As you may have guessed, the main reason for there being a separate major league for African-American players was because blacks were banned from playing in the National and American Leagues until Jackie Robinson broke the color barrier in 1945. Separate Negro Leagues began as early as 1887 and lasted until approximately 1951. The two most successful leagues were the Negro National League (1933-1948) and the Negro American League (1937-1951. This league continued as a barnstorming unit until about 1960.)
Many of the players were of Major League caliber, but due to their color, they were nevertheless ineligible until the color barrier was broken shortly after World War II. Among the greatest players of the Negro leagues (and all of whom would surely have been successful in the Major Leagues) were slugging catcher Josh Gibson; pitchers Satchel Paige and Rube Foster; first baseman Buck Leonard; and outfielder "Cool Papa" Bell.
Probably the greatest team of the Negro Leagues was the Homestead (Pennsylvania) Greys, which included both Paige and Gibson at one time. They remained in continuous operation for 38 years. The Indianapolis Clowns were the last Negro League team in operation, barnstorming (much in the manner of basketball's Harlem Globetrotters) long after the league folded until about 1980.
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