As far as batting average goes that would be Hall of Famer Rogers Hornsby who played with the Cardinals, Giants, Braves, Cubs, and Browns between 1915-1937. His career batting average was .358 and he is second all time in career batting average behind Ty Cobb.
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Mickey Mantle had a Right handed career batting average of .334 with 2,208 at bats, Left handed he had a career batting average of .282. with 4,517 at bats.
Mickey Mantle's Left Handed Batting Average .282Hitting left handed Mickey Mantle had a career batting average of .282 with 343 home runs, 867 RBIs in 4,517 at bats.Hitting Right handed Mickey Mantle had a career batting average of .334 with 136 home runs 397 RBIs, in 2,208 at bats.
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No, former baseball player Ricky Henderson never hit left-handed. He threw left-handed and hit right-handed. He started his MLB career in 1979 and was inducted into the Baseball Hall of Fame in 2009.
There have been a number of major league players who batted cross-handed early in their career, but nearly all changed to the conventional grip before playing in the Major Leagues. Cross-handed hitting was more common in the late 1800s and there were more players that started hitting cross-handed then. Ezra Sutton, Frankie Frisch, Sherry Magee, and Christy Mathewson were all major league players from the early days of baseball who hit cross-handed early in their career. Ezra Sutton hit cross-handed for at-least part of his first major league season. Frankie Frisch was a switch hitter and there are baseball cards showing him hitting left-handed with a conventional grip and right-handed with a cross-handed grip. Latter players who hit cross-handed included baseball greats Mickey Mantle and Hank Aaron. Mickey Mantle switched to a conventional grip while still young through (12 years old). Hank Aaron switched to a conventional grip during his first season in the minor leagues (1953) so he also never hit cross-handed in the Major League (first season with the Milwaukee Braves was 1954). In 1952, Hank led the Negro League with a batting average of .467 while hitting cross-handed though.