A Probabilistic Model of Winners' Outs versus Losers' Outs Rules in Basketball

We examine what happens to the game of basketball when one of the principal rules is changed. When a team scores a basket, we assume this team receives the ball on the next possession, a rule we call “winners' out.” This is, of course, the opposite of the usual “losers' outs” rule, where the opposite team receives the next possession. The implications of this rule are studied in the game where the first team to score a certain number of points wins and also in the game where the team that is ahead at the buzzer wins. In both games the main result, surprisingly, is that the probability that a given team wins remains essentially constant under the two sets of rules. That is, neither team should really care which set of rules is in effect.