This year’s NCAA Tournament might have been played without popular schools including Maryland, Kentucky, Louisville or Tennessee under a plan advanced by U.S. Secretary of Education Arne Duncan aimed at increasing the current player graduation rates of each of those programs.

Duncan announced a proposal on March 17 to restrict men’s college basketball teams from participating in the “Big Dance” or any postseason play if they do not graduate at least 40 percent of their players.

If his idea was in effect this year, at least 12 programs wouldn’t be tournament eligible, according to a study from the Institute for Diversity and Ethics in Sport at the University of Central Florida.

The Associated Press reported that the ineligible schools would include No. 1 seed Kentucky, one of the teams President Obama recently predicted would reach the Finals. Kentucky graduated only 31 percent of its players last year.

“Frankly, that’s a low bar, and not many teams would be ineligible,” said Duncan, who played college basketball at Harvard University. “Over time, we should set a higher bar. But it’s a minimum, a bright line, which every program should meet to vie for postseason honors.”

According to the AP, Duncan said that, of the 65 teams in this year’s NCAA tournament field, 45 teams graduated 70 percent or more of their White players, 12 more teams than last year. Yet only 20 teams graduated 70 percent of their Black players, the same number as in 2008.

Maryland is one of two teams that graduated no Black players that enrolled from 1999 to 2002.

NCAA spokesman Bob Williams told the AP that the association is also concerned about low graduation rates, but said he believes restrictions based on graduation rates wrongly punish some current student-athletes as well as schools with players who transfer or decide to play professionally.

“What we want to do at the end of the day is change behavior so that when people come to college, they have to be prepared to do the work and institutions are prepared to support them academically,” Williams said. “We shouldn’t measure success by how many teams receive a ban.”

Georgetown University coach John Thompson III, whose school has high graduation rates, agreed with Williams, calling Duncan’s proposal “harsh.”

“That’s just my initial thought,” Thompson said, one of four African-American coaches to reach the tournament this year. “When you say graduate, what time frame are we talking about? What are the other factors that fall into place? Are we talking about a four-year window, five-year window, 10-year window? Our responsibility is to help young men grow up.”