That’s why some students are applying to 20 or more schools: to increase their odds of making a single match. The most important elite college admissions statistic, then, is not the percentage of applications top schools accept. It’s the percentage of top students who are admitted to at least one top school. And that number isn’t 5 percent or 20 percent or even 50 percent. It’s 80 percent. It turns out that four out of five well-qualified students who apply to elite schools are accepted by at least one.

These numbers come courtesy of Parchment.com, a website that helps students submit college transcripts electronically and navigate the admissions world. Services like Parchment and the Common Application are among the reasons it has become easier for students to submit more applications and drive down institutional admission rates. This year, 800,000 students used Parchment to send more than 1.6 million transcripts.

Parchment began by identifying a subset of students with combined SAT scores (or an ACT equivalent) of at least 1300. Then it identified high-scoring students who had applied to at least one of the 113 schools identified by Barron’s Profiles of American Colleges as the most selective. The average overall admission rate among those schools was about 32 percent. Yet 51 percent of the applications submitted by top Parchment students to the same colleges were accepted. Why? Because top schools receive a substantial number of applications from underqualified students who are almost always summarily rejected. Once the wheat and chaff are separated, the success rate for the wheat looks much better.

And the real odds of success were even higher than 51 percent. The top students in the Parchment database applied to 2.6 elite colleges, on average. Flip a coin twice and, according to probability theory, you’ll get heads at least once 75 percent of the time. Sure enough, 80 percent of top students were accepted to at least one elite school.

Since there has never been a time when 100 percent of well-qualified students were successful in the college admissions market, the truism that elite colleges are far more difficult to crack than in years gone by can’t be correct: 80 percent is too close, mathematically, to nearly everyone.

This doesn’t mean that aspiring students can drop out of the college admissions rat race entirely. There’s a keeping-up-with-the-Joneses aspect to sending out applications. The Parchment data suggest that students who apply to many schools are more likely to strike gold than those who apply to only one or two, which makes sense given the idiosyncrasy of the admissions process.

But this is mostly a matter of optimizing odds that are very good to begin with. So the next time you read about terrifyingly low college admission rates, don’t panic: If you work hard and get good grades and test scores, there is very likely a place in the best schools for you.