INDIANAPOLIS — Cash counts in college sports — even in the classroom.

On Wednesday, as the NCAA released Academic Progress Rate numbers showing record highs, the same stats revealed the richest athletic departments are making the grades. Others aren’t so fortunate.

Fifteen of the 21 teams hit with postseason bans and 23 of the 28 teams being sanctioned with some other penalty are from institutions defined as limited-resource schools. And that comes after the NCAA implemented a higher cutline, 930, for some of those schools two years ago.

No school in the Football Bowl Subdivision, which includes the five wealthiest conferences of the ACC, Big Ten, Big 12, Pac-12 and SEC, was penalized.

Overall, the numbers are improving. Fewer teams were penalized this year, the four-year average, 978, is a two-point increase over last year’s previous record high, and two sports that have traditionally lagged others, men’s basketball and football, both produced significant increases.

Football scores improved five points to 956 while men’s basketball increased its score to 961, up four points. Scores in baseball (969) and women’s basketball (975) both jumped two points, mirroring the overall increase.

“We are pleased and proud of their accomplishments,” NCAA President Mark Emmert said. “Our goal always has been to encourage students to achieve academically and earn their degrees. Every year, Division I students prove that both academic and athletic success are achievable.”

Scores are calculated by awarding an athlete one point each semester they remain academically eligible and another point each semester if they stay in school. A perfect score is 1,000.

Critics have long contended that the APR is not an accurate measure of academic progress because the numbers can be skewed by various factors such as clustering athletes in certain classes or majors or steering students to certain instructors. They also say athletic departments at the wealthiest schools are seeing the dividends of investing heavily in academic resource centers and tutors — something other schools cannot do.

Teams competing in the five power conferences had an average APR score of 985. Teams in all the other conferences had an average score of 979. The power conferences also had better scores in eligibility (987 compared with 981) and retention (979 to 974).

Five Football Championship Subdivision teams — Alabama State, Florida A&M, Gardner-Webb, Savannah State and Tennessee State — received postseason bans. Men’s basketball teams at Alcorn State, Central Arkansas, Florida A&M and Stetson also will not be eligible for next year’s NCAA tournament. The only women’s basketball team on the banned list was Savannah State.

All of those schools with the exception of Central Arkansas, Gardner-Webb and Stetson are considered historically black colleges or universities.

Emmert believes the improvements are not necessarily driven by finances even as he promised to continue looking for more ways to help.

The Committee on Academics, which is chaired by Ohio University President Roderick McDavis, is expected to make a formal recommendation in January to the NCAA board to help low-resource schools achieve more academic success.

“The academic performance of limited-resource schools is improving faster than that of any other part of the Division I membership,” Emmert said. “The goal of the academic performance program is to encourage teams to improve academically, not punish those who underperform. We will work with HBCUs and limited-resource schools to make sure their college athletes have every opportunity to succeed academically.”

Another troubling trend showed up in transfer rates between four-year schools, particularly in men’s basketball, which hit a record high of 13.4 percent in 2013-14. In 2003-04, the first year of the report, it was 9.4 percent.

That’s a huge increase when compared with football, which has seen the percentage of transfers go from 3.6 percent in 2003-04 to 3.7 percent last year, and is more than double the increase in women’s basketball, which has climbed from 7.6 in 2003-04 to its current 9.2 percent.

McDavis said nearly 14,500 college athletes also have returned to school and earned their degrees since the NCAA first started measuring the APR in 2003-04.