Thursday, March 05, 2009

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.

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At Thursday, March 05, 2009 1:22:00 PM, Anonymous Anonymous said...

"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."

Sorry can't say I remember where I read it but I just recently read an article that suggested that technology advances had a large effect on the improvement of bowling scores. Specifically the highly specific amounts of oil that are used on the length of the bowling lane. This allows modern bowlers to spin the ball with greater precision and control than in the past, thus allowing them to consistently hit the pins at the proper angle and force.

At Thursday, March 05, 2009 1:26:00 PM, Blogger Phil Birnbaum said...

Actually, now that you mention it ... last time I saw bowling on TV they showed the different oil patterns and I think talked about how they affected the bowlers. So, yeah, I should maybe take that back about bowling.

However, the article talked about "more 300 games". If the chance of a strike by the best players went from (say) 80% to 82%, that would lead to 34% more perfect games (take both percentages to the 12th power). So it's still possible that foul shooting and bowling strikes have increased by roughly the same amount.

At Thursday, March 05, 2009 2:47:00 PM, Anonymous Anonymous said...

Good article, Phil. I agree that a jump from 71% to 77% is actually pretty decent improvement...

One other thought I had in reading this. Not only are players being selected for "major" skills instead of minor ones, maybe there is a negative correlation between these skills. And the link for this would be hand size.

Have you ever tried to shoot a free throw with a tennis ball? I would guess it is much more difficult than a basketball. That's what its like for Shaq and all the other large large men. I would bet that average hand size has increased over the past 25 years because average height has almost certainly increased. Add to that any relative increase in foul ratio on the largest men and the impact is amplified. Just a thought.

At Thursday, March 05, 2009 3:49:00 PM, Blogger Phil Birnbaum said...

Hmmm, could be. It would be hard to check ... even if you found a negative correlation between size and free-throw percentage, it might just be that the tall guys were better in so many other ways that their foul shooting wasn't as important.

Sounds plausible, though.

At Thursday, March 05, 2009 4:48:00 PM, Anonymous Anonymous said...

you're right, the easy part of the check is just to graph nba player height vs. career ft%. that would probably give us the negative slope. but the reason for that could either be the physics of how a hand shoots a set shot or it could be as you describe: the taller you are, the better on average you are in major skills, thus the more broad the ft% abilities can be and still make the cut.

At Thursday, March 05, 2009 9:55:00 PM, Anonymous Anonymous said...

Hi Phil – Here’s a thought. What if players are improving in FTs but we don’t see it in the overall stat because the defenses foul the poor shooters more frequently? Nowadays, every team has a gizzilion stats and they adjust their strategy accordingly. I don’t know how to measure for that, but I thought I’d put it out there.

At Friday, March 06, 2009 2:10:00 PM, Blogger Micah said...

You may not want to underestimate the similarity between increases in free-throw and field-goal shooting accuracy. Offensive and defensive strategies have some effect but these are probably short-term and may be negligible in the long-term. I would presume that the changes you see in shooting accuracy are primarily related to changes in shooting skill and changes in shot-location preferences. (FT shooting, of course, only has one of these two variables.)

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