Tarpey earned UMass' first All-America award in baseball, being named third-team by the American Baseball Coaches Association in 1955. A member of two consecutive NCAA Tournament teams (1954-55), he helped UMass advance to the College World Series in 1954, the school's first ever appearance. In 1955, Tarpey was the MVP of the NCAA Regional, a member of the NCAA Regional All-Tournament team, and winner of the E. Joseph Thompson Memorial MVP trophy (team MVP). A native of Gardner, Mass., Tarpey was a managing partner of the Bulkely, Richardson, and Gelinas law firm in Springfield, Mass. He was inducted into the UMass Athletic Hall of Fame in 1999.