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Review of Industrial Organization
Published in: Review of Industrial Organization 2/2018

14-10-2017

Modeling Competitive Imbalance and Self-Regulation in College Sports

Author: Rodney Fort

Published in: Review of Industrial Organization | Issue 2/2018

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Abstract

The principal-agent relationship between athletic directors and their university administration suggests a conference equilibrium of revenue-maximizing athletic directors. With smaller- and larger-revenue departments, revenue maximization predicts conference competitive imbalance. The larger the revenue dispersion, the greater the imbalance. Pooled revenue sharing increases the absolute level of talent and reduces competitive imbalance. That national championships are determined across conferences may explain the widespread adoption of nearly complete revenue sharing. The model also explains the form of the amateur requirement and predicts that competitive imbalance is invariant with respect to that amateur specification. This has obvious implications for balance-based arguments for or against increasing compensation to athletes.
previous article Athlete Pay and Competitive Balance in College Athletics
next article Rent Sharing and the Compensation of Head Coaches in Power Five College Football

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Appendix
Available only for authorised users
Footnotes
1
See the survey of the work on these values in Fort and Winfree (2013, Ch. 3).
 
2
Under the uncertainty of outcome hypothesis, fans prefer outcome uncertainty with respect to games and final standings rather than results that are more highly predictable (i.e., outcomes that are known beforehand because some teams are much stronger than others).
 
3
Under the NCAA amateur requirement, athlete compensation is limited to grants-in-aid: Scholarships that are equal to the full cost of attendance, as determined by the university registrar.
 
4
Under Rottenberg’s (1956) “invariance principle” (IP), which was offered originally for profit-maximizing professional team owners, the distribution of talent is invariant with respect to changes in the rights over the value that is created by talent. The NCAA amateur requirement result in this paper mimics that invariance principle in the context of revenue maximizing ADs.
 
5
The pro side of the pay-for-play argument is almost always couched in terms of fairness. A recent comprehensive example is Branch (2011). There are others too numerous to list.
 
6
See the college sports chapters in Fort and Winfree (2013), a general description in Fort (2015a), and a descriptive model and empirical assessment in Fort (2016).
 
7
The hierarchical oversight description runs from the board of governors to UAs and then to the budget control over ADs. The presentation here abstracts to just the eventual, inherited directive that follows from that hierarchy: revenue maximization by ADs.
 
8
Oversight can be predicted to fail under well-known circumstances. In this paper, strictly speaking, failure would involve the economic oversight of athletics. However, the principal-agent approach in examples like the academic scandal at the University of North Carolina and the sexual abuse scandal at Penn State is still valuable in pointing to directions for reform of the oversight process.
 
9
Institutional support is included in revenues because there is no logical reason to do otherwise (Fort and Winfree 2013, Ch. 3).
 
10
Sales maximization has also seen extensive development in the literature on hospitals. Originally, see Newhouse (1970) and Pauly and Redisch (1973), followed by Finkler (1983). A cogent survey on subsequent work on hospitals is in Liu and Mills (2008).
 
11
North American pro league modeling proceeded from Rottenberg (1956) to El-Hodiri and Quirk (1971) and Quirk and El Hodiri (1974), to Fort and Quirk (1995) and Vrooman (1995). There is a large sports economics literature that integrates these earlier works into modern industrial organization as well. See the literature reviews in Winfree and Fort (2012) and Fort (2015b).
 
12
Once the national letter of intent is signed, unless that university releases them, athletes must sit out 1 year and lose that full year of eligibility if they move to a different university, unless: (1) they drop to a lower NCAA division; or (2) if they can use the graduate transfer rule. Under the latter, upon graduation, a student can change colleges to pursue a graduate degree not offered at their college of graduation and use their remaining eligibility.
 
13
Contest success functions typically relate one participant’s share of total talent to winning. A comprehensive introduction and early literature review is in Skaperdas (1996).
 
14
Some of the results in this paper are similar to those in the professional sports literature on “win maximization”. This is unsurprising since revenues are a monotonic function of winning in the model here. For the pro sports win maximization literature, see the review and extensions by one of its creators in Kesenne (2014).
 
15
RSD = ASD/ISD, where ASD is the actual standard deviation of final standing winning percentages and ISD is the “idealized” standard deviation that would characterize equal probability that any team beats another in the conference (the first formal derivation is in Fort and Quirk, 1995). Thus, RSD = 1 means that ASD = ISD and the conference is as balanced as an equal win probability conference. As RSD increases beyond unity, the conference is increasingly imbalanced relative to that idealized alternative. Other measures lead to the same conclusion in Salaga (2015) and Salaga and Fort (2017).
 
16
The organization that is named “The College Football Playoff” is composed of the commissioners of the Power 5 conferences, the sports broadcasting network ESPN, and the committees of the so-called New Year’s Six bowl games (Cotton, Fiesta, Orange, Peach, Rose, and Sugar). Their chosen rules and procedures can be found at www.​collegefootballp​layoff.​com.
 
17
In college sports, only Brown (1994) examines the incentive effect of revenue sharing on individual AD choices but not on competitive balance. In profit-maximizing pro leagues, there has been much more work on revenue sharing. See Winfree and Fort (2012), and their references.
 
18
No insight could be gained by directly comparing (26) to (18). Suppose that all shadow prices are equal to each other, so that the right-hand-side of (18) is one. After simplification, the comparison that is dictated by (26) would be \(\frac{{MR_{1} }}{{MR_{2} }}\frac{ > }{ < }1 \Leftrightarrow \frac{{dR_{2} }}{{dz_{1} }}\frac{ > }{ < }\frac{{dR_{1} }}{{dz_{2} }}\). But nothing in the model dictates any particular result for this last comparison.
 
19
The tumultuous evolution of this NCAA version of the amateur requirement is documented in Falla (1981) and Byers (1995).
 
20
There are some sports where partial GIAs are the rule due to remaining NCAA scholarship restrictions. Since these are uniform across all departments at any NCAA level, they are ignored here. Also, for point of reference, the limit for FCS departments (Division IAA prior to 2006) is 63, and partial scholarships are more common at this level.
 
21
One could start from the pooled sharing equilibrium instead. But the implications are the same, and the exposition is simpler using the equilibrium without sharing.
 
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Metadata
Title
Modeling Competitive Imbalance and Self-Regulation in College Sports
Author
Rodney Fort
Publication date
14-10-2017
Publisher
Springer US
Published in
Review of Industrial Organization / Issue 2/2018
Print ISSN: 0889-938X
Electronic ISSN: 1573-7160
DOI
https://doi.org/10.1007/s11151-017-9591-y

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