- Made major league debut on 15 April 1915.
- Mays, pitching for the New York Yankees, hit Cleveland Indian's Ray Chapman with a pitch, resulting in a depressed fracture just above the left ear. Chapman died the next day. It is the only fatality in major league baseball history. (16 August 1920)
- Led the American League in shutouts in 1918 (8) and 1920 (6).
- In 1921 led American League pitchers in wins (27), winning percentage (.750), games pitched (49), and innings pitched (336-2/3).
- Pitcher with the Boston Red Sox 1915-1919[start]), New York Yankees (1919[end]-1923), Cincinnati Reds (1924-1928), and New York Giants (1929).
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