In a year in which Yale received a record-breaking number of applications, the University still came in at the middle of the Ivy League in terms of admissions selectivity.

Nearly all Ivy schools saw a drop in admit rates this spring as a result of increased numbers of applicants. Yale’s 13.5 percent admit rate dropped at a greater rate than most Ivies, bringing the Bulldogs back into the top half of the league in selectivity.

Yale administrators said they pay more attention to matriculation rate — the number of students that chooses to attend the University — than the admit rate.

The admit rate is the percentage of students admitted out of those who applied. Greater selectivity indicates that a school has a lower admit rate and accepts a lower percentage of applicants than less selective schools do.

Harvard, Princeton and Columbia universities saw the lowest undergraduate admit rates of the Ivies at 10.7, 11.7 and 12.2 percents, respectively. Stanford University was also ahead of Yale with a 12.7 percent rate for undergraduates.

Columbia’s 12.2 rate incudes applicants for the liberal arts school, but not its school of engineering and applied sciences. Combining applicants for the two schools brings Columbia to a 14.3 percent admit rate.

These four schools’ admit rates are all less than a one percentage point drop from last year. Yale’s admit rate dropped 2.3 percentage points this year — from 15.8 percent to 13.5.

Yale has shifted its position among the top few Ivies for selectivity over the past few years. Three years ago Columbia edged out Yale for the third-lowest Ivy League admit rate, and last year Brown University bumped Yale from its seat at number four.

But Yale is back in the fourth position this year, in part because Brown saw a slight slip in selectivity. Yale’s new position reflects its rise in applications and a planned 50-person freshman class cut. In all, Yale accepted 2,000 of its 14,809 applicants.

Brown’s admit rate came in at 15.9 percent this year, slightly higher than last year’s record 15.1 percent.

Rounding out the Ivies, the University of Pennsylvania, Dartmouth College and Cornell University had rates of 21.5, 22.8 and 25.9 percents, respectively.

Penn and Dartmouth’s rates did not change very much from last year. But Cornell’s rate was a nearly five percentage point drop, raising the school’s selectivity.

Admissions officials said greater numbers of applicants allow them to select better classes.

Among the most touted qualities of an admitted class is its diversity. Stanford’s admitted class stands out in diversity with 49.9 percent coming from minority groups. In contrast, 35 percent of Princeton’s, about 44 percent of Harvard’s and 42 percent of Yale’s acceptances are students of color.

But these figures are subject to change.

Admit rates will go up if schools must dip into their wait lists to fill out their classes. And the diversity of the actual classes can be very different from the diversity of the admitted classes, based on who chooses to enroll where.

So in the meantime, admissions officials are making phone calls and welcoming students to visit campus.

“I think the challenge is to enroll as many of the students as possible and really roll out the red carpet to them,” Penn’s Dean of Admissions Lee Stetson said.