By now you know the story: Three days ago, University of Missouri footballers offered administrators an ultimatum: University system President Tim Wolfe had to go or the team wouldn’t play. Monday morning, Wolfe resigned. Credit players and protesters, led by hunger-striking grad student Jonathan Butler, for drawing attention to Wolfe’s failure to address campus racism.

But beyond applauding the activism of students, it’s important to understand what’s at stake at Missouri and other campuses — like Yale University, where students at the Silliman residential college have taken on their live-in faculty advisers over competing views about the impact of racially insensitive Halloween costumes — is college survival itself: In hostile environments, students of color graduate at lower rates, jeopardizing not only their academic careers but also future success.

In one sense, given the controversies at Mizzou — where a hostile campus climate serves as a mechanism by which students of color remain outsiders — the students didn’t have a choice. It would be illogical, and self-defeating, if they didn’t use the power they had at their disposal.

Campus racial climate has been linked to academic success. And research has long shown that academic preparedness is only one of many factors that determine why students do or don’t graduate. The psychological attitudes between and among groups, as well as intergroup relations on campuses, influences how well students of color perform and whether they stay on track toward graduation. Graduation rates lag when schools don’t provide an environment that fosters the scholastic pursuits of minority students, particularly black men.

Researcher Sylvia Hurtado explains that “Just as a campus that embraces diversity provides substantial positive benefits, a hostile or discriminatory climate has substantial negative consequences.” Her research found that “Students who reported negative or hostile encounters with members of other racial groups scored lower on the majority of outcomes.”

A study of students at the University of Washington found that black students there were the only campus group to suffer a clear statistical GPA disadvantage from a nasty campus climate: “Results indicate that campus climate is significantly related to academic achievement of African American students, as represented by GPA, accounting for about 11 percent of the variance.” That means black students facing adverse conditions are likelier to leave college early — and would, presumably, be likelier to stay in what they felt to be a safe space.

In “Interactional Diversity and the Role of a Supportive Racial Climate” the University of Maryland’s Leah Kendra Cox found much the same thing: “In unhealthy climates, students — both majority and minority — are less likely to thrive academically or socially.” She found that a supportive racial climate had more impact than any other factor on the strength of diversity on campus.

Perhaps not coincidentally, a Gallup survey last month illustrated that students at Historically Black Colleges and Universities, or HBCUs — where the climate, by design, nurtures students of color — were far more likely to “strongly agree that their colleges prepared them for life after graduation (55%) than black graduates of other institutions (29%).”

In that context, consider the reports of what’s taken place in the Mizzou community. In September, Missouri Students Association President Payton Head, who is black, took to Facebook to report being called the n-word by a driver in a passing car as he walked down a street near campus. In early October, the Legion of Black Collegians tweeted that intoxicated white students had shouted the n-word at them during a campus protest. Later that month, tensions flared when someone smeared feces in the form a swastika in a campus bathroom — creating the kind of climate that alienates and marginalizes minority students, who have just as much right to pursue their education on the Missouri campus, free from harassment, as anyone else. Students still remember the 2010 incident in which two Missouri students were suspended for dropping cotton balls in front of the campus’ Black Culture Center.

Wolfe’s inaction, in the face of repeated demands to better address students’ frustration with the charged campus environment, precipitated his ouster. Though he later apologized, many cite his failure to engage with students — remaining cloistered in his car — when approached by the campus group ConcernedStudent1950 at a homecoming parade, as one of the last straws that ended his administration.

And while commentators like Rush Limbaugh say Wolfe resigned for “committing the crime of being a white male,” their argument, beyond the hyperbole, is the wrong way to evaluate the relationship of the university to its students. Wolfe’s job was to use the resources at his disposal to build a campus community where all students feel they can pursue their academic careers in an environment where they’re respected and taken seriously. But as Butler told The Post:

When you localize it to the hunger strike it really is about the environment that is on campus. We have reactionary, negligent individuals on all levels at the university level on our campus and at the university system level, and so their job descriptions explicitly say that they’re supposed to provide a safe and inclusive environment for all students … but when we have issues of sexual assault, when we have issues of racism, when we have issues of homophobia, the campus climate continues to deteriorate because we don’t have strong leadership, willing to actually make change. So, for me, I’m fighting for a better tomorrow. As much as the experiences on campus have not been that great for me — I had people call me the n-word, I had someone write the n-word on the a door in my residence hall — for me it really is about a call for justice. I’m fighting for the black community on campus, because justice is worth fighting for. And justice is worth starving for.

So is education. The U.S. Department of Education found markedly lower graduation rates for blacks and Latino men (33.2 percent and 44.8 percent, respectively, graduate from college within six years) compared with their white and Asian peers (57.1 percent and 64.2 percent, respectively). These disparities have been depressingly constant in recent years. One factor contributing to these disparities is that universities frequently place a premium on meeting the (short-term) needs of black athletes in revenue generating sports while paying lip service to the needs of other students of color.

From the disciplines faculty teach in to the traditions they uphold, predominantly white institutions haven’t fully dealt with the changing demographics of collegians. For many students, especially first-generation collegians, these institutions often place the burden on students to adapt to an unwelcoming environment. But the Missouri case illustrates the imperative for colleges to transform what they are and who they serve if they are to fulfill their mission of addressing societal problems, training the workforce and educating the public. And black student-athletes, who are overrepresented in the major-revenue sports — football and basketball — may be uniquely empowered to move university leaders who, in the case of the University of Missouri, at least, didn’t demonstrate they were otherwise compelled by the data.

If colleges can prioritize the needs of students of color in their athletic programs, they also can prioritize the development of scientists, historians and teachers of color. In order to do this, postsecondary institutions must change at a structural level.

One approach would be to transition their merit-based scholarships into need- or place-based scholarships. First-generation collegians should have access to living-learning communities in which dormitories provide wrap-around supports. Colleges must attract and retain black and brown faculty at much higher levels. Faculty must embrace their role as counselors, not just instructors or researchers. Academic support for first-generation collegians shouldn’t be treated as remediation. Finally, faculty and administrators should be held accountable for graduation rates.

Success isn’t just on students’ shoulders.