By Carter Sullivan '24
Introduction
During the 2020-21 NBA season, the league had a massive problem. Players would pump fake, then jump into their defender as they shot the ball, abruptly veer off path when dribbling, and even hook their defender’s arm while shooting, all in search of foul calls (which they often received). By the end of this season, league executives had seen enough, and it was decided that “non-basketball moves” (like those mentioned above) would no longer be called fouls. Fans, pundits, and coaches alike were delighted with this rule, as it was common consensus that non-basketball moves were ruining the NBA. More specifically, many complained that modern NBA games involved far too many free throws, implying that NBA games from 10, 20, or even 30 years ago involved fewer free throw attempts than games from more recent seasons. In this paper, I’ll first investigate the truth behind this widely-believed increase in free throw attempts over the years, and if it is false, I will investigate why this may be. Finally, I will analyze the NBA’s free throw attempt data from this season (2021-22), and attempt to evaluate the impact of the league’s rule change regarding non-basketball moves.
Hypothesis
Given the prominence of non-basketball moves in the past few seasons, I predict that the average number of free throw attempts per team per game (which we’ll call “FTA”) will be much higher in recent seasons (approximately 2015-16 through 2020-21) than in older seasons, and that there will be a steady increase in FTA over the years.
Statistical Methodology
FTA Over the Years - Is it Increasing?
First, I addressed the question of whether FTA has been increasing over the years. To do so, I downloaded data containing the FTA of each NBA season since 1979-80 (when the 3-point shot was introduced) into a spreadsheet, and generated the following line plot [1]:
As the plot shows, FTA has actually been decreasing over the years, contradicting my initial hypothesis (and the intuition of NBA fans all over).
Why the decrease?
Although the decrease in FTA initially surprised me, I came up with a reason for it based on two critical facts. The first is that today’s NBA is far more 3-point-heavy than the NBA of old. This is apparent in the largely positive slope of the graph below [1], which plots the average number of 3-point attempts per team per game (which we’ll call 3PA) over the past 31 NBA seasons.
The second fact is that players are fouled far less often on 3-point-attempts than 2-point attempts, which is quite apparent in the table below [2]:
Note that this chart only accounts for 3-pointers taken near the arc, which is why the percentage of shooting fouls does not add up to 100%. Regardless of this small discrepancy, and the fact that this chart’s data is from the early 2000s, we can still be confident that the majority of NBA fouls occur in front of the 3-point line; the game hasn’t changed that much since the early 2000s, and even if we account for players drawing fouls on 3-point attempts, there’s still far more fouling action close to the basket.
With the two aforementioned facts in mind, we conclude that FTA has decreased over the years due to the league’s moving behind the three-point line. Players simply don’t get fouled as often shooting threes, and consequently, the number of fouls (and therefore, FTA) has trended down over the years.
Using a Model to Find Statistical Evidence of non-Basketball Moves
I was unsatisfied with this conclusion, as it was obvious to me (and any NBA fan) that non-basketball moves had impacted the league in recent seasons like never before. In pursuit of statistical evidence for this impact, I formulated the following hypothesis: If I created a model to predict FTA of a season based upon the percentage of that season’s shot attempts that were 2-pointers, then trained this model on data from older NBA seasons (before non-basketball moves became common), the model would consistently underpredict the FTA of the past few seasons due to the tendency of players to draw fouls using non-basketball moves.
Creating the Model
First, I downloaded a data set of FTA, average percentage of shots that were 2-pointers per team per game (which we’ll call “%2ptFGA”), and a variety of other metrics over the past 30 NBA seasons [1]. Next, I split the seasons into two categories: “pre-non-basketball moves,” (pre-NBM) containing the 1979-80 through 2014-15 seasons, and “post-non-basketball moves,”(post-NBM) containing the 2015-16 through 2020-21 seasons. Note that because there are no publicly available metrics about the number of non-basketball moves per season, I decided upon the 2015-16 cutoff in a qualitative manner. More specifically, this cutoff was decided because James Harden’s foul drawing was beginning to pick up more publicity around 2015-16, and it was also a season where more players around the league began to pick up and use non-basketball moves. Next, I used R to run a linear regression on the pre-NBM data to predict FTA in a given season based upon that season’s %2ptFGA. The resulting equation was:
Where FTA-hat is the predicted number of FTA. The adjusted R2 for this model is 0.80, indicating a good fit, and this fit may be seen visually below:
Predicted FTA for Post-non-Basketball Move Seasons
With our model created, it’s time to test its predictions on the 2015-16 through 2020-21 seasons, which we’ve distinguished as post-NBM seasons. The results can be seen in the plot below:
In this plot, the blue dots represent post-NBM seasons, the red dots represent pre-NBM seasons, and the trendline represents our model’s predicted FTA for each season. The trendline consistently underpredicts FTA for each of the six post-NBM seasons, reflecting that the actual FTA of these seasons is greater than what we’d expect based on the percentage of field goal attempts from two-point range. Although our initial plot of FTA over time showed a decrease in free throw attempts, which was somewhat misleading, this model makes things much clearer; because it accounts for the distribution of two-pointers vs. three-pointers, we can clearly see that recent NBA seasons have seen more foul calls than we’d expect, which provides statistical evidence of players drawing calls with non-basketball plays.
Conclusion - has the NBA’s rule change been effective?
Finally, we will use our model to calculate and compare the residuals (predicted FTA - observed FTA) for various seasons. Because our model calculates assuming absence of non-basketball moves (the model was trained on pre-NBM data), each season’s residual may be interpreted as how far that season is from being non-basketball move free. Loosely speaking, a large residual indicates a large amount of non-basketball moves in a specific season, and vice versa. I calculated the absolute residuals for all six post-NBM seasons and the 2021-22 season in a spreadsheet, and they are plotted below:
As shown above, the 2021-22 season has quite a small absolute residual, with only the 2017-18 season having a smaller absolute residual. Further, the absolute residual from 2021-22 is far smaller than the residuals of each of the three prior seasons, giving us an indication that the NBA is now far closer to an ideal, non-basketball move-free league than it was recently. Fans, players, and coaches may rejoice; the NBA is returning to a league of pure basketball, and until players find another way to hack the game and its rules, we’ve got some fantastic seasons to look forward to.