Pickup Dilemma

When playing 21 basketball at the AFC or Dell Courts, I often find that myself and the other defender at any given time tend to sag off the offensive player to hunt for the rebound if he/she misses, which often leads to open shots and points for the offensive player. Although our lackluster defense could be attributed to laziness and subpar physical endurance, I like to believe that public choice offers a reason why we end up continually making this bad strategic decision on the court. This situation is essentially a prisoner’s dilemma.

            Some assumptions need to be made for this analysis to work. If Player A has the ball, defensive Players B and C are actors in a prisoner’s dilemma. In this analysis, any points for a player can be represented as negative points for the other players, who both experience the cost of the score.   

Let’s assume Player A is shooting a 2-point jump shot that goes in 33% of the time when undefended and 10% of the time when defended. Therefore, an undefended shot for Player A will grant them an average of .67 points, and -.67 points for both Players B and C. A defended shot for Player A grants them an average of .2 points and -.2 points for Players B and C. Also, possession of the ball gives 1 point per possession for the average player. Therefore, a rebound is worth 1 point and -1 point for the non-rebounding players.

The Prisoner’s Dilemma looks like this:

B, C	B defends the shot	B sags off and hunts for the rebound
C defends the shot	-.2, -.2	.8, -1.2
C sags off and hunt for the rebound	-1.2, .8	-.67, -.67

            If Players B and C are fighting for the rebound on equal ground (either they both defended the shot or both sagged off to hunt for the rebound), the 50% rebound chance cancels out and grants them an additional 0 points. However, if Player B defends the shot and Player C sags off and hunts for the rebound, either Player A makes the defended shot or Player C definitely gets the rebound, which is the worst possible outcome for Player B (-1.2 average points). Therefore, both players are incentivized to sag off and hunt for the rebound to avoid this outcome, leading to a Pareto-Inefficient Equilibrium of -.67 points from the undefended Player A jump shot.

An enforcer would be necessary to compel the defenders to both defend the shot to achieve the Pareto-Efficient Equilibrium of -.2 points from a defended Player A jump shot. One enforcer could be trash talk from Player A: pickup basketball players love taunting “you shouldn’t have left me open!” when they make undefended shots, causing enough humiliation to incentivize Player B and Player C to make the Pareto-Efficient Move and both defend the shot.