Winning Probability—in a Game, in a Series, and Afterwards

Abstract

Two teams, A and B, are facing off in a best-of-seven series of games. What is the probability P(A) that Team A will win a game? What is the probability P₇(A) that Team A will win the series? Different people will answer the questions differently based on many subjective criteria. The answers may be modeled by random variables with support [0, 1]. How are the distributions of P(A) and P₇(A) related? After the number of games played and the winner of the series are known, a posteriori, what is the distribution of P(A)?