Career wise, that would be Tony Gwynn (1982-2001) with a .338 career average. As of the start of the 2008 season, Gwynn ranks 20th all time in MLB career batting average. For a single season, that would be George Brett (1973-1993) with a .390 average in the 1980 season.
Stan The Man had a life-time batting average of .331
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.
The best career average for a major leaguer was .367 (Ty Cobb)
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Ted Williams played his final game on September 28, 1960 and finished his 19 year career with a lifetime batting average of .344. The HOF player also hit a career 521 home runs, and 1839 RBI's
Derek Jeter has a career batting average of .3129. This ranks him at number 80 all time; in between Ed Morgan (.3128) and Elmer Flick (.3130)
Reggie Jackson had a career batting average of .262
As of the start of the 2009 season, the active MLB player with the highest batting average is Albert Pujols of the St. Louis Cardinals at .334. Ichiro Suzuki of the Mariners is second at .331 and Todd Helton of the Rockies is third at .328.The highest all time career MLB batting average is Ty Cobb at .366.Now its Derek jeter in 2009 with .400
Your batting average would be .333
Strictly going by batting average, the best hitter in the history of MLB was Ty Cobb who batted .366 for a career that lasted 24 seasons (1905-1928). He hit over .400 in three seasons and, other than his rookie season when he had 150 at bats and hit .240, never batted below .316 for a season (his second season). For a four year stretch (1910-1913) he batted .402 (.4018). Rogers Hornsby is second in career MLB batting average with .3585 over a career that lasted 23 seasons (1915-1937). Hornsby hit over .400 in three seasons and did Cobb one better by having a FIVE season (1921-1925) batting average of .402 (.4024).
As of May 6, 2017, Mays is fifth on the all-time home run list with 660. He had a lifetime batting average of .302 and is one of 29 players to have 3,000 career hits.Mays was arguably the greatest ballplayer of his generation.