The stories of Fidel Castro being scouted by major league baseball teams, or even offered a contract in some tellings, are apocryphal; Castro could pitch a little, and apparently did for the law school at University of Havana, which would qualify as something like intramurals as best I've been able to figure. But Cuba was then and is now baseball-obsessed; there's a nice photo of Castro pitching with the revolutionaries wearing an Oriente cap.
Cubans shared that passion for baseball with Americans, along with a parallel passion for boxing. You have read The Old Man And The Sea, right? But where the mutual love of music also survives (see Buena Vista Social Club), baseball is no longer America's national pastime, that's now television, and the new national sport is the more violent and uniquely American football. Even MMA fighting seems to have replaced boxing for Americans.
Metaphorically it marks a change for the worse in modern America that Cuba, cut off in many ways, has been unable to follow. And note that when Cuban baseball players defect to the major leagues, they inevitably establish their residencies in the Dominican Republic, trying to escape MLB's cartel monopoly on amateur talent. Viva la revolucion! Actually, much like Ho Chi Minh, Castro, while holding no illusions, originally seemed to think he could reason with the Americans. So imagine what might have happened had John Foster Dulles not snubbed Castro to golf when the Cuban came to Washington in 1959, and taken him to ballgame instead.
In 1959 the Havana Sugar Kings were champions of the AAA minor International League, and took on the Minneapolis Millers of the American Association in the 'Little World Series'. There's a nice photo of Fidel with a group of Millers including Gene Mauch, the future Phillies and Angels manager. It was also during that season Fidel formed a pick-up team, called Los Barbudos ('the Bearded Ones') and actually pitched a couple of innings against a team from the Havana police before a Sugar Kings' game. Of course a minor league franchise in Havana couldn't survive the embargo on Cuba, and Cuban baseball became a strictly amateur (in the Eastern European sense of 'state-sponsored') sport which Cuba dominated internationally for many decades.
When I worked for Major League Baseball I was told this story, by a long time baseball coach: Two scouts are talking during the Cuban missile crisis in 1962. One mentions that he scouted Castro for the Washington Senators, who in that era boasted two Cuban pitching sensations, Camilio Pascual and Pedro Ramos. 'Imagine if we'd signed Castro,' he muses to his friend. 'How different history might have been.' 'Bull,' says his friend, spitting tobacco juice on the ground. 'The Senators were crap and one more Cuban pitcher wouldn't have made a damn bit of difference.'