Davidson was an umpire at the 1976 Major League Baseball All-Star Game and for the 1982 World Series, in addition to being part of the umpiring crew for the National League Championship Series in 1971, 1974, 1978 and 1981. Davidson also officiated on April 17, 1976, when Mike Schmidt hit four home runs in one game. He retired from baseball in 1985, citing back problems.