The selection of the Sunday singles lineup by a Ryder Cup captain is a decision that is often times widely scrutinized at the conclusion of this biannual International tournament. This thesis explores the impact of optimizing the Sunday singles lineup for the United States Ryder Cup captain. Through optimization modeling based on predicted player matchup performance and proposed opposing strategies, we analyze the expected outcome of different lineup decisions. We developed an order logistic regression model comparing the average World Golf Ranking points per event of two competing players in order to estimate the probability of a match's final outcome. Opposing captain's lineups are modeled with respect to the possible lineups strategies of frontloading, backloading, and past Ryder Cup tendencies. To examine the effectiveness of our model, we focus the 2002 Ryder Cup where Curtis Strange, the United States captain, was heavily criticized for his perceived poor lineup selection in a final day collapse of the American team. We evaluate the predicted performance of the actual USA lineup along with the proposed optimal lineups generated through our optimization model. These lineup decisions are compared based on expected points earn across the twelve Sunday singles matches and the probability of the United States earning a desired number of team points.