Baylor, the country’s largest Baptist university, has named the first woman president in its 172-year history. Linda Livingstone takes over from interim president David Garland, as fallout continues from the school’s campus rape scandal, which includes accusations that the school covered up assaults by members of its football team. Former Baylor president Ken Starr was pushed out last year over his mishandling of the mess. Now Livingstone will be in charge of cleaning it up.

Livingstone’s historic appointment is a rather extreme example of a phenomenon known as the “glass cliff”: the tendency of women to be appointed to leadership only when an organization is in crisis. The phrase was coined in 2005 by two researchers intrigued by a British news article that observed that companies with more female board members seemed to perform worse on Britain’s top stock index. Was it really true that “companies that decline to embrace political correctness” are superior? Actually, the researchers found, it’s not that women are bad for business, but that businesses tend to embrace women only when times are bad.

Glass cliffs are everywhere once you start to look for them, in both politics and business. Prime minister David Cameron, who called the referendum delivered Brexit last year, and Boris Johnson, its top promoter, left the chaos they created to Theresa May. CEOs including Mary Barra, Marissa Mayer, and Meg Whitman were all installed in times of turmoil. A 2013 analysis of CEO transitions in Fortune 500 companies found that men of color and women were significantly likelier than white men to become CEOs when firms were performing weakly; if the firm continues to flail, then white men are likely to replace them, a phenomenon researchers call the “savior effect.”

Man or woman, Baylor really needs a savior. Its current troubles started in 2015, when a former Baylor football player was convicted of raping a student. During that trial, it emerged that the school had investigated the star player but never punished him. Several similar cases soon became public. At least five women said that a different Baylor football player had assaulted them between 2009 and 2012, for example. A damning independent report commissioned by the college in 2015 prompted Starr’s demotion and the firing of longtime football coach Art Briles.

Baylor’s religious character makes its predicament even thornier. Its faith-based conduct code, which forbids drinking and premarital sex, may have inhibited women from coming forward to report assaults in the first place, for example. Several women accused the college of threatening them by saying they would tell their parents what they had been doing at the time of their alleged assaults. Other women received alcohol violations after making sexual assault reports, despite a school policy that allows for amnesty in such cases. Baylor students do not need to be religious to attend, but the university still calls itself “unambiguously Christian,” and it belongs to a consortium of evangelical colleges. In that context, Livingstone’s appointment looks like even more of a high-wire act. A large 2014 study of evangelical nonprofits and colleges found that women make up just 16 percent of top leaders in those settings, compared to 40 percent of CEOs in similar secular settings.

The Baptist tradition is not known for its embrace of female leadership. But with experience in both Division 1 sports and crisis management, Livingstone seems as prepared as anyone for the job. She was a popular faculty member at Baylor in the 1990s, and she most recently served as business school dean at George Washington University. Baylor alumni Laura Seay, a government professor at Colby College, told me that progressive alumni seem heartened by her appointment, in part because her background is in academia rather than politics or preaching. Seay notes that Livingstone has her work cut out for her, however: She’ll have to raise a lot money to cover the legal settlements on the horizon, and will have to take a firm hand with an unusually entrenched leadership structure. “The inevitable decline in Baylor’s football program that’s going to happen this fall won’t help with that steep challenge,” she added.

Steep indeed—it sounds something like a cliff.