Moses Fleetwood Walker is generally regarded as the first black to play in Major League baseball. It was with the Toledo Blue Stockings of the American Association in 1884. That year he played in 42 games and hit .263 and 23 runs scored. He bounced around the minor leagues the rest of his career.
In 1882 Walker was the catcher for the Michigan Varsity baseball team. Walker also played on Oberlin's first varsity team in 1881.
The first black ballplayer in organized baseball would be Bud Fowler. Fowler played in the minor leagues.
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