“There are more women in middle management, in the pipeline, so I’m hopeful that that will translate into more women in those roles,” said Williams, the first black woman hired as a Power Five athletic director. “I think women have proven that we are fully capable and competent and hard-working — maybe even more in some cases — and willing to learn and do the work to advance.”

And while football failings have upended the career of more than one athletic director, regardless of sex or employer, the sport and its gendered history loom especially large over top women in conferences like the A.C.C. and the Big Ten.

In an interview last month, Barbour recalled that in the mid-1990s, around the start of her time in Tulane’s ranking sports job, she asked her host at a speech if there were any subjects she should discuss. He replied that she should address how she would lead a football program when she had never played herself.

Reflecting on the episode more than 20 years later, just before a season when her football team was expected to be a Big Ten title contender, Barbour said: “Being a C.E.O., being a great leader, does not have a gender label on it. I don’t tell my football coach who to play, who to recruit or what to do on third-and-short.”

While the links between gender, football and leadership hiring may be fading, it is a slow process. Lyke and Williams said that influential male athletic directors were helping progress by mentoring women in a treacherous industry.

Lyke, who was captain of the softball team at Michigan and later earned a law degree, credited Gene Smith of Ohio State for helping fuel her rise to Pitt, where she was hired after a stint at Eastern Michigan.