CINCINNATI — Xavier bristles whenever anyone suggests it’s doing quite well for a mid-major school. Another trip to the NCAA’s round of 16 might finally remove the hyphen.

There’s no mid-anything about the Jesuit school, which is growing a reputation as a major player in college basketball.

The Musketeers (26-8) are in the NCAA tournament’s round of 16 for the third straight year. Only one other school — Michigan State — can match that. And the Musketeers’ pre-eminence has nothing to do with March surprises or tournament upsets.

They drew it up that way. They spend that way. They win that way.

“Everything in our program is first-class — how we travel, how we recruit, the use of charter planes, the Cintas Center, how we schedule,” coach Chris Mack said, in an interview.

There’s a formula for winning in college basketball, one that applies to programs big and small. In the last decade, Xavier has gotten it right.

The Musketeers are making their ninth NCAA tournament appearance in 10 years and their fifth in a row, set to play Kansas State in the regional semifinals on Thursday in Salt Lake City. Only a dozen schools have made the NCAA tournament each of the last five years: Xavier, Duke, Kansas, Michigan State, Tennessee, Pittsburgh, Marquette, Gonzaga, Texas, Texas A&M, Villanova and Wisconsin.

The small university — 4,200 undergraduates — began emerging as a regular NCAA tournament team in the 1980s, when it played in a Midwestern Collegiate Conference that was the definition of mid-major. As the acclaim grew, the school’s administration decided the basketball program could raise its profile and give it a face across the country.

It wasn’t going to be easy or cheap to become one of the best.

“The formula is simple,” athletics director Mike Bobinski said, in a phone interview. “Being successful isn’t all that simple. If it was that easy, there would be more than just a couple of teams advancing deep in the tournament every year.”

Xavier moved up to the Atlantic 10, which had some of the nation’s top teams in Temple and Massachusetts, for the 1995-96 season. Five years later, it opened the state-of-the-art Cintas Center on campus, which became a springboard to much bigger things.

“If you want to be successful at a high level, your investment and commitment need to be at a high level,” Bobinski said. “You can’t have one without the other.”

In terms of facilities and finances, Xavier had left the mid-major ranks. It was competing with the big boys. Soon, it would be beating them, too.

Since the 10,250-seat arena opened, Xavier has won or shared six A-10 regular-season titles, including the last four. The Musketeers have been a regular in the national rankings, making it up to No. 7 last season. And at tournament time, they’ve excelled.

A big part of the equation is Xavier’s willingness to play the nation’s best in the nonconference schedule. In the past three seasons, that schedule has included schools such as Duke, Florida, Tennessee, Kansas State, Missouri, LSU, Indiana, Virginia, Auburn, Virginia, Butler, Wake Forest, Marquette, Memphis and Creighton.

“The double-edged sword is that you’ve got to be good at it,” Bobinski said. “If you are going to put that out front, it behooves you to be successful more often than not.”

They’ve been successful so often now that they can’t help but wince when someone suggests the program is something less than a major success.

“I mean, I don’t know a lot of mid-majors that make three consecutive Sweet 16s,” said center Jason Love, the only senior on the team. “So you can throw that out of the door right now.”

The school has a knack for hiring the right coach to take the program to the next level — Pete Gillen, Skip Prosser, Thad Matta, Sean Miller and now Mack, a Cincinnati prep star who played at Xavier and has watched the program outgrow the mid-major label.

“It gets under our skin,” Mack said. “I guess I just have a hard time defining that label. There’s nothing in our program that we feel isn’t high-major, from how we recruit to the travel to the facility to the nonconference schedule to the NBA players (from Xavier). I think it all speaks to a high-major program.”

With each NCAA tournament win, the Musketeers make their point.

“I would say all you have to do is lay out our accomplishments on paper,” Bobinski said. “The last 10 years speak for themselves.”