The son of famous early White Sox catcher Billy Sullivan, Billy Jr. attended Notre Dame with the young Ed Walsh, son of the star White Sox pitcher. It was rumored that Chicago owner Charles Comiskey paid their tuition in hopes they would duplicate the playing ability and drawing appeal of their fathers. Billy Jr. had played mostly third and first, but as a publicity stunt, he and Walsh appeared as a battery once, late in 1932. Sullivan began catching regularly only after joining Cleveland in 1936, and never caught more than 99 games a season. He turned out to be a much better hitter than his father; his .351 average in 1936 was seventh in the league. A top lefthanded pinch hitter, he was extremely difficult to strike out, fanning only 119 times in 2,840 at-bats.