Tuesday, February 12, 2013

Gut reactions about foul shooting and luck

This is just something I've been thinking about lately.  I'm not sure what my point is, or even if I have a point, but I'm finding it interesting.

For the past few seasons, Dirk Nowitzki has been one of the best free throw shooters in the NBA, with success rates ranging around 90 percent.  Now, let me give you six scenarios.

1.  One game, Nowitzki has a bad night and goes 3 for 6.  And, the Mavericks play roughly as expected but lose by a point.  Would you say Dirk was unlucky?  Would you say the team was unlucky?  

2.  In an alternate universe, the NBA decides that free throws are boring for fans to watch.  So, before the season starts, every player shoots a few hundred free throws.  The scorekeepers have the results.  Any time there's a foul, they go to the sheets, take the player's next shots off the list, and adjust the score accordingly.

Nowitzki still shot 90 percent overall.  But this game, they were at the part of his sheet where had three misses in six shots.  The Mavs lose.

Again, how unlucky was Nowitzki?  How unlucky was the team?  More, or less than the previous scenario?

3.  Same situation, but, this time, instead of progressing on the sheet in the order in which Nowitzki took his 800 preseason shots, the scorekeepers choose randomly.  There's a big urn labled "Nowitzki 90%," with 720 white balls and 80 black balls.  Whenever Nowitzki gets fouled, they reach into the urn.  

This game, they happen to pull three white balls and three black, and the Mavericks lose by a point.  Again: how much luck would you say determined the outcome?

4.  In another alternate universe, all free throws are saved up and taken at the *end* of the season, before the playoffs.  Nowitzki winds up shooting 90 percent, as usual.  But, when it comes time for the shots that are going to apply to *this* game, they tell Dirk, "you need to sink four to tie, five to win."  To everyone's surprise, Nowitzki sinks only three, and the Mavericks lose.  

Does that make a difference?

5.  This time, Nowitzki is not told the score, or what game his end-of-season free throws are going to apply to.  But the session is televised, and the announcers know.  They tell the viewers.  There is tension in the booth.  Nowitzki steps up and hits 3 of 6 again.  

If Nowitzki didn't know the situation, does that make it feel more unlucky?  

6.  Finally ... almost the same thing, but, this time, Nowitzki starts by just taking the shots, without anyone knowing which game they apply to.  It's only afterwards that they determine the game, by randomly spinning a big wheel.  They get to the part where Nowitzki's next six shots happen to be 3 makes and 3 misses.  The NBA spins the wheel, and it comes up that particular game, and they add Nowitzki's 3-for-6, and the Mavericks lose by 1.

This one is the most unlucky so far, right?  

And what if Nowitzki had taken the 800 foul shots *before* the season, but the wheel was still spun after?  To me, that scenario seems the most like bad luck.


As I said, I don't have a specific point here.  I just find it interesting how my gut reaches different conclusions about each situation, even though my brain thinks they're really almost the same.  

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At Tuesday, February 12, 2013 10:29:00 PM, Anonymous Anonymous said...


You think about the world a lot like I do if I were only smarter.

At Tuesday, February 12, 2013 11:27:00 PM, Blogger Phil Birnbaum said...

Thank you! I think. :)

At Wednesday, February 13, 2013 7:01:00 AM, Blogger Ari Berkowitz said...

This issue takes up a large part of Daniel Kahneman's books "Thinking Fast and Slow". I highly recommend reading it.

At Wednesday, February 13, 2013 9:47:00 AM, Blogger Phil Birnbaum said...

Hi, Ari,

I did read it! What part specifically did you mean?


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