Abstract
The standard model of a professional sports league is well known in the literature, and we only briefly describe it here. A much more detailed treatment can be found in Fort and Quirk (1995)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In Chap. 6, market size is measured using metropolitan area population and total income.
- 2.
The Nash talent conjecture by itself is not sufficient to assume a completely elastic talent supply since it says nothing about the behavior of the wage rate for talent. Later, we will assume that the marginal cost of talent is constant which implies the Nash talent conjecture; however, there is no reason the Nash conjecture could not hold with elastic talent supply. Although talent is not taken away from other clubs, the marginal cost of talent could still increase with new talent acquisitions.
- 3.
On the MR side, we need to assume that the elasticity of ticket demand is elastic and identical for each club. We also need to assume that there is no technology shift in the production function that translates talent into winning percentage.
- 4.
We could not obtain ticket price data for the 1986–1990 seasons.
- 5.
This is the Tullock contest success function \( w_{i} = t_{1}^{r} /\left( {t_{1}^{r} + \mathop \sum \nolimits t_{j}^{r} } \right) \) imposing the condition r = 1 and the adding up constraint.
- 6.
Defining \( \varepsilon = \left( {\partial w_{1} /\partial t_{1} } \right)\left( {t_{1} /w_{1} } \right) \) as the elasticity of winning percentage to the talent stock, it is simple to show that \( \varepsilon = 1 \) in the case of a closed talent league and \( 0 \le \varepsilon \le 1 \) in an open talent league. In other words, the open system reduces the effect of talent on winning in proportion to the response of overall talent to the increase in team one’s talent. If league talent increases in proportion to team one’s increase, then an increase in team one’s talent has no effect on team one’s winnings. If there is no effect on league talent, then an increase in team one’s talent leads to a proportional (unitary) increase in wins.
- 7.
In fact, each club could have a different cost function. The model only requires that each club share the same marginal cost of talent. Each club takes the marginal cost of talent as given and constant when deciding their behavior. The market determines the marginal cost in which each club has the same equilibrium MRP and the winning percentages must satisfy the adding up constraint.
- 8.
This technicality is addressed in the next chapter.
- 9.
Roman Abramovich, owner of Chelsea FC, and the Abu Dhabi United Group, owner of Manchester City FC in the EPL are examples. It has been reported that without the injection of approximately £100 million from its Champion’s League victory in 2012, Chelsea FC would have incurred substantial losses (http://www.guardian.co.uk/football/2012/may/28/eden-hazard-roman-abramovich-chelsea).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Rockerbie, D.W., Easton, S.T. (2014). A Model of a Professional Sports League. In: The Run to the Pennant. Sports Economics, Management and Policy, vol 5. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7885-0_3
Download citation
DOI: https://doi.org/10.1007/978-1-4614-7885-0_3
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-7884-3
Online ISBN: 978-1-4614-7885-0
eBook Packages: Business and EconomicsEconomics and Finance (R0)