would ignore large parts of perimeter players’ defensive tasks and impact, rotating and closing out on opposing shooters. To further refine the OPA metric, I will differentiate between defended shot attempts at the rim, other 2-point attempts and shots from beyond the arc, and the respective DFG% differences in a future updated version.

Another way to decrease the value of an opponent’s possession is to disrupt the offense with a deflection. The effect is assumed to be equivalent to that of a blocked shot rebounded by the opposing offense. Although it doesn’t end the possession, it decreases its efficiency by reducing the time left on the shot clock.

3) Increasing the value of an offensive possession

Fouling increases the opponent’s expected points per possession (e.g. shooting fouls) or even gives them an extra possession (e.g. clear path fouls). It hurts a team’s defense by allowing an opponent to score more efficiently. In the 2016-17 regular season, NBA players made 77.2 percent of their free throw attempts, making a trip to the free throw line significantly more valuable than an average offensive possession. Shooting fouls do in fact end an offensive possession (thus accounting for 1.088 opponent points averted), but in turn grant the opponent an even more valuable scoring opportunity. (Note that goaltending increases a possession’s value in a similar manner and will be included in future versions of the OPA data.) The preliminary version of OPA thus deducts 0.772 points for every additional free throw a defender causes (e.g. by committing a technical foul) and 2*0.772 points for every shooting foul. Admittedly, this not only underestimates the negative effect of fouling on a three pointer or other low-percentage field goal attempts, but also ignores the potential positive effect of fouling bad free throw shooters or denying high percentage looks, particularly dunk or layup attempts. Unfortunately, there is no data available (as far as I know) to accurately measure these and similar effects of “smart” or “ill-advised” fouls.

Although turnovers are generally viewed as part of a player’s offensive game, they also hurt teams’ defenses. Taking care of the ball offensively therefore averts opponents’ points defensively. This holds especially true for live-ball turnovers.

Offensive possessions following live-ball turnovers are far more efficient than any other possession, so these turnovers are included in OPA as a way to cause opponents’ points. During the 2016-17 regular season, NBA teams scored an average 1.23 points per possession following a live-ball turnover, as against the league average offensive efficiency of 1.088 points per possession. In order not to unduly punish players carrying a heavy playmaking burden – who inherently bear a higher risk of turning the ball over -, the effect of any player’s turnovers is adjusted for his usage rate and assist percentage.

4) Beyond the box score: on-off defensive ratings

Of course, there is much more to a player’s defensive impact than can be measured by analyzing these countable actions. Many defensive efforts, even very impactful ones, are not accounted for. If, for example, a defender fulfills his task so well that his opponent doesn’t dare to shoot or maybe doesn’t even get the ball, it won’t have any impact on this kind of metric. In an attempt to account for these effects, I include a measure of players’ “Individual Defensive Impact” (IDI) based on their teams’ defensive efficiency while they are on and off the court. Defensive efficiency is a team effort. Therefore, I adjust any given player’s individual on-off defensive rating for the teammates he has shared the floor with as well as their respective on-off numbers. In so doing, I try to estimate the teammates’ share of any player’s effect on his team’s defensive efficiency.

In the spirit of keeping the on-off component as “mathematically simple and easily replicable” as the box score component, I confine myself to a very rudimentary, simple adjustment instead of a more sophisticated (and certainly more accurate) Regularized Adjusted Plus-Minus (RAPM). Let’s assume a given team relies completely on “hockey substitutions” to alternate between its starting five and its bench unit. The starting five’s defensive rating (the points allowed per 100 possessions) then is 5 points better than the bench’s defensive rating. Since the starters play 100 percent of their possessions with each other, each one of them is assumed to be responsible for improving the team’s defense by (i.e. “averting”) 1 point per 100 possessions while he’s on the court. In reality, of course, lineups and player’s on-off defensive ratings vary immensely. Sample sizes, teammate and opponent lineup configurations and many other variables cause – not unlike with almost any other metric – a lot of noise, measurement errors and general uncertainty regarding the validity of the results.

Ignoring opponents’ lineup configurations, OPA probably tends to somewhat underestimate the value of good and very good defensive players, as they (especially elite perimeter defenders) generally guard opponents’ best offensive players and face their opponents’ best offensive lineups. Ending a possession led, influenced, or used by James Harden or Stephen Curry is obviously worth more than the league average points per possession. Alternatively, box score-based OPA (BoxOPA) can obviously be combined with existing RAPM data.

5) The randomness of opponents’ three-point percentage

The surprisingly bad defensive stats of Spurs superstar and two-time Defensive Player of the Year Kawhi Leonard during the 2016-17 regular season inspired several studies on the formation of these numbers. One of the main findings was the randomness of opponents’ three-point percentage, which appears to be mostly independent of the quality of individual defense. Leonard seems to have suffered from a streak of bad luck, as the Spurs’ opponents shot 37.6 percent from distance while he was on the floor and a disastrous 29.2 percent with him sitting on San Antonio’s bench. Therefore, I adjust every player’s on-off defensive rating for three-point percentage allowed.

To that end, I convert every three-point shot taken to the league average 3P%. Let’s assume Player A has an on-court defensive rating of 110 points allowed per 100 possessions. His team’s opponents attempt 40 threes (again, per 100 possessions), hitting 50 percent for an aggregate of 60 points. Player B posts an impressive on-court defensive rating of 90 while opponents hit just 25 percent of their 60 shot attempts from distance (45 points). The league average 3P% is at 40 percent. So, the expected value of 40 3PA is 48 points, reducing Player A’s adjusted defensive rating to 110 – (60-48) = 98 points per 100 possessions. Expecting 60 3PA to produce 72 points, the same adjustment raises Player B’s rating to 90 – (45-72) = 117 points per 100 possessions. Accounting for (bad) “luck”, Player A thus appears to have a better on-court defensive rating than Player B, whose numbers now seem much less impressive.

6) The formula

Box Score Opponent Points Averted (BoxOPA) =

League Avg PPP * (Contested DRB + STL + BLK + Offensive Fouls Drawn + Loose Balls Recovered + Defended FGA * (League Avg Uncontested eFG% – League Avg Contested eFG% – Defended FG% Difference) – Loose Ball Fouls + Shooting Fouls)
– Live-Ball Turnovers * (1 – (Usage   Rate + Assist Percentage) / 2) * (League Avg PPP after LBT – League Avg PPP)
– League Avg FT%(2 * (Flagrant + Clear Path + Shooting Fouls) + Technical + Def. 3 Sec.)

Teammates’ Defensive Impact (TDI) =

Individual Defensive Impact (IDI) = On-Off DRtg – Teammates’ Defensive Impact (TDI)

Opponent Points Averted (OPA) = ( BoxOPA – IDI ) / 2

7) The results

So let’s finally get to the good stuff. I calculated various versions of OPA and compared them to existing metrics such as Jeremias Engelmann’s (Defensive) Real Plus-Minus, Dan Myers’ (Defensive) Box Plus/Minus and (Defensive) Win Shares (based on Dean Oliver’s Defensive Rating). For sample size reasons, I will use 2016-17 regular season data as an example, and publish updated 2017-18 numbers shortly.

We’ll start with the boxscore-based numbers. Unsurprisingly, big men appear to be by far the most impactful defensive players. The highest ranked non-big among 349 qualified NBA players (at least 1.000 possessions played during the 2016-17 regular season) is the Milwaukee Bucks’ Giannis Antetokounmpo (#12), while former Rookie of the Year Michael Carter-Williams leads all guards at #18. Overall, Philadelphia 76ers’ then-rookie center Joel Embiid emerges as the most effective defender. His BoxOPA of 13.84 “opponent points averted” per 100 possessions leads the league by a significant margin, followed by Anthony Davis (11.9) and Draymond Green (11.82).

On average, the 108 ranked big men averted 7.15 points per 100 possessions. In comparison, wing players average a BoxOPA of 5.34 per 100, while guards reach a mean value of 4.71. Looking at the “best” and “worst” defenders at every position, the numbers for bigs and wings appear to pretty much match the eye-test. Established defensive anchors like Embiid, Green or Rudy Gobert, as well as stud perimeter defenders like Antetokounmpo, Robert Covington and Kawhi Leonard, occupy top ranks, while names like Boris Diaw, Meyers Leonard, Arron Afflalo and Doug McDermott can be found at the bottom of the table. While Carter-Williams emerging as the BoxOPA leader among guards seems surprising, elite point of attack defenders like Patrick Beverley, John Wall, Mike Conley, Danny Green and Chris Paul are also ranked in the top-10.

But how does BoxOPA fare against other popular boxscore-based defensive metrics? Compared to Defensive Win Shares, the most visible difference is the devaluation of players whose main defensive contribution seems to be (partly uncontested) defensive rebounding. Some of the NBA’s best rebounders – Andre Drummond, Hassan Whiteside, Dwight Howard, Pau Gasol, and Russell Westbrook – are among the most extreme outliers (far left from the regression line in the figure below; sweep the cursor over the data points to see player names and values). The overall correlation between both metrics is fairly strong (R2 = 0.55).

For the 2016-17 regular season, BoxOPA is even more highly correlated with Defensive Box Plus-Minus (R2 = 0.61).

Including the Individual Defensive Impact (IDI) does not affect Joel Embiids position at the top of the ranking, but has a huge effect on the previous two seasons’ Defensive Player of the Year. Kawhi Leonard, whose San Antonio Spurs allowed 8.6 more points per 100 possessions with Leonard on than off the court, slides from #28 (#6 among wings) in BoxOPA to #307 out of 349 qualified players in OPA per 100 possessions. As mentioned above, the Spurs’ opponents’ accuracy from three-point range accounts for a significant part of this. They shot a staggering 8.4 percent better during Leonard’s minutes on the floor, the highest mark in the entire league. Considering the number of attempts per 100 possessions, he is the second most “unlucky” player in the NBA behind Indiana’s Kevin Seraphin. If the Spurs had allowed a league average 35.8 percent from distance at all time, Leonards On-Off Defensive Rating would be a mere +1.8 points per 100 possessions – a massive 6.8 point improvement. On the other end of the spectrum, Anthony Davis benefitted hugely from the Pelicans allowing just 33.5 percent from three in his minutes on the court. Adjusting for this “luck”, Davis slides from #3 to #15 in OPA per 100 possessions.

The adjustment for opponents’ varying three-point shooting percentages also improves OPA‘s correlation with Jeremias Engelmann’s benchmark defensive metric, Defensive Real Plus-Minus (R2 = 0.71), with Joel Embiid still being an OPA darling outlier, along with Giannis Antetokounmpo, Michael Kidd-Gilchrist, and Nerlens Noel, among others.

Finally, here are the complete rankings for the 2016-17 regular season.

Data from,,,, and Special thanks to‘s Evan Zamir (follow him @thecity2 on Twitter) for sharing some of his data. I am grateful for any (positive or negative) feedback or questions @SimonsHoops. An article featuring 2017-18 OPA numbers will (hopefully) be published shortly.

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