For the next ten and a half seasons, Dempsey would remain as the Orioles' starting catcher. He became known for his exceptional ability to handle pitching staffs, his strong throwing arm, and for his agility behind home plate. In 1979, the Orioles defeated the California Angels in the 1979 American League Championship Series to reach the World Series. In the 1979 World Series, the Orioles won three of the first four games against the Pittsburgh Pirates and seemed to be on the verge of winning the championship, when the Pirates, led by Willie Stargell, rebounded to win the final three games. It was one of Dempsey's greatest disappointments of his playing career.