Rationality and Bad Beats

Deadspin reports on a freakish occurrence in Boston, with video.  Team A is up by 2 points with a player on the line for one shot.  There's one second on the clock.  What's the rational choice in this situation: 1) intentionally miss the free throw so that the opposing team has only one second to recover the rebound, turn, and fire off a hail mary, potentially winning the game? or 2) try to make the free throw, allowing the opposing team to set up a play, with a more manageable three-point attempt.  In this actual case, the player chose 1, the opposing team got the rebound and made the hail mary, winning the game.  Deadspin argues 2 was the better choice. 

It's difficult to be certain in the abstract.  Much of this depends on the likelihood of making a 75 foot shot, as opposed to a shot at half court or closer.  But most of us who have played basketball know this: the chances of making a 3 point attempt decrease exponentially the further out you are.  For many, the odds in making a half-court shot are nil, as the distance is too far for them to reach the goal.  But the average high school player can hit the rim from half court with a running start.  Move it back to full court and the odds must be incredibly small.  Ergo, I go for 1.  Bad beats don't prove that we've played the game incorrectly; bad beats occur just as do black swans.  All we can do is walk away bemoaning our bad luck.