NBA 2014-2015 Regular Season - Page 16

An important problem facing a basketball team is determining the right proportion of 2 and 3 point
shots to take. With many possessions remaining, a team should maximize points—a 3-pointer is simply
worth 1.5 2-pointers. 3-point attempts have roughly double the per-shot variance as 2-point attempts,
but a team should be “risk neutral.” As time remaining decreases, the trailing team should place an
increasingly positive value on risk; the opposite holds for the leading team. Our game theoretic analysis
yields a testable optimality condition: 3-point success rate must fall relative to 2-point success rate when
a team’s preference for risk increases. Using four years of play-by-play data, we find strong evidence this
condition holds for the trailing team only. As a lead decreases, the leading team should become more
risk-neutral, but teams in this circumstance actually tighten up and become more risk averse, contrary
to what their risk preferences ought to be to maximize the chance of winning the game. We also show
that if the offense shoots more 3’s as it becomes risk-loving this implies the attack can be varied more
readily than the defensive adjustment. 3-point usage does increase with the trail team’s preference for
risk, but actually falls for the leading team. Teams get it right when losing and wrong when winning.
We also find a strong motivating effect of losing—the trailing teams displays an overall boost in efficiency
for both shot types.