“You can’t go to a college fair anymore and say you have these grades and you’re in,” said Eric J. Furda, the dean of admissions at the University of Pennsylvania. While an applicant’s high-school GPA and test scores still carry considerable weight in admissions decisions at Penn, which had 40,000-plus applicants in the admissions cycle that ended this spring, those numbers are what Furda called a “snapshot” of a student’s life—grades from a few years of high school, or how one performed on a test on a particular day.

Furda encourages his admissions counselors to balance the “absolute merit” of grades and test scores with what he calls the “relative growth and trajectory” of applicants. “Our evaluation process looks at where they are right now and what can we expect from them once they come to our campus,” Furda said. Take, for example, applicants from private high schools or top public schools. “We expect them to have high test scores and grades,” he said. “That’s a given. So another way for us to think about merit for those applicants is, what did they do with that opportunity they were given? How far did they travel in their high school journey?”

Applicants will have a far harder time acting on such guidance than if securing admission were as clear-cut as getting a 1500 on the SAT and a 3.8 GPA. It was never quite that simple, but Furda noted that the admissions system has changed drastically in the past few decades: For the high-school graduating class of 1991, Penn accepted nearly half of its applicants. This year it accepted just 8 percent, a record low.

Applying to college has become much more stressful in the intervening years—and it only is becoming more so, as high test scores and GPAs become less certain indicators of acceptance. These days, applicants and their parents demand “absoluteness” in admissions, said Furda, who every April answers complaints from rejected applicants who compare their academic backgrounds to those of accepted students they know. The issue for Penn and other top colleges is that as applicants’ test scores and grades rise, the ability to distinguish among them becomes ever more difficult, if not impossible.

This challenge comes as Penn and other selective colleges are under pressure to increase their enrollment of low-income and first-generation students. Whatever changes they make to their admissions policies, particularly how they weigh test scores and grades, will surely be noted by competitors but also by less selective schools. “The admissions process is what it is because of the top colleges,” said Jon Boeckenstedt, the associate vice president for enrollment management and marketing at DePaul University. “They have the influence to change it.”

Indeed, when I told one admissions dean at an Ivy League school that I’d heard that another selective college might drop its standardized-testing requirement in the coming months, his reaction was one of relief. “That would give me an opening to follow,” he said. “We just can’t be first.”