McCoy worked in the World Series in 1977 and 1988. He also umpired in six American League Championship Series (1973, 1976, 1980, 1986, 1990 and 1997) and three All-Star games (1978, 1985 and 1996), calling balls and strikes for the 1985 game. McCoy worked in the American League Division Series in 1981, 1995 and 1998. He was the third base umpire on April 20, 1986, when Roger Clemens became the first pitcher to strike out 20 batters in a nine-inning game. McCoy was also the first base umpire for David Cone's perfect game on July 18, 1999. He was the plate umpire for the Ten Cent Beer Night held by the Cleveland Indians on June 4, 1974, that ended in a forfeit win for the Texas Rangers. He was also the home plate umpire in Phil Niekro's 300th career win in Toronto on October 6, 1985.