“The Curious Case of Curt Flood,” a new HBO Sports documentary (Wednesday, 9 p.m.), raises a tantalizing question: what if Flood’s legal challenge to baseball’s reserve clause had had a better advocate before the United States Supreme Court than Arthur J. Goldberg, a former associate justice?

Flood lost the case by a 5-to-3 vote. Would a better argument have swayed two justices to rule against Major League Baseball? Had Flood won, free agency would probably have arrived a few years before it was achieved in arbitrators’ rulings in favor of Catfish Hunter, and for Andy Messersmith and Dave McNally.

Goldberg looked like an ideal choice to deliver an oral argument before some of his former colleagues on the court. He was a successful labor lawyer and former general counsel to the United Steelworkers of America. He was a baseball fan who carried a coffee urn as a vendor at Wrigley Field in the 1920s.

Flood needed a lawyer who could deftly argue against the reserve clause, which tied players unilaterally to their teams until they traded or discarded them. Players had no rights to sell themselves to the highest bidders in this relationship, as Flood learned when he was traded by the St. Louis Cardinals in 1969 to the Philadelphia Phillies. He refused to report to the Phillies, starting him on his legal odyssey....