Why hasn't foul shooting improved?

Free-throw shooting percentages haven't changed much over the past 50 years, according to this New York Times article. Between 1950 and 1970, the conversion rate was around 72 percent. Since 1970, it's fluctuated between 72 and 77%.

Here's the NYT graph:



So it looks like free throwing hasn't really improved over the decades. That makes foul shooting an anomaly, because most other skills have improved: marathon times are better, football kicking is better, and "swimming records seemingly fall at each international event."

Why hasn't foul shooting improved? According to the article:

Ray Stefani, a professor emeritus at California State University, Long Beach, is an expert in the statistical analysis of sports. Widespread improvement over time in any sport, he said, depends on a combination of four factors: physiology (the size and fitness of athletes, perhaps aided by performance-enhancing drugs), technology or innovation (things like the advent of rowing machines to train rowers, and the Fosbury Flop in high jumping), coaching (changes in strategy) and equipment (like the clap skate in speedskating or fiberglass poles in pole vaulting). ...

“There are not a lot of those four things that would help in free-throw shooting,” Stefani said.

And that's fair enough. But what about, say, bowling? The article says explicitly that "bowling a 300 game is not as unlikely as it once was," and there are strong similarities between bowling and foul shooting. Physiology doesn't seem like it would help either way; technology and innovation don't seem like issues; and it's hard to see how coaching would be of more help in bowling than in foul shooting.

I'd propose another explanation: foul shooting is an ancillary skill in basketball – players are chosen for their overall ability, not just their free-throw potential. And so "natural selection" won't weed out mediocre shooters or reward the best shooters, at least not very much compared to other skills.

Compare this to other sports: bowling strikes is the primary goal of the game, the most important skill of all. And, in football, field-goal kickers are chosen for one thing: their ability to kick field goals. Any kicker below average in accuracy is out of the league instantly. But any NBA player who can't hit free throws can make it up in other aspects of the game (like Shaq). (A version of this argument was also made in the first comment of a discussion on Tango's blog, here). And coaches don't force their players to shoot underhand, which would make many players more accurate; that provides support for the idea that the NBA thinks free throw percentage doesn't matter that much.

If you want to *really* see if the skill is improving, don't look to NBA players, who may not be the best in the world at the skill. You'd have to look at free-throw specialists. I Googled "free throw shooting contest results," and got a link to an Iowa State contest where the winner made 49 out of 50 throws. That's 98%, and about 4 standard deviations away from the NBA average of 75%. Even considering that the contest had 72 entries, that's pretty significant.

And here's another argument: if foul shooting isn't considered a major skill, young players won't practice it as much, and it stands to reason that you won't get as much improvement over time if there's not as much energy expended to get better at it.

One last point: if you consider the graph's increase from 71 to 77 percent to be real, then that's actually pretty good evidence of an increase in skill. When you're already at a 71% level, it's harder to improve than if you start from, say, a 34% level (as field-goal percentage did). In 1950, players were missing 29% of their foul shots. In 2008, they were missing only 23%. That means that over the past 58 years, players learned to convert 20% of their misses into hits. That's pretty good. The field goal percentage improvement, from 34% to 46%, looks more impressive, but results from converting 18% of misses into hits – almost an identical improvement (although they probably shouldn't be compared directly, because field goals are influenced by where they're taken from, and the quality of the defense).

In summary:

-- there are good reasons you wouldn’t expect foul-shooting to improve as much as other skills over time;
-- if you look at the numbers more closely, there actually *is* a significant amount of improvement.

So I don't think there's as huge a mystery there like the Times does.