09/30/2014 11:04 am ET Updated Nov 30, 2014

You Can't Study College Coaches Without Looking at the Players

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According to Deadspin, in 2013 the highest paid public employee in 27 different states was a college football coach. In 13 other states, it was a college basketball coach. For some, this might suggest that the public is devoting too much money to college sports. In fact, one might even argue that these coaches are overpaid.

In a recent article in the New York Times, though, a different story was told. According to an unpublished study by two University of Vanderbilt researchers, college coaches are worth the money because of the revenue these coaches bring to the university. In the words of Randall Thomas (the lead author of the study): "Coaches are running large programs that have tremendous value. They are creating great value, and they are being paid for creating that value."

The Vanderbilt study reaches this conclusion by comparing the salaries paid to college football coaches to the salaries paid to CEOs of public companies. Although the authors acknowledge some differences between the two sets of leaders -- for example, college coaches tend to get fired faster and thus college contracts are more focused on how employment can be terminated -- they find that in general the compensation of college coaches compares favorably to the wages paid to CEOs. In both cases wages are high. However -- as the authors argue -- it appears this compensation is "structurally aligned with value creation" for the employer (shareholders of firms or universities). And if you think the level of CEO pay is warranted, you would have to conclude that what college coaches receive is reasonable as well.

One could easily argue that CEOs may not be worth their compensation. But I think there is a more significant problem with the argument made in this study. If you read through the 53-page study, you will not find any mention of one very large difference between the labor market a typical CEO faces and the labor market that exists in college sports.

A typical CEO must hire labor in a competitive labor market. This means that firms often have to offer higher wages to attract better talent. In college sports, though, this is not allowed. Teams are prohibited from paying their players beyond the cost of attending the institution.

We can see the impact of this restriction if we make another -- perhaps more relevant -- comparison. As part of my testimony in the Northwestern University football player's union case, I noted that in 2013 the 32 NFL head coaches were paid an average wage of $4.6 million. That same year, the average wage of the top 32 college football coaches -- according to data from USA Today --was $3.4 million. So top college coaches are paid about 74 percent of what a top NFL coach receives.

Now let's turn to a different comparison. The U.S. Department of Education reports how much revenue each college football program earned from 2003 to 2012. If we look at the top 32 programs (ranked in terms of revenue) in 2012, we see that the average program earned $56.9 million. That same year -- according to (data we can find at the website of Rod Fort at the University of Michigan) -- the average NFL team earned $286.5 million in revenue. So a top college program earns less than 20 percent of the revenue earned by a top NFL team. This disparity, though, is not reflected in the wages paid to the coaches.

One might argue that a college coach does more than an NFL coach. After all, a college coach has to not only coach the players, he must also recruit these athletes. In other words, a college coach is both coach and general manager. But even when we look at the wages paid to GM/Coaches in the NFL (i.e. Bill Bilichick and Mike Shanahan in 2013), it still appears that college coaches are paid much more than their organization's revenues would suggest. In 2013, Belichick and Shanahan were each paid 1.8 percent of their respective team's revenues. In contrast, the coaches at the top 32 college programs in 2012 were paid 5.5 percent of their respective revenues; or three times more than one might expect when looking at NFL compensation. In sum, it appears college football coaches -- relative to their counterparts in the NFL -- are overpaid.

But isn't the success of a college team -- unlike what we might believe about the NFL -- all about the coach? Certainly that seems to be the story told when a college fires a coach and spends significant money on a new leader for the program. A recent study in the Social Science Quarterly, though, cast doubt on this tale. Looking at data from college football from 1997 to 2010, the authors of this study found "that for particularly poorly performing teams, coach replacements have little effect on team performance as measured against comparable teams that did not replace their coach. However, for teams with middling records -- that is, teams where entry conditions for a new coach appear to be more favorable -- replacing the head coach appears to result in worse performance over subsequent years than comparable teams who retained their coach."

This study is consistent with a number of studies of coaching in sports. Academic research typically fails to find that coaches have a significant impact on outcomes in sports. And this may be why professional teams pay more to their players than they do to their coaches and/or managers.

Of course, that is not the case in college sports. Once again, wages in college football are restricted by NCAA rules. To see how much they are restricted, let's think about what professional players are paid. Stefan Szymanski at the University of Michigan recently noted that National Football League players were paid 52 percent of revenues in 2012.

A college football program has 85 scholarship players. If these players were paid 52 percent of team revenue in 2012, the average player at a top 32 program would have received $337,284. However, the average Football Bowl Subdivision program -- according to the USA Today -- offered a scholarship worth only $27,293 in 2011. This suggests that because of NCAA restrictions, college football players are dramatically underpaid.

And that suggests -- once again -- that college football coaches might be overpaid. Unfortunately, the Vanderbilt study doesn't touch upon the role the players play in this story. In fact, one might conclude from this study that it is the coaches who are primarily responsible for creating the value we see in these programs. And again, that story is inconsistent with other academic studies of coaching.

But anyone who watches college football has to notice that there are players on the field. And clearly those players matter. We can see this -- as Rod Fort and Jason Winfree noted -- by looking at the tremendous effort coaches expend to recruit specific players. In fact, the Vanderbilt study notes that prospective coaches are evaluated in terms of their ability to recruit. If those specific players didn't matter, coaches could just collect a few players from local high schools and then employ the coaches wisdom to achieve victory. Instead, coaches at each program search the nation (and in other sports, the world) to find the athletes they need to achieve success.

When that success is achieved, the coaches get paid while the players -- relative to what they would be paid in a professional sport -- get paid much less. To offer a study of college coaches that ignores the nature of the college sport player market seems to be -- at a minimum -- incomplete. And certainly not enough to conclude that college coaches are worth -- in the words of one agent for the coaches -- "every penny" they are paid.