Puig and Olivera learned how to hit from the same person.
"His father was my hitting coach," Puig explained in Spanish.
The 29-year-old Olivera, whose deal with the Dodgers is pending a physical examination, is the son of former Cuban league batting champion Hector Olivera Sr.
When Puig played for Cienfuegos in Cuba's Serie Nacional, the elder Olivera was the team's hitting instructor. Puig started working with him when he was 15.
"He was a tremendous influence on me," Puig said.
Puig said the instruction he received from the elder Olivera was similar to what he gets now from Dodgers batting coach Mark McGwire.
"You can see why his son can hit too," Puig said.
The younger Olivera is almost six years older than Puig and played for rival club Santiago de Cuba, but Puig said he was able to get to know him because of his relationship with his father.
"That's my brother," said Puig, who described Olivera as reserved and respectful.
Puig and infielder Alex Guerrero playfully talked Wednesday about the Dodgers' growing collection of Cuban players. Guerrero is also from Cuba, as is minor league shortstop Erisbel Arruebarrena, a childhood friend of Puig.
"We're a Cuban team now," Puig said.
Puig said that with Guerrero, Olivera and Arruebarrena, the Dodgers are almost in position to field an all-Cuban infield.
"We have to look for a first baseman too," he said, joking that they could perhaps one day acquire Jose Abreu of the Chicago White Sox.
Puig and Guerrero speculated about which Cuban player the Dodgers might sign next.
"We have the money," Guerrero said.
The Dodgers already have invested more than $160 million in players from Cuba, including $42 million on Puig, $28 million on Guerrero and $25 million on Arruebarrena.
To the DL?
The Dodgers are expecting Brandon League to start the season on the disabled list, as the right-hander underwent an MRI examination on his right shoulder Wednesday.
"He hasn't pitched in a while," Manager Don Mattingly said. "You guys can do the math part."
League has pitched in only two games this spring, the last on March 9. He received a cortisone injection in his shoulder almost two weeks ago.
League said he felt discomfort in his shoulder as he warmed up for a scheduled bullpen session Tuesday.
"From the first time I picked up the ball yesterday, I could tell something was different," League said.
League didn't offer a timetable for his return.
Building a case
To prepare for spring training, infielder Darwin Barney worked out extensively at shortstop over the off-season, he said. A former Gold Glove second baseman, Barney figured he would be competing for a utility role.
"Basically, any work I did defensively was at shortstop, just to get comfortable, just seeing balls on the left side of the infield again," Barney said. "Your feet just have to be a little more active over there. I was a shortstop my whole life, so it was basically remembering what to do with my feet on certain throws."
Barney has played five games at shortstop this spring, including in the Dodgers' 9-5 victory over the San Diego Padres on Wednesday, which he entered as a pinch-hitter. He has also played four games at second base.
Barney, who is considered a defensive specialist, is batting .333 in the Cactus League. But competition for places on the Dodgers' bench is intense. Utilityman Justin Turner is batting .486 this spring and is a lock to make the team. Guerrero is batting .364 and has the right to refuse a minor league assignment.
"I don't look at it that way at all at this point," Barney said. "I'm going out every day, getting my work done, playing the game. That's what spring training is for, get yourself ready to compete. What happens, happens."
The Dodgers were valued at $2.4 billion by Forbes, making them second in baseball to only the New York Yankees. The Yankees were valued at $3.2 billion.
The Dodgers generated $403 million in total revenue, including a league-high $120 million from television, according to the magazine.