Amanda Graves is a senior at a public high school in New Jersey.

Harvard University. (AP Photo/Lisa Poole)

Dear Amanda,

As the Dean of Yale College, I write to congratulate you on your academic success and to introduce you to Yale’s diverse opportunities and communities…. As you consider your college options, I hope that Yale remains among your top prospects.

This is part of an e-mail I received from the prestigious Ivy League university this September. I admit, it made me feel pretty special, having Yale, one of the best universities in the world, court me, a fairly average high school senior from New Jersey.

But why me?

My grades are nothing to brag about, and I didn’t qualify for the National Merit Competition. I haven’t led a team sport, conducted scientific research or been in all-state band. My mom might tell me I’m brilliant, but I’m not even in the top quartile at my public high school (though admittedly, that quartile is jam-packed with overachievers, and ranges from 3.9 to 4.54).

Naturally, I went to Google. I learned that each year, Yale courts not only me but roughly 79,999 other prospective students (down from 240,000 in 2005) for its class of 1,300. For the class of 2018, Yale rejected 93.7 percent of its applicants.

Immediately, that grandiose vision of me, strolling through New Haven in a bulldog sweater, conversing about important intellectual matters with my esteemed peers and professors, was halted by an abrupt reality check.

I’m not alone. Each year, colleges reach out to thousands of students with fancy brochures and solicitous e-mails, inviting them to apply. They contact many more students than they’ll accept, buying names for less than 50 cents a pop from places like the College Board, which has data on students’ PSAT or SAT range, self-reported GPA, ethnicity, religion and potential major. (Students must opt in before their data is shared).

Here’s why: Colleges want prestige, and a high ranking on the infamous U.S. News and World Report lists. One way to get it? Low acceptance rates, which come from lots of applications.

How to get lots of kids to apply? Swarm them with enough love and attention and eventually, some will succumb to the appealing notion that they’re good enough for top college X, Y or Z. (It’s working. According to Bloomberg, the number of high school graduates dropped 2.2 percent between 2008 and 2011. But college application numbers are soaring.)

Then, a big chunk of them are rejected.

This, I assume, is how I ended up hearing from Yale, even though I have approximately zero percent chance of getting in. According to the College Board, 95 percent of Yale’s enrolled students were in the top decile of their high school; 100 percent were in the top quartile.

Colleges defend their outreach, arguing that they’re reaching students who might otherwise never apply. According to William Fitzsimmons, dean of Harvard admissions, “There are so many students out there in the world who might not automatically think about Harvard as a place to go…. The odds of reaching the top of anything are not good, but is that a reason not to try?”

These colleges argue that the best low-income students don’t apply to the most competitive schools because they haven’t heard of them, don’t have an ally to guide them through the application process, or don’t realize that most top schools offer extensive need-based financial aid.

But these kids don’t need pamphlets and false hope. They need experienced guidance counselors who can help them through the complicated process.

The majority of the students that Fitzsimmons is talking about don’t consider Harvard because they’re not academically qualified. It’s like telling a slow runner with no chance at the Olympics to “train, train, train.”

One last example: When I was a sophomore in high school, the University of Chicago started sending me brochures and e-mails about how I should:

“discover all the extracurricular opportunities that the University of Chicago has to offer and consider becoming part of our talented, motivated, and involved community. Whether it’s fighting zombies or giving back to the community, at UChicago there’s not just something to do every day — there’s something you want to do.”

As a naive high school sophomore, I felt pretty special having all of this attention from such a great school.

Going into sophomore year, however, I had a weighted 2.9 GPA. I scored 110 out of 160 on the math and critical reading sections of the PSAT, equal to an 1100 on those sections of the SAT.*

For the class of 2016, UChicago’s middle 50 percent of test scores for math and critical reading were in the range of 1440 to 1540. And for last year, only 1 percent of enrolled first-year students had GPA’s between 3.00 to 3.24 (there’s no data for the 2.50 to 2.99 category). Though my GPA has thankfully gone up (as has my SAT score), I was not nearly qualified when UChicago started courting me.

Even now, it’s extremely unlikely that I’ll get in. No students were taken below the top quartile for the class of 2018, and altogether 91 percent of its applicants were rejected that cycle. Nice try, but I’d rather apply at places that I actually have a chance at getting into.

So Yale, UChicago (and Brown and Cornell and Dartmouth and Columbia), stop giving me a false sense of hope.

UChicago did send me an unsolicited fee waiver a while back though, and did extend its Early Action deadline just for me. Maybe the university really does want me?

Clarification: An earlier version of this piece compared the authors unweighted GPA to Chicago’s weighted statistics. The author’s GPA has been updated.