The NCAA's annual men's basketball tournament, which starts Tuesday, is both a great athletic contest and a crassly commercial enterprise - a dichotomy common to college sports that has led to legal and ethical questions about whether student athletes should be paid and organized like professional employees of their universities. Even aside from the confused status of student athletes, college sports is burdened with myths. Here are five of the most common ones.

1. College sports provide enormous profits for schools.

College athletics generate eye-popping sums of money. The NCAA sold 14 years of TV rights to its March tournament for $10.8 billion in 2010, and athletic programs routinely generate more than $20 million a year in ticket sales. In 2013, the University of Texas athletic department pulled in $165.7 million. It's logical to think that the universities' non-athletic programs benefit from all that money.

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Even the Chronicle of Higher Education has made the connection, writing that "there is no revenue in training doctors and lawyers, but colleges and universities make a substantial, direct and immediate income from their student athletes." In fact, most schools lose money on their sports operations, as the NCAA confirms in its financial reports.

Extravagant compensation for athletic department employees, especially coaches, as well as waste and mismanagement leave many programs in the red. In 2009, Duke's highly successful men's basketball team lost $2 million, Florida Atlantic University had a profit margin of minus 253.7 percent, and Louisiana Tech posted one of minus 306.9 percent. Schools including Rice, Tulane and Colorado State all lost more than $1 million on their men's basketball programs that year. When a sport does turn a profit, that money is far more likely to stay in the athletic department, subsidizing other sports, than to fund academic programs.

2. Title IX has allowed women to participate equally in college sports.

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In many ways, Title IX, the law prohibiting gender-based discrimination in schools, has succeeded. When it was implemented in 1972, just 16,000 women played college sports; today the number is more than 200,000.

But in one glaring way, the law's passage has seen equality for women in sports decrease: coaching. As of 2012, only 43 percent of women's college teams were led by women, down from more than 90 percent in 1972, the year two former professors began tracking the numbers. Title IX created higher salaries for the coaches of women's programs - and the better pay ended up attracting men to those positions. Judy Sweet, the first woman to be president of the NCAA, has said she doesn't expect the downward trend to stop: "It requires breaking this cycle of male university presidents hiring male board members hiring male athletic directors hiring male coaches." And even the presence of men has not led to pay parity for the coaches of women's programs. The average salary for a coach of a NCAA Division I men's team was $267,007 in 2010. Coaches of women's teams on average earned $98,106.

3. Multimillion-dollar coaching salaries help teams win.

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The University of Michigan has high hopes for head football coach Jim Harbaugh. The school lured him from the San Francisco 49ers by matching his NFL salary - $5 million a year - and adding a $2 million signing bonus and performance incentives. The Wolverines expect that he'll help them win the Big Ten and take them to the College Football Playoff. The previous coach, Brady Hoke (who was making $2.8 million a year), was fired in December after the team finished with a losing record.

That happens all the time in college sports: Losing coaches are dumped and replaced with more expensive ones. "Schools justify these salaries on the grounds that it's a competitive marketplace, that they have to pay to get a good coach," says Andrew Zimbalist, an economist with a focus on sports.

But the coaching arms race doesn't pay off. New hires often produce poorer records than the coaches they replace - in short, they are paid more for losing more games. A 2012 study following the highest-paid football and men's basketball coaches over six seasons showed that replacing a coach with a higher-compensated one resulted mostly in no short-term change - most of the teams that were not ranked in the top 25 did not climb into that echelon with the new coach. In fact, 20 percent of the new hires triggered "short-term downward mobility," meaning their teams fell in ranking, sometimes dropping out of the top 25 altogether. In the longer term, over four seasons, the numbers were comparable.

4. Sports generate great publicity for schools.

Countless publications and entire TV networks cover college sports, and schools pay nothing for those sweeping shots of campus broadcast during big games. Applications tend to spike for schools appearing in the NCAA men's basketball tournament. "We couldn't afford to buy the kind of exposure our team earned," Butler athletic director Barry Collier said of the school's surprise success in the 2010 tournament. George Mason University estimated that its 2006 tournament run won it $677 million worth of free publicity.

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But when scandals occur on or off the field, the media does not disappear - in fact, more reporters arrive on campus - and the bad PR costs schools dearly. After enjoying years of good press for its athletics, the University of North Carolina at Chapel Hill is now being roiled by a massive academic fraud scandal in its athletic program. At least one top recruit to the men's basketball team says the scandal has made him hesitate about committing to UNC, and the university made the unprecedented move of hiring a vice chancellor for communications and public affairs - a former spokesman for Disney - at the cost of $300,000 a year. (That sum pales next to the $3.2 million Penn State had spent as of 2012 on investigations, PR and legal advice as a result of its child sex abuse scandal. This does not include the $60 million fine levied by the NCAA.)

5. College sports bring in alumni donations.

College presidents and school officials frequently explain their obeisance to their athletic departments by saying that without big-time sports programs, they'd never get any money out of their alumni. As Texas Tech athletic director Kirby Hocutt told the Wall Street Journal, "Nothing can unify a community and alumni base of a university like college football can." While some studies have shown that winning can have a positive effect on alumni giving, others have shown no correlation or even that a winning record can decrease donations.

A more general examination of alumni showed that the economy and news stories about an alma mater most strongly influence giving among young alumni; athletic performance ranked lowest, along with diversity initiatives. The U.S. News & World Report annual college rankings for schools with the highest percentage of alumni who give are filled with schools that do not play big-time football or basketball. Small liberal arts colleges, almost all in Division III, post the best numbers.

Sperber teaches in the Cultural Studies of Sport in Education program in the University of California at Bekeley's Graduate School of Education and is the author of four books on college sports, including "Beer and Circus."