Winning not the only thing? A college football ethics shift.

The signs may be modest, but amid public scrutiny a high-profile coach has been fired and the Southeastern Conference is poised to toughen policies on the conduct of players who transfer schools.

In recent weeks, the first outlines of a culture shift in college football have begun to appear.

Most obviously, Baylor University fired Head Coach Art Briles last week after an independent investigation found the university had mishandled accusations of sexual assault against his players.

For a university to fire a coach like Mr. Briles, who had almost single-handedly made Baylor a college football superpower – was “ a milestone,” wrote ESPN columnist Ivan Maisel. “Someone in the gridiron-industrial complex stood up and said some standards are more important than winning.”

But another, less-heralded development this week suggests the shift could be bigger than one coach or one team. The juggernaut Southeastern Conference (SEC) is set to expand a year-old rule that prohibits signing transfer athletes disciplined for “serious misconduct” – defined as sexual assault, domestic violence, or other forms of sexual violence.

Critics say these are just two small steps toward colleges choosing principle over the massive money generated by football. Last year, 28 colleges had athletic departments that made more than $100 million in revenue – up from three in 2008.

But the moves of the past two weeks are not insignificant and point to a trend line, others say.

True, the changes might be mostly the result of colleges doing damage control in a media era that has made coverups harder. But those very factors could fuel the trend further.

“This wasn’t a conversation people were having 10, 15 years ago,” says Dan Lebowitz, executive director of the Center for the Study of Sport in Society at Northeastern University in Boston. “Whether [these changes] should have come earlier, or how they came, is secondary to fact that they came.”

Indeed, the SEC rule is part of “a larger idea that has been in the works for some time,” adds Michael McCann, founding director of the Sports Entertainment and Law Institute at the University of New Hampshire School of Law.

The 14-school SEC passed its new transfer rule in May 2015. This week, the SEC is expected to expand that rule, redefining “serious misconduct” to include “dating violence or stalking and conduct that raises serious concerns about the safety of others.” The schools will also be expected to complete an “appropriate inquiry” into any potential transfer before giving a scholarship offer, CBS Sports reported.

The move, says Mr. McCann, represents “some concrete steps that are being taken to mitigate the underlying issues.”

And the idea appears to be gaining more support, at least within the SEC. A big difference between this spring and last year is that “there is unanimous agreement on the changes” among the conference’s head football coaches, The New York Times reported.

The expanded policy is hardly a cure-all, experts say. For one, it does not cover incoming freshmen, who make up the bulk of recruits every year.

A 2011 Sports Illustrated/CBS Sports criminal background check on every player in the top 25 college football programs found that only 7 percent had been charged with or cited for a crime. But Mr. Lebowitz suggests that the rule should apply to freshmen, too.

“If we’re trying to set a standard, we should set a standard.”

There are concerns about the pendulum swinging too far the other way, with schools cracking down in ways that abridge the rights of the accused or don’t allow for reform.

The SEC policy, for example, was adopted after the University of Georgia dismissed defensive lineman Jonathan Taylor in 2014 following a domestic violence arrest, only for Mr. Taylor later to transfer to the University of Alabama, where he was again charged with domestic violence. But Taylor’s accuser at Alabama recanted her statements after he was dismissed.

To critics, the policy is simply a way to avoid negative PR. The SEC not only leads the nation in producing national champions, it has led the nation in football player arrests every year since 2011, according the website arrestnation.com, which tracks the arrests of professional and college athletes.

“This is about marketing, this is about public perception,” says Richard Johnson, a Cleveland-area lawyer with years of experience arguing cases against the NCAA.

“They’re mimicking what the professional leagues are doing,” he adds. “If a player is caught beating his girlfriend or doing drugs it looks bad on the product, and the product is college football.”

But those changes have come about because of intense media scrutiny and public outrage. And those aren’t expected to diminish. Moreover, the United States Department of Education is more actively investigating Title IX sexual violence investigations.

In short, there is a sense that society’s expectations are slowly shifting, and college football is having to cope.  

The “sport has come a long way from the cesspool in which it resided 30 years ago. The sport is cleaner than it used to be,” wrote Mr. Maisel of ESPN.

For his part, Lebowitz says he wouldn’t be surprised if other conferences begin adopting similar policies to the SEC.

“When people think about college football they think about the SEC,” says Lebowitz. “They’re the conference that everyone has their eyes on, so when they adopt a policy that’s integrity-based people have their eyes on that, just like they have their eyes on who wins the national championship.”