“The single biggest concern that I have among the threats to the collegiate model is simply the threat of integrity,” says NCAA President Mark Emmert. (David J. Phillip/Associated Press)

Amid a spate of recent high-profile scandals in college sports, NCAA President Mark Emmert said Thursday that he is serious about reviewing the organization’s penalty structure if sanctions are not deterring individuals from cheating.

“We cannot have coaches, administrators, parents or student-athletes sitting out there deciding: ‘Is this worth the risk? If I conduct myself in this fashion, and if I get caught, it is still worth the risk?’ ” Emmert said during a news conference Thursday in advance of the Final Four. “We don’t want those kind of cost benefit analyses going on.”

The NCAA’s enforcement arm has been under scrutiny in recent months because of investigations at Connecticut, Tennessee, Ohio State and Auburn, among other schools. Comments by Emmert, who succeeded the late Myles Brand in 2010, came one day after reports surfaced that Auburn boosters allegedly paid former football players and that a Texas-based football trainer allegedly shopped around a top prospect.

Among those who have been critical of some recent penalties handed down by the NCAA or by universities is ESPN broadcaster Len Elmore, the CEO of iHoops, a joint venture by the NCAA and NBA to improve the quality of youth basketball. Elmore said in an interview last month that “right now, if I am a young coach, and I am looking at the enforcement resources, I will take that chance to get that blue-chipper. What’s going to happen to me?

“If you go by precedent, what am I going to get, an eight-game suspension, maybe my salary cut in half. If I win a lot of games, I am going to sign a new deal and everything blows over. If I am a young, up-and-coming coach, I might take that route. What we need to have is sure, swift punishment that is going to deter.”

One of the most publicized and controversial recent rulings was the NCAA’s decision to clear Auburn quarterback Cam Newton, the eventual Heisman Trophy winner, to play in the Southeastern Conference title game even though the organization said his father broke rules by shopping him to another school. Critics argue that the ruling opened a Pandora’s box so parents can ask for money so long as their child pleads ignorance.

Wednesday brought plenty of new allegations for NCAA investigators to address in the coming weeks:

Four former Auburn football players told HBO’s “Real Sports with Bryant Gumbel” that they received thousands of dollars while being recruited by or playing for the Tigers. Auburn will now investigate claims that Stanley McClover, Troy Reddick, Chaz Ramsey and Raven Gray received cash payments in bookbags, envelopes and handshakes.

In addition, a former Texas A&M coach told ESPN that Texas-based football trainer Willie Lyles told Texas A&M that it had to pay more than $80,000 if it wanted to sign prospect Patrick Peterson in 2007. Peterson ultimately signed with Louisiana State and now, as a junior, is expected to be a top choice in the NFL draft.

Also on Wednesday, Ohio State football coach Jim Tressel apologized for letting people down in the wake of a scandal in which Tressel failed to report that his players sold memorabilia and received improper benefits. Ohio State has recommended that Tressel be suspended the first five games of this season, but the NCAA could levy additional penalties.

“The single biggest concern that I have among the threats to the collegiate model is simply the threat [to the] integrity,” Emmert said. “I have heard concerns expressed by people all around the country about the integrity of intercollegiate athletics right now, that people are seeing things that they don’t like and that I don’t like and that many people are concerned about.”

The college sports world also learned this week about the extent of nefarious behavior by Fiesta Bowl president and CEO John Junker, who was fired for “an apparent scheme” to reimburse employees for political contributions and “an apparent conspiracy” to cover it up. The Bowl Championship Series could cut ties with the Fiesta Bowl.

“They are certainly embarrassed and upset by it, as should anyone be,” Emmert said of the Fiesta Bowl. “Assuming that report is accurate, what has gone on there is utterly unacceptable. It is the kind of thing that, again, spreads exactly the wrong interpretation on what goes on in intercollegiate athletics.”