Rose accepted a permanent ban from Baseball in 1989 for breaking Major League Rule 21 which defines misconduct, specifically Rule 21(d) which states in part:
"Any player, umpire, or club or league official or employee, who shall
bet any sum whatsoever upon any baseball game in connection with which
the bettor has a duty to perform shall be declared permanently ineligible."
MLB investigated Rose on the allegations that, while manager of the Cincinnati Reds, he bet on MLB games including Reds games and concluded that the allegations were true although they came up with no evidence that Rose had bet against the Reds. MLB issued him a lifetime suspension which could be appealed after one year. Rose has twice appealed the suspension without success.
Rose has since admitted that he bet on MLB games, including Reds games, during his time as manager of the Reds.
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The only reason that Pete Rose is not in the Baseball Hall of Fame is because he was banned from playing baseball and subsequently made ineligible for entry into the hall of fame.