SCOTTSDALE, Ariz. (AP) — Yasmany Tomas took his last practice swings, packed his bat and carried his oversized No. 24 duffel bag toward the clubhouse.

On the way, a dozen fans waited just outside a fence, calling the 6-foot-2 Cuban slugger’s name, holding out balls and gloves and begging for autographs and selfies.

“Where’s the fat guy?” the 24-year-old Tomas asked, suddenly uneasy with the small frenzy.

He called again for his interpreter and full-time assistant, Ariel Prieto. “Gordo! Gordo!” he shouted, using the Spanish word for fat.

Realizing his countryman was on another field at the Arizona Diamondbacks practice facility, Tomas paused, then walked toward the fans alone. He grabbed a ball from a young girl with blonde hair, signed it and rushed out.

“Gracias,” she said.

For Tomas and dozens of Cubans arriving in the majors, even simple moments can be daunting adjustments. Learning English. Finding their way in a new country. Dealing with dual pressures of pro sports and being away from family for the first time. Tomas made one of essentially three choices for Cubans hoping to make a living playing baseball: stay in Cuba and make $2,500 a month at best if you’re a star; play in other countries like Japan for a modest shot at earning a salary in the low seven figures with the government’s blessing; or give up family and life in Cuba on hopes of hitting the jackpot in the majors, where the average salary is more than $4 million.

Since the U.S. and Cuba began 2015 with steps to improve rocky relations, players and their families now navigate those choices and life changes through uncharted political waters.

“I would love to be there in the stands when he starts to play, to give him the support we’ve always given him,” said Tomas’ mother, Melba Rosa Bacallao, holding back tears as she sifted through an album with pictures of her son from her two-bedroom house in Havana. “He always tells me that his daughter and we are his priorities, that he wants to get ahead in life for us.”

Optimism in both countries and demand from U.S. teams are clearly growing despite the complicated landscape. The governments have made few tangible policy changes that significantly impact players, their relatives and the game. Baseball is treading carefully, not wanting to step on diplomatic toes.

There were 74 Cubans on major or minor league rosters on opening day, 11 more than last year and more than double the 29 in 2008. Most developed in state-run academies where kids breathe baseball from an early age.

Baseball’s lure has rippled through Cuba, where attitudes toward the U.S. have softened in the last few years as the island adapts to social, political and economic changes. President Barack Obama met recently with Cuban president Raul Castro, and the island will be taken off the list of state sponsors of terrorism.

Players in Cuba talk openly about wanting to play in the United States, commenting in ways that used to be considered sinful by authorities who severely punished big league dreams. Officials have also discussed playing spring training games on the island, MLB Commissioner Rob Manfred said. And through deals in other countries not limited by the U.S. embargo, Cuba has shown signs it is willing to let players enter baseball’s free market.

“Of course I would like to play where they play the best baseball in the world,” Yulieski Gourriel, star infielder for the national team, said during the Caribbean Series in Puerto Rico in February. “As long as we have authorization, we’ll always want to do so.”

Gourriel made $1 million in Japan last season, then returned his pro team in Havana. After accounting for Japanese taxes, he paid 10 percent to Cuba’s baseball federation (which acted as his agent), taking home enough to be rich in a communist country with limited options for spending and investment.

Leaving isn’t always as difficult and dramatic as it used to be. Teen sensation Yoan Moncada, who in March agreed to a record $31.5 million signing bonus with the Boston Red Sox, left Cuba last year thanks to 2013 laws that allow citizens to travel abroad without an exit visa. No midnight speedboat to Mexico, no shady smugglers. He asked for and was granted release, established residency in Guatemala, then worked out for MLB clubs.

Ballplayers released by the federation can travel elsewhere legally, said Antonio Diaz, a spokesman for Cuba’s baseball federation. Moncada “was discharged because he was of no interest to the national team,” he said.

But, in accordance with the embargo, those hoping to play in the U.S. must sign an affidavit that says they won’t return to Cuba.

Face-to-face contact with family becomes tough. Cuban law allows defectors to revisit eight years after departing, which former MLB players Jose Contreras and Rey Ordonez utilized two years ago. But U.S. immigration and strict tourist regulations regarding Cuba haven’t changed.

“It’s very difficult. It takes a lot of time to get a visa for your family in Cuba,” said Seattle Mariners pitcher Roenis Elias, who fled Cuba in 2010.

Changes in Cuba-U.S. policy since December have come mainly from the American side and aren’t specific to baseball. In January, the U.S. quadrupled the amount U.S. residents could send to Cubans to $2,000 per quarter. It also eased travel restrictions for Americans and loosened controls on U.S. businesses to spur the island’s small private sector. Netflix, MasterCard and online home rental service Airbnb have entered the Cuban market, though few on the island have high-speed Internet and most credit card issuers prohibit transactions from the country.

No MLB on-demand yet.

“Everybody is kind of figuring it out as we go, taking our lead from the diplomatic talks,” Dodgers general manager Farhan Zaidi said. “That’s the optimistic view, that there’ll be greater openness.”

Teams aren’t shy to spend huge amounts to snatch up the next big-league stars like Yasiel Puig or Jose Abreu. Boston signed Rusney Castillo last year for $72.5 million over seven years, and Tomas signed with the Diamondbacks for $68.5 million for six seasons.

“They’ve shown that they’re ready to play in the major leagues, and that they can do it almost immediately,” said Junior Noboa, the Diamondbacks VP for Latin America.

Next in line for a big bonus could be infielder Andy Ibanez, the youngest player for Cuba during the 2013 World Baseball Classic. Ibanez left the country illegally.

Departing Cuba and signing a contract are but the first of many issues for players and their families.

“They have to start from zero, they have no idea what’s going on,” said Prieto, a 45-year old former Oakland Athletics pitcher hired by the Diamondbacks to mentor Tomas. “They know baseball, but they don’t know the different philosophy of U.S. teams.”

Tomas said he passed on offers from Japanese teams, leaving behind his immediate family and a then 8-month-old daughter.

He is focused on life’s new encounters: autograph seekers, income taxes, local traffic laws. The sport and its universal language help the transition — baseball, after all, is called “beisbol” in Spanish, a home run is a “jonron,” and a strike is, well, a “strike.”

Away from the field, his thoughts drift home to Havana, where a flat-screen TV and new Chinese refrigerator are some of the perks his newfound riches have provided his family. Tomas thinks improved relations should make it easier for players to reunite with relatives.

“It would be something good, beautiful, to be able to be with your family after so much time without seeing them,” Tomas said.

His mother just wants to make sure he’s eating well and handling his unique opportunity properly.

“I think he doesn’t know what that kind of money means,” she said. “Even I can’t imagine.”

The shy slugger intimidated by a kindergarten-aged fan is far from the rambunctious son she remembers.

“He always raised his voice, like thunder,” Bacallao said. “I hope he speaks a little softer over there.”