ABSTRACT

The game of basketball, like just about any other game, can be described as a sequence of random events, with the probabilities of different outcomes determined by the skill levels of the players involved. More specifically, during each offensive possession of a basketball game, the team with the ball attempts to score, and this attempt results in some number of points ranging between 0 and 3 (or, rarely, 4). At the end of the game, what matters is not the absolute score of a given team but the differential score, defined as = (total points scored by team A) − (total points scored by team B). The goal of team A is for the game to end with > 0. As such, this differential score is the primary random variable for describing a basketball game in the statistical sense. Understanding its expected value and variance, and how basketball teams can influence them through strategic decisions, is the main focus of this chapter.