The lack of resources doesn't mean lack of ambition. Some dream of playing Major League Baseball -- following in the footsteps of Cuban defectors like Orlando Hernandez or Yasiel Puig.
But in a country where television is state-run, and Internet is expensive and slow, actually watching those Cuban stars in the Major Leagues is tough.
On Cuban TV, it's still rare to see a Cuban player in the weekly MLB broadcast, but in the past year it has happened a few times. Before then, Cuban players would literally be edited out of the games before they went to air. Short supply has created high demand for MLB coverage -- especially games involving Cuban players.
Enter "el paquete," -- bought, sold and traded in Cuba's underground market for American media. Paquete is the word Cubans use to describe the USB sticks, hard drives, DVDs or sometimes even VHS tapes loaded up with American TV shows, movies and baseball games and sent to the island nation.
Cubans will pay a few convertible pesos (on par with the US dollar) to get what's on the latest paquete. Those baseball games, movies and TV shows are sometimes copied and re-sold several times. Often, by the time they trickle down to the masses, they're out of date.
"They don't care [that the games are old], they just want to see the stars," said baseball writer Ray Otero who runs the website BaseballdeCuba.com.
Otero says the influx of American media isn't something the Cuban government likes, but there isn't much it can do about it.
Jorge Ramirez, a Cuban taxi driver who lives in the eastern city of Santiago de Cuba buys a new paquete every week.
"You can see things on [American] TV that you can't see here," he said.
He's never been to the United States, but thanks to the paquete, he watches American baseball -- proudly keeping track of the Cuban stars.
"I feel good because they have progressed. I can see how they have progressed," he said.
Cuba, does have its own baseball league. Tickets cost just 3 National Pesos (about 12 cents US), and some players freely mingle with fans after the game, before heading home on their bicycles.
"The line between the players and the fans is so thin," said Peter Bjarkman, an American baseball historian and author who has written extensively about Cuban baseball.
The problem is that the Cuban league only pays players about $125 per month -- so it's not surprising that so many are leaving. Their departure is partially what's fueling the "paquete" trade -- a chance for Cubans to watch homegrown talent succeeding on the highest level.
As beloved as the underground tape-swap is on the island, most fans would trade it in an instant for the opportunity to simply turn on their TV and watch their national heroes live -- or better yet, see them in person. If glacial deep freeze between the US and Cuba continues to thaw out, that might not be so far off.