Stanford is the most-selective school in the country, admitting about 5 percent of its applicants, making it more difficult to get into than Harvard (5.3 percent), Yale (6.5 percent) and Princeton (7 percent). And for several years now, Stanford has been drawing more financial support from donors and alumni, too. The school’s leaders say it’s because Stanford, in California’s Silicon Valley, is acting like the tech companies that have boomed around its edges, coming up with “bold ideas.”

“Trust in the institution and trust in the leadership,” Stanford’s outgoing president John L. Hennessy said. “We try to come up with bold ideas with a different approach to thinking about things, with something we can argue will really create an opportunity for more great things to happen in the world.”

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Stanford’s latest “bold idea,” a leadership program for graduate students, has landed the school its single largest individual donation — a $400 million gift from Nike co-founder and chairman Phil Knight. The money will fund 300 scholarships for high-achieving students with demonstrated leadership and civic commitment. Students must take courses designed to make them effective leaders in addressing environmental, health, education and human rights problems around the world.

“I have every confidence that the program is going to be great,” said Knight, who earned his MBA at Stanford in 1962. “The distinguishing thing is it has great leadership. John has been — if he’s not the best president of any university in the country, he’s certainly in the top two or three. He will lead this program and that’s what’s going to make it succeed.”

Hennessy will become the program’s inaugural director once he steps down as president this summer. During his 16 years at the helm, Stanford has received some of its largest charitable contributions, including a $400 million donation from the William and Flora Hewlett Foundation.

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Alumni have been especially generous to Stanford. Knight previously gave the school $105 million to fund the graduate school of business in 2006. Real estate mogul John Arrillaga gifted the school $151 million in 2013, two years after Robert and Dorothy King gave $150 million to establish the Stanford Institute for Innovation. The Kings also contributed $100 million to the new scholars program.

In the 12 months ending June, Stanford raked in $1.6 billion in charitable contributions, more than any other college or university in the country, by far, according to an annual survey from the Council for Aid to Education. Stanford has been a top-ranked recipient for years, said Ann E. Kaplan, who directs the survey at the Council. She suspects that has as much to do with the scope of its offerings as it does with the strength of its development office.

“These are multi-purpose nonprofits, not just educational institutions,” Kaplan said of universities that receive sizable contributions. “They have medical schools, so they get money for research. They have museums, so they get gifts of art. The more programs you have … the more varied a case for support you can make.”

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Many of the same elite schools that pull in big dollars also have out-sized endowments. An analysis by Moody’s Investors Services shows the wealthiest 40 universities grew their overall assets by 50 percent in the past five years, while the schools at the bottom increased theirs by 22 percent. In other words, the richest schools get richer, while the rest compete for a fraction of their resources.

Twenty schools accounted for more than 25 percent — or $11.5 billion — of the donations reported to the council. Harvard University trailed Stanford with $1 billion in contributions, but the two of them dwarfed the third school on the list, the University of Southern California, which raised $653 million.

“Many philanthropists I’ve met think the same way Phil thinks,” Hennessy said. “They want to make an investment in something that has a compelling return, a compelling change in the world. We’re an institution that was founded in the service of humanity, and we try to remember that and put it into practice.”