Dempsey led American League catchers twice in fielding percentage, twice in baserunners caught stealing and once in assists. He played more games as a catcher than any other player in Orioles history (1230). During his career, Dempsey caught ten different twenty game winning pitchers. He was a durable player, only going on the disabled list twice in his career.

This October 24, 1983 issue of Sports Illustrated was signed in silver by Dempsey and inscribed, "1983 World Series MVP." This magazine includes a Great Moments COA.