Crossing the Finish Line, a new and impressive book by former Princeton president William Bowen, former Macalaster College president Michael McPherson, and Matthew Chingos,  relied on two massive databases on the entering class of 1999–one on 96,000 first-time freshmen and 30,000 entering transfer students at 21 flagship universities and the other on 108,000 freshmen and 42,000 transfers at less selective state colleges and universities in four states (Maryland, North Carolina, Ohio, and Virginia)–to compile a wide-ranging book of empirical research on topics impacting American higher education. This is the fourth in a series of posts on their findings (see previous installments on affirmative action, financial aid, and transfer students).

Admissions at America’s colleges and universities are affected by two countervailing trends. According to a new study, spots at the top ten percent of institutions have become more competitive over the last few decades, while about half of our colleges and universities have become less competitive.

Crossing the Finish Line features a table that would help students understand their chances of acceptance far better than the traditional average-high-school-GPA-and-SAT-scores-of-incoming-freshmen measures that are commonly used. It’s a simple grid, with high school GPA on one side and SAT score on another. In each of the cells is the percentage of students offered a seat. So, if you were a high school student with a certain GPA, you could see your chances of admission based on various SAT scores. Here’s are the admission percentages they found for North Carolina high schoolers with a 3.3 GPA applying to UNC-Chapel Hill and NC State in 1999, by SAT score range:

• Below 800: 2.6
• 800-890: 20.7
• 900-990: 22.1
• 1000-1090: 41.9
• 1100-1190: 63.3
• 1200-1290: 73.2
• 1300-1390: 92.7

These types of grids are easy to understand, don’t take up that much space, and would help prospective students gauge their chances of admission far more than current measures.

Our colleges and universities are sometimes criticized by conservatives for letting too many students in. They argue we could improve graduation rates and institutional quality simply by imposing stricter entry requirements. Crossing the Finish Line shows that’s not true.

The chart below shows the actual and hypothetical graduation rates by institutional selectivity. The “hypothetical graduation rate” was determined by retroactively rejecting all applicants with a high school GPA of 3.0 or below. As the chart shows, the effects were practically nil at selective and moderately selective institutions. Historically Black Colleges and Universities (HBCUs), which were the extreme case in that they would have had to reject 60 percent of their students in the hypothetical, would have seen their graduation rate rise only 10 percent. This suggests there is some trade-off between access and completion, but it’s not as large as one might expect (the authors did the same analysis with an SAT cutoff of 1000 and found similar results).

This chart provides a nice, empirical rebuttal to all those who say we have too many college students or that entrance standards are too lax. Let them in, then help them succeed.