No Average Joe
In 1911 and 1912, “Shoeless” Joe Jackson of the Cleveland Naps achieved batting averages of .408 and .395 respectively. Incredibly, neither average was enough to gain him the American League batting title as he was beaten in both years by the great Ty Cobb of the Detroit Tigers who posted stats of .420 and .410.
Jackson was banned from the game in 1920 after his association with the “Black Sox Scandal” in which team members of the Chicago White Sox participated in a conspiracy to fix the 1919 World Series.