Tuesday, January 01, 2013

Foul shooting and luck

I always think that performance in sports is a combination of luck and skill.  When an 80 percent free-throw shooter steps to the line, I think what happens is almost all luck. To me, the shot is like the player flipping a coin that lands heads 80 percent of the time. 

Where's the skill?  The skill is in the player having practiced enough to bring his coin up to 80 percent heads.  Personally, I'm probably a 25 percent shooter, at best.  But if I practice and practice, I'll get better; maybe eventually I'll hit 50 percent.  Once I do, my shots are like flips of a fair coin.

Some people disagree.  They reject the idea that there can be any luck at all.  It's just the player, and the ball, and the basket.  It's all under the player's control.  Where's the luck?

I think our disagreement is that they're thinking of luck only as "external" luck, something outside the player -- like a bad bounce in the infield, or getting dealt good cards in poker.  I think there can also be "internal" luck, even though if everything is, in theory, within the player's control.


We can probably all agree that coin flipping is a good example of luck.  But in a way, coin flipping and foul shooting are almost the same.  If I'm doing the flipping, and I'm trying to land a head ... it's all within my control, the same way as shooting a basket.

The difference, you might argue, is that it's impossible to influence the outcome of a coin flip.  I may *want* it to land heads, but I just can't do it.

Except that ... I think I *can* do it.  Not all the time, but better than 50 percent.  I bet you if I practiced, I could make it land heads more than tails.  Suppose that, flipping a coin that starts head up, I try to make the coin rotate exactly 10 times, and land flat in my hand.  That's hard, but ... who's to say that I can't do it often enough to get 50.0001 percent heads?  That would mean out of one million flips, I manage to convert one tail into a head because of the skill I developed.  Doesn't seem unreasonable. 

So after I've achieved that amount of skill, you hand me a coin, and I flip it, and it lands heads.  Was it luck, or skill? 

Everyone should agree that it's mostly luck.  My skill is being able to increase my chances from 500,000 out of a million, to 500,001 out of a million.  After that, the individual flip is just luck. 

It has to be, doesn't it? 


In the comments to the previous post, someone wrote that foul shooting *seems* like it's all skill because the success rate is so high.  That seems right to me; we have a default assumption in our brains that either we can do something, or we can't.  If we can, it seems like we should be able to do it all the time, and when we don't, it's our fault, we made a mistake.  At least, to me, that's how it *feels*.  When I screw something up, I feel like, geez, I did that before so many times, why couldn't I do it now?  I feels like I choked, or did something wrong.

And it might have been a choke, actually.  Even though we shoot at 80 percent normally, maybe this time we chose not to concentrate enough.  Maybe we should have bent our knees more.  Maybe we were too impatient, or too nervous.

The thing is, it *could* have been all those.  But it probably wasn't.  It's just our nature to think, we could have done it differently!  And, yes, we could have, just like we could have flipped the coin harder, or softer.  But, so what?  There was no way of knowing in advance that *this time* was one of the 20 percent what we did wasn't going to work. 

And, in a way, it's a good thing we think it was our fault.  Because it's still *possible* that we did something wrong, and it's *possible* that if we figure out what it is, mental or physical, we could get our success rate up from 80 percent to 81 percent.  Or, it could be that we've slipped up and forgotten something we knew, so that if we don't fix it, we'll fall to 78 or 79 percent. You don't want to just think, "Hey, I won't worry about it, it was just luck." 

But it probably was. 


None of this is to say that preparation and concentration and patience aren't important.  But, you'd expect, professionals would have learned to do that all the time.  That, I think, is one of the underrated skills that professional athletes have: the ability to focus and concentrate much better than we do. 

I can probably hit my trash can with a wad of paper most of the time.  It's probably 60 percent when I don't care, and 80 percent when I aim. 

Now, if I miss, it might certainly be that I didn't care, and you might be reasonable in assuming that it wasn't just luck, that it was mostly within my control -- that if I cared more, I'd have made it.  In fact, if half the time I don't care, then, I'm missing 30 percent of the time, rather than just 20 percent if I always tried my hardest. 

In a sense, then, you might have the right to say that there's more than luck involved: that maybe my misses are 2/3 luck, and 1/3 bad decisions.

The thing about the pros, though, is: I think they have the ability concentrate and prepare *almost all the time*.  I have no evidence for this, but I bet an 80 percent NBA player is seldom, if ever, even a 75 percent player, for reasons under his conscious control. 

In any case, there still has to be a substantial amount of randomness.  Because, there's no way an 80 percent shooter is able to be a 100 percent shooter, if he just takes the task more seriously.  That's just not plausible.


If you agree with me that my coin flipping is luck (despite my 50.0001 success rate), but disagree that foul shooting is luck, I have one more argument for you.

Suppose in my coin flipping, I'm trying to get the coin to turn over exactly 20 times: that is, do ten 360s, for a total rotation of exactly 36,000 degrees.  And suppose you measure a large number of my tosses, and you find that my average is indeed 36,000, and my distribution is a bell curve with a large standard deviation.  You analyze the distribution and figure out that based on my accuracy, I should indeed wind up with heads 50.0001 percent of the time. 

Now, if you agree that my coin flipping is largely luck, you have to agree that my deviations from 36,000 are largely luck. 

Now, what if you did the same thing for free throws?  You measure all my free throws.  You find that my angle of release is normally distributed with a mean of 52 degrees, and a certain standard deviation.  And that the ball goes in when my angle is within 1.3 SDs either way, which works out to 80 percent success.

Isn't that the same thing as the coin?  If my deviations of coin flipping rotation are luck, then why aren't the deviations of release angle luck? 


A summary of the overall argument is: there are natural limitations to how much humans can control their muscles.  With practice, you can develop "muscle memory," which increases the amount of control you have.  That is, you get the standard deviation to shrink.  But, humans just aren't capable of getting so precise that we can be 100% shooters of basketball free throws. 

We're all going to have our individual accuracy curves.  Good shooters will have a narrower and better-placed curve than poor shooters.  But, once you have the curve for your own personal muscle control, where you land on that curve, for any given shot, is luck. 

If you don't like using the word "luck," because it's internal to the brain, and it feels like it's under your control ... well, fine.  But then you can't call coin flipping luck, either.  Because, aside from the probability of success, it's almost exactly the same phenomenon.

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At Wednesday, January 02, 2013 1:06:00 AM, Blogger D said...

This is beautiful. Thank you.

At Wednesday, January 02, 2013 7:57:00 AM, Anonymous Kris Gardham said...

I vaguely recall reading a paper that asserted your premise. It centred around the coin-flip problem, and one's ability to achieve a desired outcome (heads). The outcome was way above 50.001%; I'm thinking it approached 60%.

At Thursday, January 03, 2013 1:13:00 PM, Anonymous Patrick (SnarkSD) said...


I think your point about release points is a valid one. Of note, I can think of several scenarios in which a release point is not changed by the player, but external variables

1) Late in the game players are tired, and hence their muscles are weaker. Well controlled smooth detailed muscle movements (including muscle memory) become much more difficult with muscle fatigue. (This is physiologically substantiated). I would presume that FT% goes down as player minutes go up.

http://www.magicbasketball.net/2011/05/09/dwight-howard-fourth-quarters-and-the-truth/ While not perfect, this post shows that atleast for the magic 10-11 season, FT% went down 20% points collectively over the 4th quarter. You could argue "pressure" confounds this assertion.

2) The basketball is never the same. The basket ball has variables outside a players control, such as the pressure of the ball effecting it's weight. Also despite the refs best effort, I'm sure there is varying degrees of sweat covering the ball, influencing the ability to generate consistent spin.

At Thursday, January 03, 2013 1:18:00 PM, Blogger Phil Birnbaum said...

Fair points. But a 20 percentage point drop in the last minutes? Controlling for shooter and deliberate misses? Really??

At Thursday, January 03, 2013 8:57:00 PM, Anonymous Anonymous said...

At the time of his retirement, Rick Barry's .900 career free-throw percentage was the best in NBA history. In one season, 1978-79, he missed only 9 free-throw attempts.

Apparently, applied skill can shrink the deviation quite a bit, if you aren't embarrassed about throwing underhanded (technique, not luck).

At Friday, January 04, 2013 12:43:00 AM, Anonymous Patrick said...

I should have been more explicit, the sum of their change was 20%. On average the drop was 1.67%.

At Friday, January 04, 2013 6:15:00 AM, Blogger LondonRaider said...

You've were obviously never good enough to shoot free throws at a high level.

At Saturday, January 05, 2013 10:16:00 PM, Anonymous Anonymous said...

Mr. Birnbaum, I'm curious: would you say shooting a free-throw is more like flipping a coin, or more like playing the trumpet (or any other musical instrument)?

By "flipping" I mean fair (ie, not "influenced) flipping, as I assume you mean when you compare an 80% shooter with flipping a 80-20 coin. By "playing", I mean hitting the right note for the correct length of time (eg, quarter or eighth note); not interpretive coloring or phrasing, etc.

--Bob Lince

At Saturday, January 05, 2013 10:38:00 PM, Anonymous Anonymous said...

It seems to me there is a way to bolster your argument, if the data can be found. Take the very best free throw shooters, NBA, career. Find out where each missed free throws in the course of a game.

For example, how many FTs Calvin Murphy missed in the first quarter, second quarter, etc. Or, if he played, say, 36 minutes of a game, how many he missed in the first 9 minutes, the second 9 minutes, etc., of playing time. If those misses are randomly scattered about these "sections" of his games, it would lend credence to the notion of FTs as the fair flipping of a fair, but biased (say, 90-10) coin. But if his misses are lumped in same "section" of games, for his career, or even significant portions of his career, that might lead us to believe something else was at work.

--Bob Lince

At Sunday, January 06, 2013 12:36:00 AM, Blogger Phil Birnbaum said...

Bob Lince: not sure what you're getting at. Free throw shooting is more like a coin in some ways, and more like trumpet playing in other ways.


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