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.