Higher education has never tapped one of its greatest human capital assets -- its alumni -- to provide a service that its students might value most.

A few months after Gallup released findings from the largest representative study of U.S. college graduates, there is much to ponder. The Gallup-Purdue Index surveyed more than 30,000 graduates to find out whether they are engaged in their work and thriving in their overall well-being. In simple terms, did they end up with great jobs and great lives?

We learned some stunning things. But one of the most important is that where you went to college matters less to your work life and well-being after graduation than how you went to college. Feeling supported and having deep learning experiences during college means everything when it comes to long-term outcomes after college. Unfortunately, not many graduates receive a key element of that support while in college: having a mentor. And this is perhaps the biggest blown opportunity in the history of higher ed.

Six critical elements during college jumped off the pages of our research as being strongly linked to long-term success in work and life after graduation. Three of these elements relate to experiential and deep learning: having an internship or job where students were able to apply what they were learning in the classroom, being actively involved in extracurricular activities and organizations, and working on projects that took a semester or more to complete.

But the three most potent elements linked to long-term success for college grads relate to emotional support: feeling that they had a professor who made them excited about learning, that the professors at their alma mater cared about them as a person, and that they had a mentor who encouraged them to pursue their goals and dreams. If graduates strongly agree with these three things, it doubles the odds that they are engaged in their work and thriving in their overall well-being.

When we looked at these three elements individually, we found that about six in 10 college graduates strongly agree they had a professor who made them excited about learning (63%). Fewer than three in 10 strongly agree the professors at their alma mater cared about them as a person (27%). And only about two in 10 strongly agree they had a mentor who encouraged their goals and dreams (22%) -- which means that about eight in 10 college graduates lacked a mentor in college.

Given how profound the impact of emotional support can be, it's thoroughly depressing to learn how few college graduates receive it. A mere 14% of all college grads strongly agree that they experienced all three elements of emotional support.

Is mentoring really too costly?

Gallup has talked with many higher ed leaders about these findings, and it has been heartening to learn how many leaders are energized by having fresh insights about the importance and value of mentoring relationships in college. But it has also been frustrating to hear how many believe it's too costly or unreasonable to ensure that every college student receives mentoring.

How is it possible that some leaders feel that this kind of experience is more expensive or less practical than building and maintaining multimillion-dollar athletic facilities or high-end residential complexes? Or that it's more difficult to provide mentors for students than it is to commit significant amounts of human and financial resources to eke out a few extra students in their admissions yield or create a massive machine to raise funds from alumni?

If your college or university wants to get serious about finding mentors for its students, it could start by looking at its own alumni base. Assuming your institution has been around for 10 years or more, your alumni are one of the greatest human capital assets it has -- not just as donors, but also as potential mentors.

Do some quick math: How many undergraduate students are currently enrolled in your college or university? And how many living alumni does it have? The number of alumni is most likely many times that of the current undergrads.

Let's use my alma mater, Duke, as an example. Duke has 6,495 undergraduate students. There are more than 140,000 members of the alumni association. If just 10% of Duke's alumni agreed to serve as mentors, it would have a pool of 14,000 alumni for its 6,500 undergrads. That's more than a two-to-one mentor-to-student ratio.

Imagine what would happen if your college applied just a portion of the staffing and budget for its development office toward recruiting alumni to mentor current undergraduates. This relationship doesn't have to be complicated. All that's required is two to three calls, Skype meetings, or Google Hangouts between an alumnus and an undergrad each year for one-to-one coaching, plus some basic framework for how they engage one another. How many of your alumni might take you up on this offer if you made a concerted effort to recruit them? As an alumnus, would you be willing to mentor a current undergrad for a few hours a year?

It's completely conceivable that, within just one year, a college or university could strive for a 100% mentoring experience rate for its undergraduates. It's simply a matter of valuing mentoring and making it happen. For example, in a recent study Gallup conducted of Western Governors University (WGU) alumni, 68% strongly agreed they had a mentor. That's more than three times higher than the national average of college graduates surveyed -- and at a fully online, adult-learner institution.

The WGU model, it turns out, includes direct mentoring for all students, from matriculation to graduation. It's possible for all institutions to do this in many different ways, and it doesn't have to be costly. And as a side benefit, imagine how much donations might rise among alumni who have a one-to-one relationship with a current undergrad.

Higher education has never tapped one of its greatest human capital assets -- its alumni -- to provide a service that its students might value most. It could be one of the most important changes a college or university makes toward supporting the success of its future graduates -- or the biggest blown opportunity in its history.

A version of this article originally appeared in Inside Higher Ed.