By Avery Borgmann '24, Luca Caviezel '24, Head of Research Devan Fink '23, Jack Maling '23, Joseph Notis '21, President Matthew Schnell '22, Treasurer Avery Sholes '24
Introduction
Suppose the Los Angeles Lakers are playing the Phoenix Suns. The Suns are trailing by three points with 15 seconds remaining in the fourth quarter, suggesting that they need to intentionally foul a Lakers player and send him to the free throw line, in a last attempt to get one more possession. LeBron James is having a poor shooting night from the field for the Lakers. Should the Suns purposefully try to foul James, one of the greatest basketball players in history, hoping that his poor shooting night will continue at the free-throw line? Generally speaking, will a shooter who is ice cold from the field also struggle at the free throw line? In this paper, we explore the relationship between a shooter’s success from the field and their success at the line within the same game, and examine whether teams should purposefully foul players at the end of close games who are not shooting well from the field.
Methods
We used the NBAStatR package in R to scrape the player performances of every game of the 2019 NBA regular season. The dataset includes all in-game statistics for each player, including points, rebounds, assists, field-goal percentage, free-throw percentage, and the opposing team. We also used this package to scrape all of the players who played in the 2019 season’s career stats, notably their career field-goal percentage and free-throw percentage. We limited our data to only include players who, in each game, played at least 10 minutes, had at least 10 free-throw attempts, and shot at least 10 field goals, which includes both two-point field goal and three-point field goal attempts. We chose these thresholds because we wanted to limit our models to only look at players who had many attempts, both free throw and field-goal attempts, in every game.
Linear Regression 1: Regressed free throw percentage on in-game field goal percentage
We want to examine how a player’s current in-game shooting from the field, including both two-point field goals and three-point field goals, will impact their performance from the free-throw line. For the first linear regression, we regress a player’s in-game free throw percentage on their field-goal percentage:
The dependent variable %FT measures a player’s in-game free-throw percentage while the variable %FG represents a player’s in-game field-goal percentage. We are most interested in our β1 coefficient, which expresses how a one percent increase in a player’s in-game field-goal percentage affects a player’s in-game free-throw percentage. We anticipate that β1 will be negative, suggesting a player who shoots worse from the field will also perform worse at the free-throw line.
Linear Regression 2, with fixed effects and controls: Regressed free throw percentage on in-game field goal percentage, opposing team, career free throw percentage, career field goal percentage
Our second regression considers more factors that might affect free-throw percentage. Factors such as career free-throw percentage, career field-goal percentage, and opposing team also affect both our treatment and outcome variables:
We are most interested in the β1 coefficient, which measures the effect of a one percent increase in game field-goal percentage on in-game free-throw percentage, controlling for the opponent, career field-goal percentages, and career free-throw percentages. Our hypothesis is that when controlling for these variables, the β1 coefficient will be negative, meaning that a decrease in in-game field-goal percentage will cause a decrease in the player’s in-game free-throw percentage. We control for career free-throw and field-goal percentage because we are most interested in how a single game’s field-goal percentage affects the free-throw percentage of that same game, keeping fixed the player’s career performance.
Linear Regression 3: Regressed rolling free throw percentage on rolling in-game field goal percentage over a 15-game span
The final regression is similar to linear regression 2, except we use a rolling free-throw percentage over a 15-game span instead of just a single game’s percentage. We did the same manipulation for field-goal percentage, taking each player’s average free-throw percentage over the past 15 games. We also control for the same variables as described above. We still anticipate that a player’s field-goal percentage will be negatively correlated with the free-throw percentage, even with the rolling averages.
Results
Generally, there was not a significant correlation between in-game field goal percentage and in-game free throw percentage, suggesting that these two skills are independent: a player can still have a successful night from the free-throw line even if he is not shooting well from the field, and vice versa. Even when evaluating the rolling samples, which would allow for more variation in both a player’s field-goal percentage and his free-throw percentage, we found little relationship.
There was almost no relationship (r2 = 0.007) between in-game field goal percentage and in-game free throw percentage among this subset of player-games:
In models that controlled for career free throw percentage as well as team defense, the relationship between in-game field goal percentage and in-game free throw percentage was never statistically significant. Even still, in both cases, the relationship was slightly positive between the two variables.
In a slightly larger sample — 15-game rolling data — there was a slight relationship between rolling field goal percentage and rolling free throw percentage (r2 = 0.123). However, the coefficient for field goal percentage was actually slightly negative (-0.489), suggesting that, for each one point increase in field goal percentage, there was actually a near half-point decrease in free throw percentage on average. However, this does not necessarily suggest that players who shot better from the field were inherently shooting worse from the line: big men, for example, may have very high field goal percentages — particularly over small samples — while not shooting well from the stripe.
Thus, in order to mitigate the effects of layups impacting this negative relationship, we looked at the relationship between rolling 3-point field goal percentage and free throw percentage. Again, this may be selecting for a specific type of player — typically guards and small forwards — but it was a necessary step to better understand the interaction, if any, between shooting from the field and free throw success.
This relationship is, again, extremely weak (r2 = 0.034). However, since this analysis may account slightly more for some positional effects mentioned above, it does yield a positive coefficient on 3-point field goal percentage (0.239). For each one point increase in 3-point field goal percentage, the average player increased his free throw percentage by about one-fourth of a percentage point. There may be confounds here as well: better 3-point shooters may be better free-throw shooters in general, so the fact that the relationship is this weak may actually suggest that the two are relatively independent. A particularly hot streak from beyond the three-point line does not correlate to a hot streak from the free throw line.
Discussion
When grouping by individual players, there appears to be a stronger relationship between rolling field goal percentage and rolling free throw percentage. Superstars like Steph Curry and JJ Redick have a high correlation between their field goal and free-throw shooting performances, while for others, including Lebron James and Tobias Harris there seems to be a minimal relationship. This indicates that while on aggregate there is no relationship between the two variables, for some players there is an effect.
While player position likely has an effect on these relationships, big men shoot higher percentages, close-range shots, and average lower free-throw percentages while guards take lower percentage, longer range shots but average higher free throw percentages. The NBAStatR package does not include any positional data. As a result we were unable to determine whether possible correlations between in-game field goal percentage and in-game free throw percentage differ based on position. This could be an area for future research.
Conclusion
Our goal for this study was to determine whether a player’s shooting percentage from the field in a particular game influences his shooting from the free throw line. To test this, we used in-game player performance data for the 2019 season from the NBAStatR package and ran three regressions: 1) free throw percentage on in-game field goal percentage; 2) free throw percentage on in-game field goal percentage, opposing team, career free throw percentage, and career field goal percentage; and 3) rolling free throw percentage on rolling in-game field goal percentage over a 15-game span. We found generally weak or statistically insignificant relationships between these variables, suggesting that a player’s current shooting from the field is not a strong predictor of his success at the line. Ultimately, regardless of players’ short-term shooting percentage from the field, they are likely to continue shooting at approximately their “true” free throw percentage.