The league does not record statistics, and its standings — even simply who won and lost — have been disputed. Some teams fill their rosters through open tryouts. The Albany (Ga.) Shockwave required only that the prospects be at least 18 and “have previous basketball experience.”

The rules are just as quirky. Shots from beyond halfcourt are worth 4 points, unless “the Official A.B.A. 3-D Light” is on, in which case those shots are worth 5. In fact, with the light on, a point is added to every field goal. The light goes on if the team with the ball loses it in the backcourt through either a turnover or a violation. If this all sounds a bit ridiculous, remember that the 3-point line was once seen as a gimmick, too.

“It’s the flexibility that’s the charm of the A.B.A., not the plague,” Newman said.

The N.B.A., which owns the trademark to the A.B.A., keeps the league at arm’s length, but has licensed the name to A.B.A. league officials, said Tim Frank, an N.B.A. spokesman.

Newman said that he did not know how many A.B.A. teams were profitable but that the league allowed a chance for nonbillionaires to own a sports team.

“Many owners would not have the opportunity to live out their dream,” he said. Still, the league has had trouble drawing fans or attention. OurSports Central, a Web site that monitors minor league sports, has stopped covering the A.B.A. because of “its inability to publish and play a schedule and the transitory nature of many of its teams,” according to a statement posted on the site.

A Rolling Front Office

The Lima Explosion, a team in the Mid-Central Division, finished the season at 14-8. They were started in 2011 by John Bell, a local businessman, with three partners who have since moved on, but the most important member of the organization is Lewis Shine, 33, the team’s general manager, coach, publicist and sometime point guard.

Shine corrals a network of volunteers, many of them friends from his church, to work the door at games, as well as the merchandise table and the scoreboard. Shine, himself a former A.B.A. player, also has occasionally thrown on a jersey and hit the court when the team was short of players.