The difference between the home and visiting teams' scores in a sports contest is modeled as a Brownian motion process defined ont∈ (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)lat timetand 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.