Counting statistics are a traditional and necessary part of player evaluation. They quantify tendencies in ways more effective than any impact metric or eye-test could do. However, there’s a widespread phenomenon that has led some to believe the box score captures a player’s value to his team, which has questionable validity. Regardless, the more a counting stat indicates toward a player’s impact, the more valuable its consideration should be. Traditional box score stats don’t fit the archetype. (I tested the explanatory power of six sets of three-year box score profiles to three-year luck-adjusted RAPM, which held an R^2 of 0.44, suggesting the box score is not as strong an indicator of a player’s value as most would think.) Play-by-play and tracking data move the needle, but a lot of these stats are either deep underground, proprietary, or lack the context to truly reflect a player’s given skill.

I’ve stat-tracked in less intensive manners in the past, but the sample sizes limited the applicability outside of player evaluation (which still requires a lot of mental filtering). My second initiative in the field plans to yield far more useful results to not only identify statistical trends and expand our knowledge of how different stats relate to impact, but to dispel a common myth among the analytics community: the scoreboard is a perfect indicator of a player’s value. I once believed a “true” form of Adjusted Plus/Minus (APM), meaning perfect coefficient estimates and stability, would be the theoretical end-all-be-all to measure impact on a team. That changed when I started to rewatch certain possessions over and over again and inadvertently gained a deeper understanding of how frequently luck plays a part in basketball. 

It was mere fortuity (and luck) the first player I did a rigorous stat-track for was Russell Westbrook. His style of play was a perfect framework to explain the effects of luck and how the scoreboard doesn’t reflect the value of certain possessions. Multiple times during his debut with the Wizards against the 76ers, Westbrook would provide a wagered form of help defense. He’d often cover a perimeter assignment near a corner while one of Philadelphia’s big men would post up (usually Embiid). Westbrook would abandon his man to rush over to the opposite block and swipe for the ball. Perhaps there is some merit to this decision, which blocks off the more efficient shot. But more often than not, the big wouldn’t have been in a distinct position to score, or even in an effective spot. If Embiid managed to pass out to Westbrook’s left assignment, the latter would have an open shot. If the shot is successful, it would represent Westbrook’s defensive action: having opened a field-goal attempt for the opposition. (Another way to think of such an event is allowing the other team an opportunity created on poor grounds.)

However, court actions don’t always have their intuitively-valid impacts (e.g. Westbrook leaving an assignment for a poor double-team will generally have a negative effect) reflected by the scoreboard. If Westbrook performed the same defensive action and his assignment missed the open field-goal attempt, he’s credited with having been on the floor when a shot was missed, thus inflating his defensive impact on the game score. To reverse some of these mislabeled possessions, I expanded the defensive box score to include “defensive errors,” an umbrella term that also stores several other statistics to categorize actions. Defensive errors, as of now, fall under one of the following terms:

• Missed rotation
• Blow-by
• Steal gamble
• Foul committed*
• Miscellaneous

* not in the fourth quarter for the purpose of getting the leading opposition to the free-throw line

Missed rotations are fairly identifiable. If a teammate makes a justified switch and the given player doesn’t counteract, he’s credited with a missed rotation. Blow-bys are simply when a player’s matchup is given an easy path to the basket due to poor man defense or a lack of attentiveness. (It’s important to distinguish between “matchups” and “assignments.” From here on out, a “matchup” refers to the opposing player a given player is guarding while an “assignment” is the opposing player a given player was expected to guard at the start of a possession, barring any switches. For example, when Westbrook left his “assignment” (the perimeter player) to guard Embiid, the “matchup” switched from the perimeter player to Embiid while the assignment remained constant.)

A gamble for a steal is one of the more ambiguous stats to track because of how different scorekeepers could interpret them in different ways.

Fun fact: similar to baseball’s “park factors” that account for ballpark dimensions and other confounding variables in setting, basketball has “court factors” that account for the variance in scorekeeper tendencies. The most common application of court factors is to normalize assists, a stat very subjective in its official definition, to compare them more accurately across teams.

For the purpose of the exercise, I would constitute a gamble for a steal as an attempt that was 1) not in a face-up guarding scenario or 2) a situation in which the defender had evidently low odds to induce a turnover based on his position relative to the matchup and the basketball. Westbrook accounted for several “reach-around” steal attempts in which his matchup would be in front of him, yet the gamble was performed. This is a perfect example of gambling for a steal. Jumping a passing lane is a more complex scenario. Westbrook didn’t have any significant examples of such an event in his seasonal debut; however, I planned to identify a gamble based on the defender’s footwork. If his natural reaction was to launch downcourt for an easy layup, he was using a high-risk, high-reward style while a defender who firmly plants his feet to prevent a lost ball on the attempt makes a “safer” attempt to steal. 

Because I hadn’t categorized every possible defensive error preceding my stat-tracking, I used a “miscellaneous” option to sort any court actions that were clear defensive errors that didn’t fit under any of the categories. Westbrook committed four “miscellaneous” defensive errors in the game, including a possession in which he attempted to rebound an airball from the opposition. He changed his mind halfway through the jump and tried to avoid contact to let the ball roll out of bounds, but he’d managed to make slight contact. You could argue that because Westbrook had the ball in his hands the error was committed on offense; but in such cases, the offensive player has yet to fully gain secure possession of the ball. The second was a fairly standard error that would likely happen often enough to make its own category: poor hustle. Westbrook showed lazy coverage in a fastbreak for Philadelphia, which led to an open man on the run, increasing the odds of poorer defensive coverage for Washington, and therefore higher odds of giving up a shot.

Missed assignments are another assist-like stat that conforms to the mind of the scorekeeper. My definition of a missed assignment is when a player attempts a double (or triple, etc.) team that leaves his assignment in a blatantly-clear position to score. The earlier example of Westbrook covering Embiid would be a good example of a missed assignment. The fourth type works tangentially to the rotations category. Rather than making or missing a correct rotation, a “poor rotation” is when a player makes a rotation with a negative marginal value (for example, when a player rotates onto the wrong matchup and puts the opposition at better odds to score). With a measure of defensive errors, I could track how luck plays a role in scoreboard-oriented metrics with a stat called “defensive error percentage,” or how likely a player is to commit a defensive error in a given possession. It’s simply the sum of all a player’s defensive errors from a given period divided by the number of possessions in which they played.

The value of defensive error percentage is how it provides a clearer picture of defenders whose scoreboard impact doesn’t reflect the value of their court actions. Take Hassan Whiteside of the Sacramento Kings as an example. He’s generally seen as one of the most error-prone defenders in the league, but his defensive impact metrics are quite good. The confounding variable in this equation is luck (as well as Whiteside being an elite shot-blocker). A greater understanding of his defensive value comes from a more comprehensive box score rather than an assimilation of steals and blocks. As mentioned earlier, Westbrook tends to gamble on steals and make some questionable rotations, so we can use his defensive error rate as a reference. Listed below are his total error percentage on defense and the proportions that come from each type:

• Defensive Error Percentage: 16.4%
• Missed Rotations: 27.6%
• Blow-bys: 13.8%
• Gambles: 17.2%
• Fouls committed*: 13.8%
• Miscellaneous: 27.6%

With this data, I could also measure the success rate of Westbrook’s rotations. Although he’s a fairly troubled defender in general, his role as a coordinator is underrated. Throughout the game, he would continuously direct teammates to correct new matchups and organize the floor to counteract Philadelphia’s offensive schemes. Westbrook successfully executed 88.9% of his potential rotations. 

The remaining defensive stats I tracked were “defensive usage” and opponent efficiency. Defensive usage is simply the percentage of possessions in which a given player’s matchup either attempted a field-goal, went to the free-throw line due to a foul from the measured player, or turned the ball over (the turnover has to be induced by the measured player). It gives additional context to a player’s defensive role to provide a better statistical tool to measure a player’s involvement in a defense. It’s the counterpart to the offensive version known as usage percentage. Westbrook had a “defensive usage” of 13.1% in the 2021 season opener. I consider my definition of opponent efficiency far more indicative of a player’s ability to affect field-goal attempts than, say, defensive field-goal percentage. My form uses effective field-goal percentage to measure the points a player allows (you’d rather concede a two than a three) and tracks the matchup rather than the assignment because players aren’t often guarding their assignment at the end of each possession. Westbrook allowed an effective field-goal percentage of 54.5% in the tracked game, which would place a few ticks higher than the expected league-average in the stat this season.

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A strong emphasis was placed on defense in the exercise because of the lack of true defensive measuring tools in the form of counting statistics, but it would be unwise to ignore any offensive counterparts. The most important stat I tracked was “opportunities created,” a concept formed by Ben Taylor nearly ten years ago. Similar to assists, an opportunity created has vague criteria, with biases likely occurring from person to person. Taylor roughly defined as drawing the defense in such a manner that creates either 1) an open field-goal attempt, 2) a clear opportunity for a “hockey” assist (pass that leads to an assist), 3) drawing a foul at the rim, or 4) an offensive rebound followed by a putback. I had one major philosophically qualm with the definition he gave because, more specifically, the last two events do not always result in an opportunity created. A foul at the rim and a putback that directly follows an offensive rebound can each be contested by a single defender only, which leaves all teammates (of the offensive player) accounted for by a defender. Therefore, my definition of an “opportunity created” was simply when the defense was tugged by a player in such a manner that a potential field-goal attempt was opened.

There was one more phenomenon to be accounted for in designating a created opportunity. When a player is located at a corner with the ball in his hands, especially one of significant shooting prowess, the weakside help will often leave space between their matchups. This distance is just enough for the defender to rush back in time to contest a shot if the assignment were to be passed to, but enough that the latter would have an open shot if the ball were immediately placed in his hands. Therefore, I was targeting “significant” defensive manipulation, which I defined as any defensive positioning that created an opportunity that also contradicted any “natural” movement. This meant players opened by the loose guard of weakside defenders wouldn’t be credited as an opportunity created. Despite a narrower definition, this stat wasn’t easy to track. It’s not always clear which player created which shot, which is a large reason for my gratitude toward pause-and-play buttons. Tracking opportunities created is similar to crediting assists; close calls are decided by your best judgment. 

A large part of my criteria on these tougher calls would be to observe the body language of the defense. Weakside defenders could stray farther away from their assignments, but if they exhibit clear attention to the assignment, then there’s no opportunity created. If the defender distinctly abandons the assignment to move toward the measured player, then it’s an opportunity created. A lot of these scenarios can be told by the defender’s eye movement (are they watching both the assignment and the handler?) and how they shuffle their feet (is there a continuous movement to one side or does it resemble more of a back-and-forth motion?). Opportunities created were difficult to identify at first (I had to watch the entire first quarter three times over to get in rhythm), but eventually, the motions and reactions of defenses become more and more clear. As I accrue enough games to build a sufficient and diverse sample size, I may build a regression model that approximates the number of opportunities created for a player, similar to Taylor’s “Box Creation” metric. 

My secondary tracking technique on offense was to grade a player’s passes on the one-to-ten scale seen in Backpicks‘s “Passer Rating” metric. Similar to a metric that approximates opportunities created, I’ll eventually construct a counterpart for passing ability to solely measure the quality of a player’s passing. I wouldn’t recommend grading passes to the more inexperienced watchers, but as you watch more and more game film and use more lenient criteria (I used increments of one), then the process becomes relatively easy. Passing quality was perhaps the most intriguing stat to track because of how unstable it can be from pass to pass.

The variability on a “per pass” basis was expected, especially for a player like Westbrook. He’s one of the very best in the world, but sometimes he’ll throw some loose cannons. A detail I needed to work out as I tracked more and more passes was to choose between bases for a potential regression model. I could take full-season samples, but it worth exploring the potential of explanatory power on a per-game basis. After all, some players have great passing games and then have poor passing games; statistics taken from the individual games may hold some merit against passing grades. I also chose to track the change in the tracked statistics from quarter to quarter, and the consistency of his passing grades was uncanny (Westbrook played roughly equal playing time during each quarter).

My plan for the future is to track all of Westbrook’s (my favorite player) games and samples of the league’s stars (for an end-of-season ranking). I may try to extrapolate game logs for players to fit a full-season estimate, although the room for error would be high. It all depends on how stable the stats are from game to game. The 2021 season is still very young, and even after hours upon hours upon hours of intensive stat-tracking, there is still a lot of room for exploratory work.

Listed below are a few interesting stats that stood among the first few games of the 2021 season:

• Russell Westbrook passed the ball sixty-one times versus Philadelphia, nearly 170% of LeBron James’s activity versus the Clippers
• Kyrie Irving’s sixteen defensive errors vs. Golden State on opening night, a mark only contested by Russell Westbrook versus Philadelphia (14)
• Russell Westbrook’s thirty-two made switches and rotations versus Philadelphia
• And the most impressive of them all, Stephen Curry’s twenty-nine opportunities created versus Brooklyn

Edited note: a few comments on my exact definition of a “rotation” for the purpose of stat-tracking

• When a player is distinctly covering one matchup and opts for a new one for the purpose of preventing penetration and/or a shot opportunity.

• If it’s simply a two-man switch to make a small change in coverage, especially on the weak side, it’s not really a rotation.

• I wanted to loosen the definition enough so that it captures a player’s awareness and movement, but strict enough so that a meaningless switch of sorts isn’t counted.

“Stephen Curry in 2016 is more fun than anything, maybe ever…” – SLATE

The greatest point guard of the century set the Bay Area into a Warriors frenzy with his electric three-point scoring and the team’s dynastical tendencies, with records being broken left and right. Curry’s season may have been highlighted by 402 three-pointers made and a unanimous MVP, but very few people knew how good he actually was that year, even those living in the eye of the storm. He entered rarefied air in his ’16 season, and no player since then has yet to match it. But exactly how good was he when he was drilling half-court shots seemingly at will? With Curry’s evaluation, I’ll try to answer a long-thought question: was Curry’s 2016 campaign the greatest offensive season in league history?

Scoring

Curry’s scoring alone took Golden State’s offense to dynastical levels. During possessions in which he attempted to score, defined as either a true shooting attempt or a scoring turnover, the Warriors posted an offensive rating of 127. That was a whopping +21 relative offense, and there’s potent evidence behind a figure of such a magnitude.

Due to Curry’s historical outside shooting, his inside scoring received far less recognition despite being one of the skill’s best. Among players who played for more than a thousand minutes, Curry was thirteenth in field-goal percentage on drives; which, considering his 6’3″ stature, is geometrically more masterly. A part of Curry’s surprising prowess in the paint was his strength; according to CBSSports, he could deadlift 400 pounds in the summer of 2016, a mark no Warriors could top except for the 6’11”, 255-pound Festus Ezeli. Paired with a solid motor, Curry was able to penetrate defenses with relative ease.

He was a very prolific paint scorer, having taken 22.5% of his attempts from within three feet of the basket. With respect to Curry’s three-point barrages and smaller stature, his frequency was unexpectedly high. He was also able to capitalize on these high-efficient looks at a 69.6% clip, strikingly greater than the league-average of 62.4%. Curry would often opt for these shots to avoid double teams on the perimeter, swinging around the arc, and finding an angle to drive. His size and vertical leap alone weren’t enough to dominate defenses in the post, so during his forward-facing drives, Curry would either go take an early step to gain ground against the opponent or his premier center of gravity. Learning to take the toll of movement with his hips instead of his ankles truly unlocked Curry’s greatest interior capabilities.

The other component to his elite finishing was Curry’s ability to split defenses. As the greatest shooter ever, he also became the most gravitational player ever. He’d rarely not see multiple defenders in his periphery when operating on the perimeter, yet it was never destabilizing. If two defenders went on either side of Curry, he’d split their position with surprising quickness and agile lateral movement. The aforementioned utilization of his hips allowed him to change direction with fast pivots, which often left defenders in the dust. Curry was one of the league’s best paint finishers, and it was the weak point of his scoring résumé.

Everywhere outside the paint was Curry’s domain… not that the paint wasn’t already his in some form either. He stuffed the stat sheet with a collection of absurd shooting scores that paint an extremely flattering picture of Curry’s outside scoring, a strong point of which was how he and his teammates set up his scoring. Curry was one of the most efficient catch-and-shoot scorers in the league that year (68.6 eFG%), only behind J.J. Redick for players who took more than 400 catch-and-shot field-goal attempts. However, contrary to the traditional tendencies, Curry’s efficiency didn’t rapidly decline on non-assisted attempts. He was the league-leader in effective field goal percentage on pull-up shooting (61.9%) for players with more than nineteen attempts. For reference, Curry took 687 of these attempts. The next most-efficient player to even take one hundred, D.J. Augustin, shot 54.3%.

Curry wasn’t an “opportunist,” as many primarily catch-and-shoot scorers are. He was a master schemer, consistently creating his own shot while also being an elite catch-and-shoot scorer. 37% of Curry’s two-point field-goals were of teammate assists, significantly lower than the league-average of 51%. From three-point range, his figure is 55%, a large decrease from the league-average of 84%. It’s probable Curry’s scoring would’ve been more scrutinized if he were the product of a system in which he was set up for high-quality attempts by teammates more than himself, although this wasn’t the case. Curry’s status as an offensive engine wasn’t exactly in question, but the rates at which he creates his own field-goals further the idea that he was a peak offensive player during his second MVP season.

No player has yet to match the historical contributions of Steph Curry’s outside scoring. He attempted a mind-boggling 886 three-point shots during his 79 games played, nearly 230 more shots than the second-place finisher in the stat (James Harden). Curry was surprisingly second in efficiency (45.4%), trailing only behind the Clippers’ J.J. Redick. However, Curry attempted more than double of Redick’s shots on far greater self-reliance, which suggests from an all-things-considered outlook, Curry was the most efficient three-point shooter in the league. Using the league-average three-point percentage as a relative comparison, Curry added 265.8 net points to the scoreboard through his three-point attempts alone. The efficiency and volume at which he made three-point shots make Curry’s ’16 significant in league history as the greatest outside scoring season ever.

Yellow star denotes Curry

The Baby-Faced Assassin had not only the greatest scoring season of the year (leading the league in both scoring rate and true shooting percentage, as well as being the only player to ever win the scoring and efficiency titles) but the history of basketball. Curry leads the all-time leaderboard in Backpicks‘s ScoreVal metric as well as (in theory) my own of similar nature: Scorer Rating. Given the circumstances of his scoring, and how his greater self-dependence is an indicator that his scoring statistics are more reflective of his true abilities than the average “opportunist,” it’s fair to say Curry had the strongest scoring peak of any player in league history. As the thirty-first highest peak in relative true “scoring” percentage (which uses a scoring turnover) estimates as a scoring attempt and the eleventh-highest peak in scoring rate with historic frequency, Curry’s mix of volume and efficiency was unprecedented.

Off-Ball / Movement

The next trip up Curry’s sleeve, and a large contributor to his assisted shots, was his world-class movement without the ball in his hands. An overlooked skill when it comes to an elite offensive player, Curry’s not often recognized for it compared to his eye-popping distance shooting. Fortunately, he was able to put it to good use as a member of the Warriors, a team with some of the most dynamic ball movement ever, comparable to the ’96 Chicago Bulls. Curry was a threat all over the court without the ball, keeping defenders on their toes with his presence alone.

With the point guard duties he had, Curry would often start his off-ball stints at the top of the perimeter. He would primarily target either the corners or the paint, two of his most efficient ranges. To do so, Curry would often make slow rotations to a corner and let his teammates go to town. These made up a lot of Curry’s “excluded” possessions, but his positioning in these spots was another outlet for shot creation. He’d sometimes feign a backdoor cut to unclog a lane in which a teammate could drive: phenomena that would occur either starting at a corner or up top. Significant credit for this is due to his creation instead of his off-ball capabilities, but the grace and effectiveness with which Curry could feign cuts was extraordinary.

Aside from his creation abilities off the ball, Curry’s movement itself rivals the all-time greats in the skill. He has a reputation for a game that doesn’t require the athleticism most do, but the quickness in his routes is a product of a strong physical foundation. The excess training of his hips provided an easier way for Curry to reposition himself on drives, otherwise known as changing direction. It’s how he gave a seasonal montage of possessions in which he was driving to the hoop and swiftly stepped back, showing an uncanny tendency to lose his defenders. Curry was by no means screen-reliant, but his ability to weave in and out of teammate screens and opponent setups was the boost he needed to improve his self-creation off the ball.

Playmaking

Even if Curry were a pedestrian scorer, his passing and creation would’ve kept him afloat as an offensive engine. The quality of his passing wasn’t the focal point of his playmaking, and the skill is accurately represented by his Passer Rating per Backpicks. Since his breakout ’13 campaign, the metric has graded him in the mid-to-high-sevens on the one-to-ten scale. A lot of his assists were products of his elite vision, which made him especially aware of the corners. With five teammates who shot higher than 40% on corner threes, a lot of these passes were tailored to Golden State’s roster. Curry was additionally proficient at splitting defenses with his quick bounce passes. A common trait among elite playmakers, he refined the tactic with his strong hips and vision approaching the hoop en route to his 1,261 points created through assists.

There wasn’t an excess number of negatives with Curry’s passing. The notable ones include his tendency to overpass against taller defenders. During games against elite defenses (especially the recurring January 15th matchup against the Spurs), he’d find himself picking the ball up early, forcing a pass into the post or out to the perimeter. Defenders like LaMarcus Aldridge and Kawhi Leonard rushed Curry into these passes, and his intentions were clear: to avoid the long arms of his defenders and skip a pass to an open teammate. However, Curry would often underestimate the launch angle of these passes, and they’d gain too much ground before their final descent. The same would occur with some of his full-court baseball passes. The main theme with Curry’s passing deficiencies was that he overestimated the necessary distances for tougher passes, but the lower frequency at which these happened made them minor issues.

PBPStats – a condensed version of Golden State’s assist network

The Warriors were a movement-heavy team, having led the league in assists per 100 possessions by a significant margin (+2.6 assists), secondary assists, and assist points created. The nucleus of this action was made up of the team’s “big three” in Curry, Draymond Green, and Klay Thompson. Curry’s strongest link was with Thompson, to whom he assisted 209 field goals. He also assisted 139 of Green’s shots and 66 of Andrew Bogut’s. Based on the positioning of these players, it’s clear a lot of Curry’s playmaking was focused on or around the perimeter. He averaged 2.5 fewer assists per 100 possessions with his star on the arc, Thompson, off the floor. Curry’s playmaking was understated that year because of how many more shots he was taking (+3.5 more attempts per 100 from the previous season); but even then, his playmaking value was near the top of the league. Golden State’s passing and Curry’s efficient teammates counteract some of that deflation, but the confounding variables almost seem to cancel themselves out.

Defense

Curry is often criticized for his man-to-man abilities, and there’s some truth to that. He wasn’t the greatest at positioning himself, keeping a naturally flat-footed and unathletic stance. Curry had solid hands in these spots, covering higher and lower passing angles with either arm, although his 6’4″ wingspan made it slightly harder to effectively clog passing lanes.

Among his more potent errors include mispositioning; he’ll sometimes miss a matchup entirely, the only other main instance of this being a tradeoff of his good rebounding. Curry would often lose his man positioning himself for the defensive rebound. This does make it a bit of a gamble, but the generally-high defensive rebounding percentages among teams (league-average 76.2%) made it so that only a small percentage of possessions would see these fallbacks. But Curry was a surprisingly good rebounder for his height, having grabbed 4.9 defensive rebounds per 75 possessions at a 2.9% clip, suggesting it was the best defensive-rebounding season of his career. 

Curry’s small frame made it hard for him to stay in front of stronger matchups, so he’d sometimes be left in the dust on defensive possessions (just as he did to the NBA’s very best defenders). Ironically, Curry was given a taste of his own medicine in these stints. He was similarly susceptible to screen action, fizzling his entire value out against stronger defenders by entirely losing his man. The strongest positive of his man-to-man game is his ability to maintain space with his matchup. Curry can string together good defensive possessions when his matchups are moving laterally, keeping close but safe gaps between them and himself. He also has half-decent hands, which allowed him to break up plays in and near the radius of his wingspan. His transition coverage and fallback play provided a lot of unseen value for the Warriors, keeping offensive matchups at bay and preventing an underestimated number of field-goal opportunities.

Impact metrics painted a consistent picture of Curry in which he was a positive defensive player. He was generally favored by more play-by-play infused and non-box metrics, with defensive scores higher than a point in PI RAPM (+1.7), PIPM (+1.47), and RAPTOR (+2.78). Although, box-oriented metrics showed him some love too, with a +1.6 score in the defensive component of Basketball-Reference‘s Box Plus/Minus model. The lowest of Curry’s defensive impact metrics was his single-year “luck-adjusted” RAPM (-0.07), which painted him as a minor negative. The aggregate of Curry’s scores suggest his defense was a clear positive to his team on the defensive end, and without any confounding variables to drastically alter the results, it’s fair to say impact metrics give strong portraits of him on that end.

Summary

With Curry’s evaluation under wraps, there’s now a fairer picture as to where his offense stands on the historical leaderboards. His world-class combination of scoring volume, efficiency, playmaking, and off-ball movement, paired with peak scalability, makes it hard to say his claim for the sport’s peak offensive season is rivaled by anyone not named Michael Jordan. Given the hindrances of Jordan’s impact from his more questionable portability, I’d deem Curry’s second MVP campaign as the greatest offensive season in league history. With his mild-positive defense in the equation, using my updated “Championship Probability Added” calculator, I’d estimate Curry would’ve provided a random team with a 10.2% increment to win the title. (Note: the percent increments will be significantly lower than previous evaluations because the calculation now considers impact on below-average teams.) His full-strength title odds would clock in at about 11.7%, which would rank as one of the fifteen best seasons of all-time.

The “efficiency versus volume” conversation is a classic today, but very few attempts have been made to provide a clear answer. Most recently, Backpicks developed its “Scoring Value” metric (abbreviated “ScoreVal”) to presumably estimate the net impact of a player’s scoring every 100 possessions. The stat alone was a success, but a more definitive solution to the “efficiency versus volume” argument was still blurry. Today, I’ll give my best attempt at settling the historic debate to determine the more important aspect of scoring between efficiency and volume.

A way to go at this is at the team level: plotting the relationship between points per game (as volume neglects attempts/”pace”) and true shooting percentage. We’d use TS% in place of, say, points per possession (the truer measure of offensive efficiency) because we’d need to use the latter as the response variable; otherwise, efficiency correlation would be perfect! Using 2020 values, points per game holds a correlation coefficient of 0.78 and true shooting holds one of 0.75. The difference is very close, and given the sample size, it’s not enough to draw a conclusion. Plus, 2020 has about as many confounding variables as any other season (COVID-19, stoppage, no access to courts at times). Paired with the concerns of the chosen variables, it’s likely that the team level won’t settle the discussion. 

The next way to approach a conclusion is on the player level. Between scoring rate in points per possession and true shooting percentage, which holds a stronger correlation with how “productive” a player is as a scorer? This is a question long thought of without a widespread solution. To answer this, I developed a statistical model that measures the number of net points a player adds through scoring, which I’ll name “Scorer Rating” (I’m open to name suggestions).

Can a player’s scoring impact on the scoreboard be summed up in a single number?

Points per possession at the team level epitomizes scoring efficiency because it redefines “scoring attempts.” TS% uses shooting attempts as the divisor, but in reality, shooting attempts aren’t the only chances a player or team is given to score. If a player commits a turnover, his team will be credited with a “scoring attempt” on that possession; because, although they weren’t given a chance to shoot, they had a chance to score that was blown. Therefore, we want to use a new measure of “scoring attempts” for players in a similar manner. To do this, I borrowed a technique from ScoreVal, which classifies turnovers as either playmaking or scoring turnovers. The model designates these turnovers based on the percentages of a player’s “offensive load” (involvement) that come from playmaking and scoring. However, this estimator provides imperfect measures when there are equitable alternatives. I used an idea discussed in the metric’s inaugural post, which designates all turnovers not committed by bad passes (per Basketball-Reference‘s play-by-play data) as “scoring turnovers.”

With a measurement of how many turnovers negated the value of a scoring possession, I could now replicate a truer scoring efficiency on the player level. For example, in his historical 2016 campaign, Stephen Curry averaged 1.34 points per true shooting attempt. Add in his non-bad pass turnovers, 95, to the divisor, and he averaged 1.27 points per “scoring possession.” This means on possessions in which Curry attempted to score, the Golden State Warriors had an offensive rating of 127; that would be a +21 rORtg! The next step is to set a player’s new efficiency relative to the league-average. Curry’s 1.27 points per scoring possession compared to the average of that season, 1.04, means he added 0.267 points per possession relative to the league. From there, it’s a measure of how often a player attempts to score per game, normalized to 100 possessions per 48 minutes. For example, Curry accounted for 23.7 scoring possessions per game in 2016, but his team played at a 99.3 pace, so his attempts receive a slight boost.

The raw number of net points Curry provided through scoring was the product of his efficiency and attempt frequency, which clocked in at 6.4 points, by far the highest mark in the NBA that year. After all, he led the league in volume and efficiency that year! However, the league-average was slightly higher than zero, around 0.1 points. Therefore, Curry added 6.2 points above the league’s average that season. The last confounding variable was playing time. Rakeem Christmas, the most notable example, had a Scorer Rating of 1.9 points, which ranked in the top-10, despite having only played six minutes the whole year. The last adjustment was using the binary logarithm of a player’s total minutes played as the “x” in an augmented sigmoid function to regularize abnormally high scores from limited playing time. Christmas’s “adjusted” Scorer Rating was then 0.6 points. 

Listed below are all player-seasons for Scorer Rating since 2016.