LAKE BUENA VISTA, Fla. — One of the most fun eras in Oakland history was the “Billy Ball” team managed by combative Berkeley-born Billy Martin, who is the subject of a new documentary “Billy,” which screened at the winter meetings and is scheduled to air on MLB Network at 5 p.m. Thursday.

Martin, best known as a bar-room brawler who managed the Yankees five times, found a brief measure of calm in Oakland in the early 1980s, as detailed by his son, Billy Martin Jr., Oakland Hall of FamerRickey Henderson, and A’s employees Mickey Morabito and Steve Vucinich in the MLB Network-produced show.

“My dad was really happy being back in the Bay Area,” Martin Jr. said in an interview at the winter meetings this week. “He gained weight, he had better color, he just didn’t have all the stress he had in New York. And back home in the East Bay, he was like the Pope, the Man. It was Billy Ball, they had it all over every commercial and billboard. I’ve never seen him so at ease.”

The documentary does not shy away from Martin’s many controversies, including fights with players and members of the public, his up-and-down relationship with Yankees owner George Steinbrenner, and his complicated personal life. His death, in a car accident on Christmas Day 1989, is examined in detail; Martin at one point was reported to have been behind the wheel, but his friend, William Reedy, was later convicted of drunken driving in the case.

The only portion of the documentary that rankles Martin Jr. is former Yankees and A’s outfielder Reggie Jackson’s suggestion that Martin’s dislike for him was racist. As Martin Jr. notes, numerous African American players, including Hall of Famers Henderson and Rod Carew, appear in the program to describe their close relationships with Martin.

“That has no basis in fact,” Martin Jr. said of Jackson’s jab. “My father was the least racist man I’ve ever known, he didn’t see color at all. Carew, Willie Randolph, Rickey, all those guys loved my dad.”

Those close to Martin hope the program revives the possibility that the veterans’ committee, which has had Martin on its ballot four times, will re-examine Martin’s Hall of Fame candidacy. He had six seasons with 90-plus wins, winning records with five different teams and led the Yankees to back-to-back pennants and one Series title.

“Billy’s record stands for itself,” said Vucinich, who noted that Martin loved Oakland so much, he took a break from a minor-league managing job to come back for an Oakland Oaks old-timers’ game.

“I know there was negative stuff with the drinking and the brawling, getting fired five times — but the bottom line is that Billy was a great baseball man,” Morabito said at the winter meetings. “He was brilliant. Tony La Russa told me he learned so much just managing against Billy. I hope this creates a new dialogue about Billy. Put the peripheral stuff aside, just look what he did as a manager.”

Stadium thoughts: Manager Bob Melvin said during a media session that he’s not certain the A’s have given up on the Laney College site for a ballpark, despite an end to the talks with the Peralta Community College district after a decision by the Peralta board of trustees.

“It obviously stunned everybody,” Melvin said. “I can’t speak for the dialogue with Peralta, but (A’s executives) definitely felt like they’d done enough, had enough conversations to feel like they were confident in the site.

“Now, I think anytime you do something like this in California on land that’s not yours, there are going to be some hurdles. ... My guess is (the team is now) kind of sitting back and looking and see what the options are, and I’m not 100 percent sure that they’re done with this site. Maybe you come back and take a look at it from another angle.”

Briefly: Melvin said that moving into the designated-hitter role won’t bother Khris Davis but “he doesn’t want to do it every single day. I think in the outfield he does well enough for us, certainly tracking balls and so forth, to where we’ll get him out there some.” … Oakland isn’t expected to take any players in Thursday’s Rule 5 draft.

Susan Slusser is a San Francisco Chronicle staff writer.