Spillovers in Sports Leagues with Promotion and Relegation
| Author | Helmut Dietl,Andreas Hefti,Markus Lang,Martin Grossmann |
| Published date | 01 February 2015 |
| DOI | http://doi.org/10.1111/sjpe.12060 |
| Date | 01 February 2015 |
SPILLOVERS IN SPORTS LEAGUES
WITH PROMOTION AND RELEGATION
Helmut Dietl*, Martin Grossmann*
,
**, Andreas Hefti* and Markus Lang*
ABSTRACT
This paper analyzes spillover effects in sports leagues that are embedded in a
system of promotion and relegation. Based on a contest model of a professional
sports league with a top division and a second division, we show that league
prizes and club efficiencies have opposing effects; while a stronger second division
that offers a higher league prize leads to a more balanced top division, the oppo-
site is true for a stronger second division whose clubs become more cost efficient.
Moreover, we demonstrate that a higher second-division prize induces a lower
investment level, but higher profits in the top division, while higher club efficiency
in the second division leads to both a lower investment level and lower profits in
the top division. These results have important policy implications for the organi-
zation of sports leagues.
II
NTRODUCTION
Peter J. Sloane’s 1971 article on the economics of professional football is an
attempt to provide a ‘theoretical framework with respect to the objectives of
football clubs and the nature of competition under which they operate’
(p. 122). One of the most important peculiarities of professional team sports
in general and professional football in particular is the organization of market
entry. In North America, for example, professional team sports leagues are
organized as ‘closed shops’ in the sense that new teams cannot enter the lea-
gue without the permission of existing teams. In European football and many
other sports around the world, market entry of new teams is usually organized
through a tiered system of promotion and relegation. Within this system, the
weakest teams of the first division are replaced by the strongest teams of the
second division at the beginning of each season.
This system of market entry and exit has important implications for the
structure of competition within each league. Sloane (1971) argues that promo-
tion and relegation are a ‘stimulus to improve performance as relegation to a
lower division may, amongst other things, lead to a financial loss’ (p. 125).
Ross and Szymanski (2002), Szymanski and Valletti (2005), and Jasina and
*University of Zurich
**Lucerne University of Applied Sciences and Arts
Scottish Journal of Political Economy, DOI: 10.1111/sjpe.12060, Vol. 62, No. 1, February 2015
©2015 Scottish Economic Society.
59
Rotthoff (2012) develop theoretical models to analyze the economic differences
between open and closed leagues. Based on their models, the authors show
that overall spending on player talent is higher in open than in closed leagues
because the prospect of promotion and relegation enhances competition
within the top and lower divisions. Noll (2002) analyzes data from English
football (soccer) to empirically support these findings. Finally, Dietl et al.
(2008) examine how a system of promotion and relegation affects the over-
investment problem in professional team sports. They find that clubs invest
more when they play in an open league compared with a closed league. More-
over, the over-investment problem within open leagues increases with the reve-
nue differential between leagues.
Our paper has a different focus because we analyze the vertical spillover
effects between divisions that are generated through such a system of promo-
tion and relegation. Particularly, we are interested in the top division and we
seek to examine how different characteristics of the second division affect the
competition within the top division.
Based on a contest model of a professional sports league with a top division
and a second division, we show that changes in league prizes do not affect
competitive balance if the two divisions are not connected via a system of pro-
motion and relegation. Surprisingly, if divisions are embedded in a system of
promotion and relegation, league prizes and club efficiencies have opposing
effects on competitive balance; while a stronger second division that offers a
higher league prize leads to a more balanced top division, the opposite is true
for a stronger second division, whose clubs become more cost efficient. In the
latter case, competitive balance decreases in the top division. Moreover, we
demonstrate that a higher second-division prize induces a lower investment
level but higher profits in the top division, while higher club efficiency in the
second division leads to both a lower investment level and lower profits in the
top division.
These results have important policy implications for the organization of
sports leagues. Suppose that a sports league planner has a total prize that can
be split between the two divisions, and if the league planner is interested in a
balanced league in the top division, s/he should choose a low prize spread. In
contrast, if the league planner prefers high talent investments and high profits
in the top division, s/he should choose a high prize spread. These results high-
light the trade-off a league planner faces between a balanced league on one
hand and high talent investment and club profits on the other hand.
The remainder of this paper is organized as follows. Section II presents the
model setup. Section III derives the optimization problem and Section IV pre-
sents the results. Finally, Section V discusses the results and concludes the
paper.
II MODEL SETUP
We model a European football league that is organized hierarchically in
ascending divisions, offering a system of promotion and relegation. Our model
60 H. DIETL, M. GROSSMANN, A. HEFTI AND M. LANG
Scottish Journal of Political Economy
©2015 Scottish Economic Society
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