# The Most Efficient Scorer in NBA History

### My attempt to come up with an unbiased method for ranking scorers by efficiency.

Who’s the most efficient scorer in NBA history? One statistic that is often used to evaluate a player’s scoring efficiency is true shooting percentage. The formula is rather simple:

`TS% = PTS / (2 x (FGA + 0.44 x FTA))`

This is essentially an estimate of points per scoring attempt, with the “2” in the denominator* forcing the value to have a scale similar to that of field goal percentage.

** Aside: I wish the “2” had never been added to the denominator. Without it, the statistic could be called “points per scoring attempt,” which would accurately describe what the formula is measuring. In my opinion, cutting that value in half muddies the waters with little added benefit.*

One of the nice things about true shooting percentage is the statistics required to calculate it are available for all NBA seasons, allowing for comparisons across eras. Let’s start by looking at the top 10 single-season true shooting percentages, requiring a player to appear in at least 70% of his team’s games:

74.5% — Robert Williams III, 2021-22

73.9% — Daniel Gafford, 2022-23

73.8% — Dwight Powell, 2022-23

73.6% — DeAndre Jordan, 2020-21

73.2% — Rudy Gobert, 2021-22

73.0% — Ryan Hollins, 2013-14

72.6% — Mitchell Robinson, 2019-20

72.5% — Chris Wilcox, 2012-13

72.5% — Powell, 2021-22

72.2% — Robinson, 2021-22

Okay, this is not exactly what I was going for, as no one on this list represents what I would call a “scorer.” These are all modern post players who scored most of their points on lobs and putbacks. Let’s change the minimum to 1,500 points (or the equivalent in seasons with fewer than 82 scheduled games):

70.2% — Artis Gilmore, 1981-82

70.1% — Nikola Jokic, 2022-23

68.0% — Gilmore, 1984-85

67.6% — Cedric Maxwell, 1978-79

66.9% — Stephen Curry, 2015-16

66.8% — Domantas Sabonis, 2022-23

66.5% — Charles Barkley, 1987-88

66.1% — Barkley, 1989-90

66.1% — Jokic, 2021-22

66.0% — Barkley, 1986-87

That’s more like it, although one of the problems with looking at true shooting percentage without any sort of adjustment is the bias toward modern players. If we extended the list above to the top 100 seasons, we’d find 97 of them occurred after the introduction of the 3-point shot in 1979-80. This makes sense, because it’s obviously easier to average more points per attempt when you have the chance to get an extra point on certain shots.

One way to account for this is to factor in the league average true shooting percentage. A simple adjustment would be to divide each player’s true shooting percentage by the league average:

`TS+ = 100 x (TS% / Lg_TS%)`

Using this method, players with a true shooting percentage greater than the league average will have a score above 100, while players with a figure less than the league average will have a score below 100. The top 10 seasons after making this basic adjustment appear below (once again using a minimum of 1,500 points or the equivalent):

133.8 — Alex Groza, 1949-50

130.4 — Artis Gilmore, 1981-82

129.2 — Wilt Chamberlain, 1966-67

129.0 — Kenny Sears, 1958-59

129.0 — Alex Groza, 1950-51

128.9 — Ed Macauley, 1950-51

127.6 — Cedric Maxwell, 1978-79

127.4 — George Mikan, 1948-49

127.2 — Macauley, 1953-54

125.2 — Gilmore, 1984-85

We’ve clearly overcompensated for the previous bias, but we’ll get to that in a minute. First a few words on two players above some readers may not be familiar with: Kenny Sears and Alex Groza.

Sears was a forward for the New York Knicks and San Francisco Warriors in the 1950s and 1960s. He finished in the top 10 in the NBA in field goal percentage in each of his first five seasons (including two as the league leader), also hitting 83.0% of his free throws over that span.

In 1958-59, Sears averaged 21.0 PPG (seventh in the NBA) with shooting percentages of 49.0% from the field (first) and 86.1% (third) from the free throw line. His true shooting percentage was 59.1%, a whopping 7.1 percentage points higher than the next-closest player.

Groza was the captain and center of the University of Kentucky’s “Fabulous Five” that won NCAA men’s basketball championships in 1948 and 1949. Selected in the first round of the 1949 BAA Draft by the Indianapolis Olympians, Groza was named All-NBA First Team in each of his first two seasons, ranking first in the league in field goal percentage and second in scoring average each season.

However, Groza’s pro career to an abrupt end following the 1950-51 season, as he was implicated in a point-shaving scandal that occurred while he was at Kentucky and banned for life by NBA president Maurice Podoloff. A little trivia: Groza and Bob Pettit are the only players in NBA history to average at least 20 PPG and 10 RPG in their final season.

Getting back to the results, it’s obvious we’ve replaced a bias for modern players with a bias for players from the 1940s and 1950s, as six of the top nine seasons occurred in that span.

Why did this happen? To answer that question, we’ll look at a statistic called the coefficient of variation, or CV. The CV measures the variability around the mean of a distribution. It’s calculated as follows:

`CV = 100 x (standard_deviation / mean)`

For example, a CV of 10 means the value of the standard deviation is 10% of the value of the mean. The CV allows us to compare the variation of distributions that have different mean values; the greater the CV, the greater the variability around the mean. The plot below illustrates how the CV of true shooting percentage* has changed over time.

** Technical note: To calculate the standard deviation of true shooting percentage, I weighted each player’s true shooting percentage by his scoring attempts. All players were included in the calculation of the league mean and standard deviation, not just qualified players.*

As the plot clearly shows, variability around the mean steadily decreased until the 1970s, and since then has basically bounced around between 7.5 and 9.0. In other words, extreme performances relative to the mean were much more likely to occur in the 1940s and 1950s than they are today.

We can account for this difference in eras by calculating a standardized score (or z-score) for each player:

`z = (TS% - Mean_TS%) / (SD_TS%)`

A z-score measures the number of standard deviations an observation falls from the mean. Let me walk you through the calculation for Wilt Chamberlain’s 1966-67 season. Chamberlain recorded a 63.71 true shooting percentage in a league in which the mean and standard deviation were 49.33 and 4.29, respectively. Thus his z-score is:

`z = (63.71 - 49.33) / 4.29 = 3.35`

In other words, Chamberlain’s true shooting percentage was 3.35 standard deviations above the league average. Chamberlain’s 1966-67 season ranks as the third-highest single-season z-score among qualified players:

3.74 — Artis Gilmore, 1981-82

3.51 — Cedric Maxwell, 1978-79

3.35 — Wilt Chamberlain, 1966-67

3.14 — Gilmore, 1984-85

2.99 — Stephen Curry, 2015-16

2.98 — Kenny Sears, 1958-59

2.81 — Charles Barkley, 1987-88

2.75 — Alex Groza, 1949-50

2.67 — Charles Barkley, 1988-89

2.67 — Reggie Miller, 1993-94

That’s more like it. As you can see, this list contains a nice mix of players from different eras.

I also calculated a career z-score for each player. To do this, I computed a z-score for each season, then calculated a weighted mean of those z-scores using each season’s scoring attempts as the weights. Below are the top 10 career z-scores, requiring a minimum of 15,000 career points:

2.57 — Artis Gilmore

1.91 — Reggie Miller

1.87 — Adrian Dantley

1.73 — John Stockton

1.72 — Kareem Abdul-Jabbar

1.70 — Charles Barkley

1.69 — Steve Nash

1.67 — Oscar Robertson

1.64 — Stephen Curry

1.60 — Magic Johnson

Let’s return to the question I asked at the beginning of this post: Who’s the most efficient scorer in NBA history? My choice would be Artis Gilmore, who owns two of the four highest single-season z-scores and has, by a good margin, the highest career score. Gilmore played 13 NBA seasons and ranked in the top 10 in field goal percentage in 11 of them, including four straight seasons as the league leader.

By the way, Gilmore didn’t enter the NBA until the 1976-77 season, when he was already 27 years old. He spent his first five seasons playing for the ABA’s Kentucky Colonels, averaging 22.3 PPG with a true shooting percentage of 59.1%. None of those seasons were included in this analysis.

If Gilmore — who averaged 17.1 PPG in 909 NBA games — doesn’t satisfy your definition of what a “scorer” should be, then I’d go with Adrian Dantley. Dantley averaged 24.3 PPG in 955 career games, winning scoring titles in 1980-81 and 1983-84. He’s one of only three retired players with a career scoring average at least 20 PPG on 50% shooting from the field and 80% shooting from the free throw line:

Adrian Dantley (24.3 PPG, 54.0 FG%, 81.8 FT%)

Alex English (21.5 PPG, 50.7 FG%, 83.2 FT%)

George Gervin (26.2 PPG, 51.5 FG%, 84.4 FT%)

Although Dantley stood just 6-feet-5-inches tall, he was primarily a post player on offense, with a knack for getting to the free throw line. He averaged 7.15 free throws made per game, the fifth-highest such rate in NBA history among players with at least 400 games played.

I like TS Add (which I think you invented, Justin, although I "invented" it separately before you posted it on BBRef).

I like TS Add because it combines *volume with efficiency*.

Top TS Add P/G:

3.43 Wilt

3.38 Oscar

3.26 Dantley

3.07 Durant

3.02 Kareem

2.98 Curry

2.92 Gilmore w/ABA

2.88 West

2.77 Barkley

Top TS Add per 36 MP:

3.28 Dantley

3.12 Curry

3.00 Durant

2.96 Gilmore w/ABA

2.96 Kareem

2.89 Oscar

2.73 Harden

2.72 Barkley

2.70 Wilt

Since these points are raw numbers (although adjusted to league TS%), you probably should adjust for context, i.e., Wilt and Oscar played in a higher scoring context.

Any idea what Gilmore’s numbers look like if you do include the Kentucky years? Is that possible? Thanks for this!