Why are NBA players so bad at shooting free throws?

It’s probably the most asked question about professional basketball. And, to be fair, the confusion makes sense. They’re called *free *throws for a reason. Yet NBA players this season have hit just 77% of these charity shots. Some players connect on less than half of their free throws. What gives? How can such an easy task be so difficult for professional basketball players?

A common theory is that many players suffer in their free throw shooting ability due to a psychological component. In 2013, Dwight Howard hit 81.7% of his free throw attempts during his practices with the Los Angeles Lakers. In the 2013 season, Howard shot free throws at a dreadful 49.2% rate. So he clearly had the ability to be a solid free throw shooter, yet he could never come close to that level during actual games. Maybe part of the problem is that players struggle with it when they know every single person in the stadium is staring at them and them alone. In this regard, it would’ve been an interesting case study in sports psychology to see how free throw percentages were impacted if the NBA or NCAA played games without fans due to the coronavirus pandemic.

Anyway, the question of why players struggle with free throws is far too intricate to sum up with a simple theory. Instead, I’m going to focus on a different question that’s somewhat related: do NBA players improve at shooting free throws throughout the course of their career? We can certainly assume that they’re practicing free throws during their playing days, and they obviously get additional practice from playing in actual games. Does this make them better? Let’s find out.

A brief look at the data suggests that players do improve at shooting free throws over time. Since 1997, rookies have collectively hit 72.03% of their free throws versus 73.60% for second-year players. All other veterans combined for a free throw percentage of 76.04%. There’s definitely a trend there. We can also notice a trend if we graph free throw shooting percentage versus age for players who played at least ten seasons.^{1}

It certainly seems as if players tend to improve at shooting free throws until they’re around 27-years-old, which is when improvement seems to plateau. Free throw shooting seems to deteriorate in a player’s late thirties, but it’s never nearly as bad as it is for players younger than 21. It seems like the free throw shooting age curve is quite similar to the general NBA age curve. Players tend to hit their basketball prime at 27, while they generally decline in their thirties.

However, this isn’t what people really mean when they talk about improving free throw shooting. Of course there’s an age curve involved. But how many players actually improve on a year-to-year basis?

So, I looked for pairs of seasons from 1997 to 2020 in which a player shot at least 100 free throws in each season. I ended up with 3,121 different pairs of seasons.

We would expect that due to random chance, there would be an improvement (or regression) of more than two standard deviations from the mean in approximately 2.5% of these instances.^{2}

In 71 of the 3,121 instances, players exhibited an improvement in their free throw percentage of over two standard deviations above the mean. That’s about 2.27% — less than the 2.5% we would expect due to random chance. Meanwhile, there were 82 instances in which a player’s free throw percentage *decreased* by more than two standard deviations from the mean — that’s 2.63% of all instances. There doesn’t seem to be a statistically significant difference here — a gap of just 11 over the course of 23 seasons.

It appears that free throw shooting is actually more random than one may think. The mean change between seasons is nearly zero and the distribution of positive and negative changes in free throw percentage is almost symmetric.

Some free throw shooting data just doesn’t seem to make all that much sense.

In 2018, Hassan Whiteside hit 70.3% of his free throws. Then, in 2019, his free throw percentage plummeted to an abysmal 44.9%. Somehow, his free throw percentage shot back up in 2020 to a more respectable 68.0%. Similarly, Ian Mahinmi holds the title for the largest increase *and *decrease in free throw percentage between two seasons since 1997. His free throw percentage dropped to 30.4% in 2015 after he maintained a 62.1% rate in the prior season. In 2016, his free throw percentage increased to 58.7%.

In his rookie season, LeBron James hit 75.4% of his free throws. League-average at the time was 75.2% — I’m sure plenty of fans thought that it was a strong performance from him, considering the fact that he’s basically *destined* to improve. After all, he was just 19-years-old. This season, LeBron’s free throw percentage of 69.7% is significantly lower than it was back in 2004. In nearly every other facet of the game, he has improved greatly. His shooting efficiency is up, his playmaking is at its best, his finishing has improved, he’s a better rebounder, he’s playing better defense, etc. But he has somehow gotten worse at free throw shooting.

Like most other skills in basketball, there is a general aging curve involved in free throw shooting. But on a year-to-year basis, randomness seems to be far more involved than one may expect. It’s clear that simply practicing free throws doesn’t mean that a player will get any better at them. I thought that Zion Williamson’s awful 64.5% free throw percentage in his rookie season was basically guaranteed to go up over time, but it’s very possible that it won’t. Free throws are weird.

- The ten season requirement is an attempt to account for survivorship bias. It stands to reason that players that are good at basketball will last longer in a professional basketball league than players who are not good at basketball. Of course, shooting free throws is a facet of playing basketball, so players who are in the league for a longer period of time are probably better at shooting free throws than those who flame out of the league before their 25th birthday. By not including these players in the data, we should get a better picture of free throw shooting progression.
- According to the empirical rule, or the 68-95-99.7 rule, approximately 95% of the values in a normal distrubition lie within two standard deviations of the mean, so 5% of the remaining values lie further than two standard deviations of the mean. Therefore, 2.5% of the values should be greater than two standard deviations above the mean, while 2.5% of the values should be greater than two standard deviations below the mean.

“Since 1997, rookies have collectively hit 72.03% of their free throws versus 73.60% for second-year players. All other veterans combined for a free throw percentage of 76.04%. There’s definitely a trend there.”

Does this analysis control for player ID? In other words, is the trend showing that only good shooters remain in the league for multiple years, or is it showing that individual players improve over time?