END- GAME BASKETBALL STRATEGY
In this chapter we will consider the optimal strategy for two important situations that can occur at the end of a close basketball game:
• In game 1 of the first round of the 2001 Eastern Conference playoffs the
Philadelphia 76ers led the Indiana Pacers by two points. The Pacers had
the ball with five seconds to go. Should the Pacers have attempted a two-
pointer to tie or a three- pointer to win?
• During game 6 of the 2005 Western Conference semifinals, the Dallas Mav-
ericks led the Phoenix Suns by three points with five seconds to go. Steve
Nash is bringing the ball up the court. Should the Mavericks foul Nash or al-
low him to attempt a game- tying three- pointer?
I was fortunate enough to be at both of these exciting games. Reggie Miller hit a game- winning three- pointer as the buzzer went off in the Pacers–76ers game. Steve Nash hit a game- tying three- pointer and the Suns went on to eliminate the Mavericks in a double overtime thriller.
Let's use mathematics to analyze the optimal strategy in both of these exciting end-of-game situations.
To begin, let's assume we have the ball and we trail by two points with little time remaining in the game. Should our primary goal be to attempt a game-tying two-pointer or to go for a buzzer- beating three- pointer to win the game? This situation has often been used in Microsoft job interviews.1 We assume our goal is to maximize the probability that we win the game. To simplify matters, we assume that no foul will occur on our shot and that
1 Thanks to Norm Tonina for sharing this fact with me.