Michael Bloomberg speaks at Johns Hopkins Bloomberg School of Public Health on January 14, 2013.Patrick Semansky / AP

Michael Bloomberg, the billionaire philanthropist, announced a double-take-causing donation to Johns Hopkins University on Sunday. The former mayor said he would be giving $1.8 billion to his alma mater. It’s the largest single donation to an American university in history—and the continuation of a trend for Bloomberg, who has made a habit of donating to Johns Hopkins.

Several reports and observers heralded the gift as transformational, one that would allow the university to go need-blind permanently—meaning a student’s ability to pay would have no bearing on admissions decisions. “I want to be sure the school that gave me a chance will be able to permanently open that same door of opportunity for generations of talented students, regardless of their ability to pay,” Bloomberg wrote in The New York Times, announcing the gift. The donation to Hopkins is earmarked for financial aid for low- and middle-income students. “It will ease the burden of student debt for many graduates,” Bloomberg wrote. “And it will help open up the American dream to more young people.”

But there’s often an asterisk next to large donations to elite institutions such as this one. How transformational can they really be? Johns Hopkins, Harvard, Yale, and other such colleges have incredibly low acceptance rates—and so the transformational donations, no matter how large, can affect only a relatively small number of students.

Of course, what puts Bloomberg’s gift in a class of its own is not only its size but also its intent. In being earmarked for aid for low- and middle-income students, says Ted Mitchell, the president of the American Council on Education, it highlights the need for colleges to support those students. “This gift is identifying the sore points in the system where we need to do better in order to help students succeed,” he says. Not only through philanthropy, but also in public policy.

Yes, donations such as Bloomberg’s help institutions provide aid to low- and middle-income students. And that in turn may enhance the schools’ ability to enroll more of those students. But it’s important to understand the scale of the solution. Johns Hopkins and other selective, elite universities enroll a small proportion of the roughly 13.3 million students attending four-year institutions. Hopkins, for example, enrolled 1,319 new students this fall, and each year, there are roughly 5,500 undergraduate students. Most higher-education students are enrolled in public institutions, where state funding is drying up, and transformational philanthropic gifts are rarer. Perhaps the money could have a bigger impact if it were dispersed among institutions that need it more.

Of course, wealthy people can do what they want with their money. Often big gifts are donated to institutions by alumni. And Bloomberg’s continued philanthropy to an institution whose profile has been raised alongside his giving offers a lesson: that institutions can hit the lottery if they have one graduate who strikes it big. As Walter Kimbrough, the president of Dillard University, wrote in 2015, following another largest donation ever—to Harvard University, from John Paulson: “Paulson and Harvard only need to say that Harvard is his university, nurtured him, and he is blessed to do whatever he can for something he loves like family … This is in fact the best, most succinct and sincere answer they can and should give.”

Still, there are examples of what such a large gift could do for a smaller institution. Rowan University, a public research university in New Jersey, for example, received a $100 million donation from Henry and Betty Rowan in 1992, and has since doubled its enrollment (and changed its name to honor the Rowans—it used to be called Glassboro State College).

Bloomberg’s donation puts Hopkins in a class with other selective institutions, such as Harvard, Yale, and Princeton, in terms of making highly selective education affordable for low-income students. But those institutions that are still struggling—such as the public regional colleges reliant on state funding that is becoming scarcer, and the students who attend them—are still waiting for their transformations.

It’s possible that Bloomberg’s donation will open the door for more philanthropists to best him. But history has shown that such donations have time and again gone to wealthy institutions. Maybe Mark Zuckerberg or Jeff Bezos will sink $2 billion into an institution. But if they donated that money to their alma maters, it’d be much the same situation. Zuckerberg went to Harvard, and Bezos went to Princeton.

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