Athlete Pay and Competitive Balance in College Athletics

Abstract

In this paper we analyze the argument—which has been used by both the National Labor Relations Board and the National Collegiate Athletic Association—that unionization and/or player pay will hurt competitive balance in college sports. We present a theoretical analysis of universities that recruit athletes and examine the assumptions that are needed for player compensation to decrease competitive balance. We also empirically illustrate the differences in balance between professional and college sports. Given the theoretical and empirical analysis, we argue that unionization and/or player pay is unlikely to hurt competitive balance.

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Notes

  1. 1.

    In 2013, many of the football players at Northwestern University wanted to form a player’s union for college athletes. In 2014, their case went in front of the National Labor Relations Board (NLRB) and the Chicago district of the NLRB ruled that the players were employees of the university and therefore they could form a union. Northwestern appealed this ruling and in 2015 the NLRB ruled that the football players at Northwestern could not form a union. However, the NLRB did not assert jurisdiction, which means that the ruling could be overturned in the future. Since the ruling only affects Northwestern, some have interpreted this as saying that the NLRB might reverse its decision if a national union was formed, instead of just a small union of football players at one university.

  2. 2.

    In 2014, the NCAA’s expert witnesses in O’Bannon v. NCAA, 7 F.Supp.3d 955, argued that the NCAA was a cartel, which allowed it to restrict player pay, but that this restriction would help competitive balance.

  3. 3.

    A main source of payment for many college athletes are grants-in-aid (in essence, athletic scholarships), which can vary depending upon the cost of tuition at the university. Even though an athlete might not value the education similarly to the cost, the value of a college education can certainly differ across universities.

  4. 4.

    For more discussion regarding this talent function, see Salaga et al. (2014).

  5. 5.

    The size of the market is dependent upon the marginal revenue with respect to winning.

  6. 6.

    For example, competitive balance can depend on factors such as scheduling, drafts, and many other league rules.

  7. 7.

    http://www.forbes.com/nfl-valuations/list/ and http://www.forbes.com/nba-valuations/list/. Accessed February 10, 2017.

  8. 8.

    Many stadiums and arenas are publicly funded with relatively low operations and rental costs that are charged to pro teams, which allows the (subsidized) owners to pocket more money than do universities that often own their own stadiums and facilities outright.

  9. 9.

    We note that in some cases, winning percentages may not add to 1 (or average 0.5) across the entirety of NCAA football or basketball. For example, some FBS teams play Football Championship Series (FCS) teams during the regular season, therefore resulting in no losses for an FBS team in the sample. However, the impact that these games have on the measure is likely to be extremely small given the number of teams, and we therefore assume that this is ignorable in our context.

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Correspondence to Jason Winfree.

Appendix

Appendix

If we allow for a non-zero restriction—\( \bar{\rho } \)—that does restrict both teams, then Eqs. (9) and (10) become

$$ \left. {\frac{{\partial \pi_{L} }}{{\partial \varphi_{L} }}} \right|_{{\rho = \bar{\rho }}} = \frac{{\sigma c\left( {\alpha_{S} + b\bar{\rho } + c \varphi_{S} } \right)}}{{\left( {\alpha_{L} + b\bar{\rho } + c \varphi_{L} + \alpha_{S} + b\bar{\rho } + c \varphi_{S} } \right)^{2} }} - 1 . $$

and

$$ \left. {\frac{{\partial \pi_{S} }}{{\partial \varphi_{S} }}} \right|_{{\rho = \bar{\rho }}} = \frac{{c\left( {\alpha_{L} + b\bar{\rho } + c \varphi_{L} } \right)}}{{\left( {\alpha_{L} + b\bar{\rho } + c \varphi_{L} + \alpha_{S} + b\bar{\rho } + c \varphi_{S} } \right)^{2} }} - 1 . $$

Therefore, the optimal level of indirect investment for the small-market team is given by

$$ \varphi_{S} = \frac{\sigma }{{\left( {1 + \sigma } \right)^{2} }} - \frac{{\alpha_{S} + b\bar{\rho }}}{c} . $$

Since investment must be non-negative, indirect investment will stop when

$$ \bar{\rho } = \frac{c\sigma }{{b\left( {1 + \sigma } \right)^{2} }} - \frac{{\alpha_{S} }}{b} . $$

As the restriction on direct investment increases, the next qualitative change in investments is either that the large-market ceases its indirect investment, or the restriction on direct investment will not be restricting for the small-market team. We will first analyze the case where large-market indirect investment stops first. In this case, \( \varphi_{S} = 0, \) and \( \rho_{S} = \bar{\rho }, \) so the impact of indirect investment by the large-market team is given by

$$ \left. {\frac{{\partial \pi_{L} }}{{\partial \varphi_{L} }}} \right|_{{\rho = \bar{\rho }}} = \frac{{\sigma c\left( {\alpha_{S} + b\bar{\rho }} \right)}}{{\left( {\alpha_{L} + b\bar{\rho } + c \varphi_{L} + \alpha_{S} + b\bar{\rho }} \right)^{2} }} - 1 . $$

Therefore

$$ \varphi_{L} = \frac{{\sqrt {\sigma c\left( {\alpha_{S} + b\bar{\rho }} \right)} - \alpha_{L} - \alpha_{S} - 2b\bar{\rho }}}{c} . $$

And this will equal zero when

$$ \bar{\rho } = \frac{{\sigma c - 4\left( {\alpha_{S} + \alpha_{L} } \right) \pm \sqrt {\sigma^{2} c^{2} + 8\sigma c\left( {\alpha_{S} - \alpha_{L} } \right)} }}{8b} . $$

If it is the case that \( a_{S} = a_{L} \), this can be simplified to

$$ \bar{\rho } = \frac{\sigma c - 4\alpha }{4b} . $$

However, the small-market team might stop direct payments before the large-market team stops indirect payments. In this case, the marginal impact of direct payments to the small-market team is given by

$$ \left. {\frac{{\partial \pi_{L} }}{{\partial \varphi_{L} }}} \right|_{{\rho = \bar{\rho }}} = \frac{{\sigma c\left( {\alpha_{S} + b\rho_{S} } \right)}}{{\left( {\alpha_{L} + b\bar{\rho } + c \varphi_{L} + \alpha_{S} + b\rho_{S} } \right)^{2} }} - 1. $$

and

$$ \frac{{\partial \pi_{S} }}{{\partial \rho_{S} }} = \frac{{b\left( {\alpha_{L} + b\bar{\rho } + c \varphi_{L} } \right)}}{{\left( {\alpha_{L} + b\bar{\rho } + c \varphi_{L} + \alpha_{S} + \rho_{S} } \right)^{2} }} - 1, $$

and therefore

$$ \rho_{S} = \frac{b\sigma c}{{\left( {b + \sigma c} \right)^{2} }} - \frac{{\alpha_{S} }}{b}. $$

So, when \( \bar{\rho } \) surpasses that point, the restriction is no longer restrictive to the small-market team.

Finally, we find the point of a superfluous restriction where it does not restrict either team. The first-order conditions are given by,

$$ \frac{{\partial \pi_{L} }}{{\partial \rho_{L} }} = \frac{{\sigma b\left( {\alpha_{S} + b\rho_{S} } \right)}}{{\left( {\alpha_{L} + b\rho_{L} + \alpha_{S} + b\rho_{S} } \right)^{2} }} - 1. $$

And

$$ \frac{{\partial \pi_{S} }}{{\partial \rho_{S} }} = \frac{{b\left( {\alpha_{L} + b\rho_{L} } \right)}}{{\left( {\alpha_{L} + b\rho_{L} + \alpha_{S} + \rho_{S} } \right)^{2} }} - 1, $$

which gives us

$$ \rho_{L} = \frac{{\sigma^{2} }}{{\left( {1 + \sigma } \right)^{2} }} - \frac{{\alpha_{L} }}{b}. $$

If we assume that \( \sigma = 2,\alpha_{S} = \alpha_{L} = .1 \), \( b = 2 \), and \( c = 1 \), then the small-market team will stop investing indirectly when \( \bar{\rho } = 0.06111 \); the small-market team will stop investing directly; and the large-market team will stop investing indirectly when \( \bar{\rho } = 0.2 \), and the large-market team will stop investing directly when \( \bar{\rho } = 0.39444 \).

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Mills, B., Winfree, J. Athlete Pay and Competitive Balance in College Athletics. Rev Ind Organ 52, 211–229 (2018). https://doi.org/10.1007/s11151-017-9606-8

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Keywords

  • College athletics
  • Competitive balance
  • Player pay