Since 1933, Stan Musial has played the most seasons with 20+ home runs with 500+ at-bats and with a batting average of .333 or above, with 7 seasons.

most seasons since 1933 with 500 ab and 20 hr and a ba of.3329
Interpreted as:
most seasons by a player since 1933 with 500 or more ab and 20 or more hr and a ba of.3329 or higher

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