Endgames for basketball, the 2-for-1

When should a team try for two shots near the end of a game or quarter?  Here is part of Mr. Winston’s request:

Hypothetically, your team is tied with about a minute left. Your team should shoot the ball with no less than 45 seconds left on the clock, so that if you miss and fail to get the offensive rebound, you are almost guaranteed to get the ball back. Here is his reasoning: “2-for-1 is a basic fundamental premise – I get 2 shots, you get 1. If we are tied before that begins, I am going to win more often than you. Period. Even if the first shot is less-than-great, you have to take a decent look early.

Here are a few points against the 2-for-1:

1. Taking a bad shot too early can lead to long rebounds and leave a team unable to get back to defend.

2. Turnovers and offensive rebounds and fouls are common near the end of games.  No one  knows how many shots are left in the game, so don’t think that backwards induction will work.

3. Your chance of drawing fouls, or inducing sheer defensive lapses, goes down if you take the rapid shot.

4. Taking the bad shot early may disrupt shooting rhythms, dispirit the team if there is a miss, and lead to too much play focused on the shot clock rather than quality execution.

5. You still might get a final shot attempt even if the first two shot attempts, by you and the opposing team, run down the shot clock a fair amount.

Overall I am not one to insist on the 2-for-1.  Basically you are immediately spending a valuable asset — a possession — without that much information about its value.  The deeper economic lesson is that infinite horizon models are more plausible than you think, because no one knows how rapidly events will be taking place.

Here is one paper on endgame strategy in basketball, focusing on the intentional foul.


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