McMahon was used almost exclusively in relief during his 18-year MLB career. He appeared in 874 games, just two as a starter, and was one of the major leagues' busiest and most dependable relievers during his era. He never once spent time on the disabled list, and in the fifteen full seasons that he played (1958–72), he averaged about 54 games and 81 innings pitched per year.

He reached the big leagues at the advanced age of 27 after playing minor league ball for about 5½ years and also spending two years in the military (May 30, 1951 – May 17, 1953). He appeared in his final game on June 29, 1974, nearly 17 years after his major league debut.

McMahon was a valuable part of two World Championship clubs—the 1957 Milwaukee Braves and the 1968 Detroit Tigers. He posted a 1.54 ERA with 9 saves in 32 games for the 1957 Braves, and a 2.02 ERA with a 3–1 record in 20 games for the 1968 Tigers after a mid-season trade from the White Sox. All together he pitched in three World Series and one National League Championship Series.

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