Conditional Probability And The Length Of A Championship Series In Baseball, Basketball, And Hockey

This paper re-examines the assumption that the probability of winning the World Series, the NBA Finals, and the Stanley Cup is constant across the series. This assumption is the primary basis for models that endeavor to explain the length of a series, but we demonstrate that this model is inconsistent with historical data in all three sports. We adjust the model to incorporate conditional probabilities and fit it with historical data. While one can always backfit historical frequencies to conditional probabilities, doing so shows that the variation in conditional frequencies within and across sports is too wide to support the constant probability model. We also define a new notion of the concept of two teams being evenly matched.