A Brownian Motion Model for the Progress of Sports Scores

Abstract

The difference between the home and visiting teams' scores in a sports contest is modeled as a Brownian motion process defined on t ∈ (0, 1), with drift μ points in favor of the home team and variance [sgrave]². The model obtains a simple relationship between the home team's lead (or deficit) l at time t and the probability of victory for the home team. The model provides a good fit to the results of 493 professional basketball games from the 1991-1992 National Basketball Association (NBA) season. The model is applied to the progress of baseball scores, a process that would appear to be too discrete to be adequately modeled by the Brownian motion process. Surprisingly, the Brownian motion model matches previous calculations for baseball reasonably well.

Key Words:

• Baseball
• Basketball
• Probit regression