Alycia Baumgardner and Claressa Shields are back at it again.

The latest entry in their back-and-forth outside-the-ring rivalry: Last Saturday, during the Richardson Hitchins-Gustavo Lemos fight card at the Fontainebleau Las Vegas, several media outlets and who-knows-how-many amateur iPhone videographers captured Shields (who served as on-air talent for the broadcast) and Baumgardner in a heated, protracted argument.

If nothing else, the confrontation brought up a question: Given the length and intensity of the fighters’ rivalry, why haven’t Shields and Baumgarder yet stepped inside the ropes to hash things out?

It’s a weighty problem.

Shields (14-0, 2 KOs), a two-time gold-medal-winning Olympian and two-division undisputed world champion, competes at middleweight. Baumgardner (15-0, 7 KOs), herself an undisputed champion, competes at junior lightweight. That’s a 30-pound gap in weight – almost certainly a bridge too far for matching the fighters.

Dmitry Salita, Shields’ promoter, recently spoke to BoxingScene about the odds of a Shields-Baumgardner happening.

“Alycia is out there speaking complete nonsense, going on Shaquille O’Neal’s podcast, talking about fighting Claressa,” Salita said. “It is like Manny Pacquiao challenging Mike Tyson. It is so ridiculous – it is not real. And people that don’t really know boxing or follow women’s boxing, they just see names. They don’t understand weight classes, [but] they think about it and talk about it.”

Salita, who has sought to revive boxing in the Detroit region with a developmental, ShoBox-like series on DAZN, has known Baumgardner for some time. A Fremont, Ohio native now training under Bill Haney in Las Vegas, Baumgardner rose to fame as a professional in Detroit working with LJ Harrison and Tony Harrison.

“I’ve known Alycia for a long time – like way, way before,” Salita said. “We have always invited her to fights. I am not one to say anything negative.”

Yet there is a certain amount of negativity, completely independent of any beef with Shields, that lingers over Baumgardner’s career. Last July, a pre-fight drug test sample from Baumgardner yielded “an adverse analytical finding for a banned substance” that put her under a microscope and led to a suspension from the Association of Boxing Commissions.

Baumgardner has since been exonerated by the WBC (the sanctioning body that collected the sample in question) and, according to the fighter, is no longer under suspension by the Association of Boxing Commissions.

But it will be difficult for Baumgardner to fully put the issue behind her until she makes her next fight.

Is there even a possibility it could come against Shields?

“I called her manager,” said Salita. “‘We will make the fight at 154.’ And like Don King used to say, ‘There is only one way to say yes and 99 ways to say no.’ So they said no in 99 ways.”

Salita said any theoretical Shields-Baumgardner fight would have to happen now “because Claressa is growing” and hasn’t fought below middleweight in years.

In any case, the promoter suspects Baumgardner was never really serious about taking on the fighter many describe as boxing’s GWOAT (Greatest Woman of All Time).

“It is all talk,” Salita said of Baumgardner’s desire for a Shields fight. “It is a way to make herself relevant, and the way she has gone about it has not been classy.”