In the fraught history of US-Cuban relations, baseball may not feature as prominently in the history books as the missile crisis, the Bay of Pigs incident or Washington's 50-year embargo against the island.

But when it comes to the island's recent moves to open up and adjust to a hostile economic climate, "la pelota" is playing an increasingly prominent role.

In the past two decades, the heartland of Latin American socialist revolution has reluctantly become a breeding ground for Major League superstars – a galling trend that has now provoked a huge reform in the way that sports are run in Cuba.

Regulations introduced in September lift the ceiling on Cuban players' salaries, which were previously little different from those of a construction site worker, bus driver or librarian, and for the first time give athletes the opportunity to sign with foreign clubs without the need to defect.

For many, the changes come too late. More than 20 players have deserted Cuba in the past four years to pursue Major League millions in the US. They include Aroldis Chapman of the Cincinnati Reds who has thrown the fastest pitch recorded in MLB; Yoenis Céspedes, who won this year's Home Run Derby and José Abreu, who holds the Cuban home run record but defected via the Dominican Republic this year and signed a $68m (£41m) deal with the Chicago White Sox.

If the defectors could form a team, they would have every chance of winning a world title. Without them, Cuba has struggled. In one of the biggest shocks of the year, the national team lost 5-0 to a US college team.

Fans watch a final play off game between Industriales and Villa Clara in the Cuban National Series in Havana. Photograph: Enrique de la Osa / Reuters

"Major League Baseball has stolen our talent," said Pedro Cabrera Isidron, the international relations director of the Cuban Olympics Committee. "They're encouraging players to abandon our country in an illegal way. The way they channel people to the US via third countries like the Dominican Republic is just like human trafficking. The US government and the Major League authorities see this and they just cross their arms."

In order to motivate players to stay, he said the new rules would loosen the egalitarian pay structure by boosting athletes' earnings by as much as 20 times. Players with several years' experience in the domestic league and on the national team will also be allowed to sign contracts in other countries, but will remain bound to the Cuban Baseball Federation, which will take between 10% and 30% of their salaries.

"We can't pay an athlete $58m. We can only afford the good education of our players and then create the conditions for them to be happy in our country so that they want to come back when they have completed their overseas commitments," Cabrera Isidron explained.

He said the change should be seen in the context of wider economic and social reforms introduced under president Raúl Castro. In the past year, travel restrictions have been eased, more opportunities have been opened for private business and the government has announced plans to abolish the dual currency system.

The changes in baseball affect fewer people directly, but the consequences are likely to be talked about far more.

The sport has long been a national obsession. Brought to Cuba in the late 19th century by returning students and visiting US sailors, it was already hugely popular before the revolution in 1959. Fidel Castro, a fan with a decent pitching arm, transformed the way the sport was organised, banning professionalism and declaring athletes to be "standard bearers of revolution".

In the years that followed, the success of the national team, which dominated international amateur competitions and later won three golds and two silvers in five Olympic baseball tournaments, was held up as a sign of Cuba's strong education system.

In the grim "special period" of the early 1990s, when Cuba faced shortfalls due to the collapse of its main trade partner and sponsor, the Soviet Union, the sport was a symbol of unity in adversity. Players had to swap their studded shoes mid-game because there weren't enough to go round. Remembering how balls were once in short supply because of the US embargo, the crowd at the Estadio Latinoamericano in Havana still applaud when a fan throws a foul ball back on to the pitch.

But values and tastes are changing. At a recent match between Industriales – Havana's biggest club – and Matanzas, many in the crowd wore New York Yankees caps and shirts.

Decades ago, Cubans had little access to information about games in the US, but with the spread of internet and satellite communications, they are now immensely popular. In a significant breakthrough this year, even Cuban state television has started airing Major League Baseball games. Players openly state that they dream of joining the Yankees.

While the new regulations do not allow contracts with US clubs, the changes could open the floodgates to other countries, even for those who have so far chosen to stay behind.

Chief among them is Yulieski Gourriel, rated by many as the best player on the island and one of the leading third basemen in the world. Now 28 and plying his trade for Industriales, he has remained on the island as many of his peers have left.

It is certainly not money that has kept him in Cuba. His standard salary increased by 26 times as a result of the new policy, but it is still only 13,000 Cuban pesos (£300) a month. Even with an additional $300 (£184) hard currency payment, he earns less than 0.5% of what he could make in the Major League.

Gourriel's loyalty is partly explained by his background. He is the scion of Cuba's first family of baseball. His father, Lourdes, was the star of Cuba's Olympic baseball gold-winning team in 1992 and went on to be a club manager.

His uncle, cousin and great-uncle were all top-level players and his brother, Yuliesky (like many Cubans, they were given Russian names during the cold war), is a team-mate on Industriales.

Gourriel has said that he owes a debt of gratitude to the Cuban revolution. But his family would also have a lot to lose if he defected.

Now, however, with a chance to leave the island on good terms, he said he wanted to make a move.

"The new rules are very good," Gourriel said in an interview before a recent game. "I'd like to go to Japan. The Yomiuri Giants have expressed an interest … If I go my life will change a lot."

Ultimately, he said that his ambition was to join the exodus to the US. "Of course it's my dream to play in the Major League, but only with permission."

That is currently not possible, but there are signs of a thaw, such as the government's decision to allow a team of veteran defectors back to Cuba for an exhibition match earlier this year. Cabrera Isidron said Cuba wants to reach out to the US authorities so players can sign legally for American clubs.

"It only requires a willingness from the Major Leagues to respect the national federation of Cuba so that players who go to the US can later return."

This is a big obstacle as they would be expected to bring back some of their income. The US prohibits money transfers to the island under a trade embargo that dates back to the Cuban missile crisis in 1962. Isidron said that this was outdated.

"Now, because of the US embargo, Cuban players who go to the US have to abandon their country, leave their families and promise that none of their earnings will come back to Cuba. That is an absurd situation in the 21st century."

To the Industriales fans in the bleachers, such diplomatic and financial shenanigans are of less concern than the prospect of losing more of the club's players.

"If Yulieski goes, it will be a huge loss not just for Industriales, but for Cuba," said Alain Quintana, a shop worker.

Until the new regulations, he was paid almost the same as the players he idolised, but he expressed no envy as he watched the game played out below a political slogan declaring: "Sport is a victory of the Revolution."

"I think the new regulations are great. Players should earn more. Even the millions paid in the Major League are worth it. After all, it is the best in the world," he said.

"I hope that these new measures halt the decline of Cuban baseball, but I'm also worried that even fewer players will stay now."

Million dollar defections

• Aroldis Chapman defected to the Netherlands in 2009, then adopted Andorran citizenship so he could sign a $30m contract with the Cincinnati Reds, where he is nicknamed the Cuban Missile and has thrown the fastest pitch ever recorded in Major League Baseball.

• Yoenis Cespédes, who sought asylum in the Dominican Republic in 2011 with 10 of his family members, and soon after completed a $36m deal with Oakland Athletics and went on to win the 2013 Home Run Derby.

• Yasiel Puig twice failed to defect and then turned up mysteriously in Mexico in 2012, from where he signed a $42m contract with the Los Angeles Dodgers. A year later, he finished second in the National League Rookie of the Year to fellow Cuban José Fernández.

• Jose Abreu, who holds the Cuban home-run record, fled to the Dominican Republic this summer, declared himself a free agent, then signed a $68m deal with the Chicago White Sox.