How much are college athletes paid? And how much would they get on the open market?Those questions gained urgency Wednesday when a regional National Labor Relations Board director in Chicago ruled that Northwestern University football players can vote to unionize. Northwestern plans to appeal to the national NLRB in Washington, and the case could end up before the U.S. Supreme Court.If the ruling stands, and Northwestern players unionize, that could eventually lead to the professionalization of college sports and a market that sets prices for college athletes’ labor. Until then, the economic questions his ruling raises are worthy of an advanced college syllabus.How much are college athletes paid? The conventional response is the face value of their tuition, room and board. In 2011, USA Today estimated that value at $27,923 annually, as a median for college-basketball players at Division I schools. A 2012 report by the National College Players Association — an advocacy group for college athletes, so not exactly a neutral source — and Drexel University Sport Management put the average value of an athletic scholarship at $23,204 annually.USA Today put more than just tuition, room and board into its calculation of student-athlete value. The newspaper calculated that college basketball players get $120,000 annually, the majority of it from the elite training they receive. That’s based on the typical cost of a year at a private training program that college and NBA players use: $60,000 to $80,000.But packing that much money into the value of a scholarship rests on several shaky assumptions. First, not only do most college basketball players not go pro, but many probably don’t plan to and would never pay for private training. Second, whatever the quality of that private training, it’s aimed at optimizing a player’s individual success. College coaching might do the same, but its primary aim is the success of the program, and some coaches teach systems that don’t translate into pro success. Third, on-the-job training isn’t considered a monetary benefit in other contexts. It’s an investment by the employer for boosting its employee’s productivity.Other extras USA Today considered, such as tickets, are more credible, though it’s doubtful that all players who didn’t get freebies would pay face value.How much should college athletes be paid? Southern Utah University economist David Berri outlined a calculation in the Atlantic last week, but his work was based only on the University of Kansas men’s basketball team, hardly a representative program. The NCPA/Drexel study compiled revenue totals for college basketball and football programs by extrapolating from pay structures in the NBA and NFL. Teams in those pro leagues pay their players roughly half their revenue, so the NCPA assumes colleges would pay their athletes the same. But it’s not obvious they would.Pro teams pay for talent because they want to draw crowds, boost TV ratings and sell merchandise. It’s reasonable to think college fans are less fickle about their teams. Current students can’t as easily follow another team or wait until their team is better in five years. Alumni also will root for the uniform, affected as much by their own fond memories as by the quality of today’s teams.That’s the theory, anyway. Last week, Michael Lewis and Manish Tripathi, researchers at Emory University’s Goizueta Business School, checked it out by studying the relationship between revenue and winning in the NBA and Division I men’s basketball. They found that NBA teams’ revenue was twice as sensitive to winning. So college teams don’t have to worry as much about getting top players as NBA teams do. “College revenues are driven more by the permanent nature of the fan base, and by the brand equity created over time,” Lewis and Tripathi wrote.Don’t read that as a defense of the status quo. Lewis and Tripathi point out that much of college programs’ brand equity comes from past players, and they argue that programs should pay their alumni as well as their current players.Most of the revenue-based payment ideas don’t really apply to the so-called nonrevenue sports, the ones without big fan bases, expensive tickets, and shoe and TV deals. Athletes in those sports wouldn’t do as well in the open market, though Deadspin has argued there’s plenty of money to pay them, too, perhaps from reducing coaches’ salaries so that they represent the same share of revenue as pro coaches’ pay. Again, though, that calculation only makes sense if coaches’ value in college matches the value of pro coaches. To the extent that coaches such as Michigan State’s Tom Izzo account for part of colleges’ brand equity, they may be worth a higher revenue share than their pro counterparts.