A Statistical Analysis to Determine if There’s Such a Thing as “Superstar Bias” in the NBA

The free throw is the one aspect of the game that does not require any strength, speed, or intelligence. There’s a 280 pound guy at the YMCA that I go to that only shoots free throws and he probably makes 90% of them. It’s a 15-foot, uncontested, straight-on with a backboard that you can “bank on” if you’re feeling ambitious.

But what makes a player get to the free throw line more frequently than others? Is it their strength, speed or intelligence? Most would say that it’s the position they play and their level of involvement/usability on the court – are they the ‘go-to’ guy to score or just there to set screens and get the shooters wide open (I was always the guy setting screens).

What about “superstar bias?” The belief is that referees give “star” players preferential treatment, in which they receive more calls in their favor compared to lesser known players.

In my hour-long search scavenging the internet to see if superstar bias affects the frequency of players getting favorable foul calls, I came up empty-handed. I couldn’t find one intellectual article that proved or disproved this belief. Then I wrote this article, which has a small dose of intellectualism.

To preface, throughout the article, I’ve normalized much of the statistics to be “per minute” based, as opposed to per game or per season. This controls for variables like players getting injured and leaving a game early, players missing games, overtime games and seasons that didn’t reach the standard 82 game season – in 2012 due to a lockout and 2020 due to COVID. It focuses on the time that the player is on the court.

Since the 1980s, as far back as the public NBA data goes, there has been a decline in both ‘Free Throw Dependability’ – the percentage of points scored from free throws and ‘Free Throw Frequency’ – the amount of free throw attempts per minute. In the past three seasons, the dependability on free throws reached a low of 16%, off of a high of 21% in 1987.

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That was interesting, but not article-worthy.

After looking at it from a ten thousand foot view, I was interested in individual player’s free throw frequency and dependability. In the 2019-2020 season, Jimmy Butler scored an eyebrow-raising 38% of his points off of free throws – an outlier in the graph below. Eyeballing the graph, any NBA fan can see that players in the top right (high free throw frequency and dependability) are elite scorers in the league.

That’s interesting…

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To no surprise, the players that are getting to the free throw line more frequently are also the players that score more frequently.

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Knowing that the elite players that score the most also get to the line the most, I decided to create buckets of players based on their scoring efficiency of points per minute. I created deciles to divide all players into ten groups based on their scoring efficiency. Ten is the highest efficiency, one is the lowest efficiency. Side note – a minimum point threshold was added to exclude players that had minimal game time (low sample size).

Revisiting the first scatter plot that showed free throw frequency and dependability, I layered on the player’s decile ranking that more clearly shows that the top players in the league (10th decile) make up the larger part of the top right quadrant – high frequency, high dependability. As you work your way down and to the left (lower frequency, lower dependability), you can see that the decile rank / player’s scoring efficiency decreases.

Interactive Link Here (You can view this chart dating back to the 80s)

This is where things start heating up…

The next step was aggregating all of those players into their respective decile to see the correlation amongst them, between points per minute (what the deciles are based on) and free throw attempts per minute. For the 2019-2020 season, by excluding the top tier scorers, the correlation is a staggering 0.99 (0.98 r-squared). The graph below shows that the top tier scorers (10th ranked decile) are well above the linear regression line, suggesting that their free throw attempts per minute are statistically considered an outlier as they are outside of the line’s 95% confidence level interval. Based on the regression’s formula (Free Throw Attempts Per Minute = 0.247 * Points Per Minute – 0.236), top scoring players are getting to the free throw line 0.037 times more per minute, which is 23% more than what it should be!

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The trend of top tier scorers getting to the free throw line more frequency has been going on since the 1980s, but as you can see in the graph below, the gap greatly widened during the 2020 season.

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Taking an additional step, I compared free throw frequency for the different tiers of players versus points per minute and shots per minute. For ease of comparison, I ranked each decile based upon how they ranked throughout the years (1 is the highest, 40 is the lowest).

What sticks out is that points per minute (the second panel) and shots per minute (the third panel) had some of best rankings ever across nearly every decile in 2020, whereas free throw attempts per minute (the first panel) had some of the worst rankings ever across nearly every decile in 2020…except the top tier (10th decile), which had the best ranking ever – highest ever free throw attempts per minute! Free throw attempts per minute really started to deviate between top tier players and all other players starting in 2017.

I’ve shared with you seven graphs thus far, but this last graph below takes the cake. To simplify the chart above, knowingly that deciles 1-9 trend in a similar direction across the statistics, I grouped the deciles into two – the top tier players (10 decile) and all other deciles (1-9) to show the percentage difference between the two cohorts over time.

It very clearly shows the two findings from the article:

  • Top players get to the free throw more than all other players, even when controlling for the fact that they naturally shoot and score more points.
  • Free throw frequency for top tier scorers versus all other players has increased since the 1980s, despite shots per minute and points per minute remaining constant.

Why is this happening? What makes players get to the free throw line more frequently?

Are superstar players better at drawing fouls when shooting? And are they getting better at drawing fouls over time compared to all other players?

Is there just a macro shift occurring in how the game is played, where superstars are relying on getting to the free throw line to pad their stats?

Are referees more pressured than ever to favor superstars when deciding to make a snap-decision call?

I don’t know.

If you have any other thought, let me know. I’d love to hear them.

David Bressler / [email protected]

Turning Strategies Into “Always On” Tactics.

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