The sport of Ultimate has grown from parking lot fun to international competition in its 35 year existence. As in many sports, the team that scores is subsequently on defense. Thus the probability that a team will score next is dependent on which team has scored most recently. Unlike in many other sports, teams switch ends after each score. Thus field conditions can affect the scoring patterns. The data and analyses described here can be integrated into a variety of courses ranging from introductory statistics to stochastic models. (Contains 2 tables and 5 figures.)