Each NBA Shot is a Decision: What’s the Decision Model?

December 11, 2010
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These days, the sports world is full of people paying close attention to statistics….

These days, the sports world is full of people paying close attention to statistics….

  1. General Managers use unconventional statistics to find hidden value in players….
  2. Fans discuss stats when debating what a player is worth, how much playing time he should get and who he should be playing against.
  3. Journalists use statistics to write stories – at best they’ll use numbers to create a new narrative; at worst they’ll use numbers to conveniently support an intuitive–but false–“story hook”
David Biderman, who writes “The Count,” a Sports and Numbers blog for the WSJ, seems to have fallen into the latter category with his recent piece on what the Miam’s Heat’s passing means for their scoring chances.  His convenient but suspicious “story hook” is that the more the Heat pass, the lower their shooting percentage gets.  Here at Team Fitzgerald, we are deeply skeptical.
Biderman’s contention is that because the Heat’s shooting % is higher when they pass less, they should start acting more selfishly, pass less, and voila…they can boost their shooting percentage.  If it were that simple….

But wait!…correlation does not equal causation.  Do players get higher percentage shots when they pass less?  Or do they pass less when they have a high percentage shot, for example on a fast break?  

Let’s take an important step back:  each pass or shot is a decision.  Professional players make it thousands of times, and coaches monitor how well they make that decision.  We praise players who take higher percentage shots when they have them, and blame them when they give up a good shot with a pass they didn’t need to make.  On the other hand, if a player does not have a high percentage thought, we praise the decision to pass…nobody admires a “forced shot” with low probability of hitting the net.

If a player has a sweet fast break, or an open path to basket, the rational choice is to shoot (or dunk) bc they already have their high percentage shot.  If the defense is able to get back, and the player can’t easily take it himself, the rational choice is to slow it down and look for a set play that may involve more than 1.  These are the decisions a player makes based on the set of facts in front of them in the moment.  By not eliminating fast break plays, controlling for shot location, etc…Biderman is left with a data sample skewed enough to result in incorrect conclusions.  Separating them would be a better way to see the impact of passing on a given basketball play.


So mathematically, let’s run a quick scenario.  During each game hundreds of “pass vs. shoot” decisions will be made.  Rational team players shoot when the odds are in their favor (high percentage shot) and pass when they don’t have a good shooting opportunity, seeking a better one.  Meanwhile, the shot clock ticks…and as time passes, the calculus changes.  Given the risk of running out of time on the shot clock, extra passes become less attractive and shots on the basket become more imperative, and players rationally are more willing to take lower-percentage, lower-quality shots.  Shooting percentages can be expected to fall, because players are forced to shoot without having found an easy layup or fast-break dunk. 

The article was based on data from only two games by one team.  We wish we could find a similar but  potentially more valuable data-set:  shooting percentages by teammate, segmented by the number of seconds on the shot clock.  This would allow us to test our hypotheses, which is that game patterns, and the related passage of time, cause patterns in shooting percentage, and that passing less is correlated with, but does not cause, higher shooting percentages.

We feel that Biderman’s piece misses is what’s at the heart of why statistics in sports are so captivating to so many of us. They allow us to reveal truths that were previously hidden.  Biderman’s piece doesn’t make an attempt to dig deeper into why the Heat score less when they pass more.  There is no hidden truth in this article, only a potential straw man. 

What do you think?