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Competitive balance in football leagues when teams have different goals

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Abstract

In the standard two-team model of professional league sports it is shown that if teams have different objectives (the maximization of, respectively, wins and profits) the competitive balance conditions get worse with respect to the case when teams share the same goal. A similar, though less clear-cut, result obtains in the three-team setup. These outcomes call for policy measures to restore the balance. Three such measures are examined here: market-size-based revenue sharing, general salary cap and team-specific salary cap. It is shown that, contrary to the same-goal-for-all case, each of them may bring more intra-league competition. A ranking of the three measures is also suggested.

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Notes

  1. See, however, Fort and Quirk (2004) who deny any direct relation between teams’ objective and competitive balance, though by applying a slightly different model (for a discussion and delimitation of this result, see Kesenne (2004). Indeed, Fort and Quirk’s paper contains one of the best comparative studies of the two homogeneous cases; yet they still fail to address the more realistic “mixed” case. The present work aims at filling this gap.

  2. Note that this pattern of behavior is little affected by the club’s listing in the stock market as even a casual look at the financial statements of the very few Italian clubs who are actually listed immediately reveals: the only difference seems to be that in such cases the losses are spread through a larger number of shareholders.

  3. The empirical analysis is carried on in a companion paper: Giocoli (2006).

  4. In other words, while from the league’s viewpoint the output is the number of games played, from the club’s perspective, it is the number, or share, of games won. This assuming that each game has a winner and a loser. In case draws are admitted, they are considered as half win each.

  5. See the previous footnote.

  6. For a more sophisticated analysis, dividing consumers into committed supporters and uncommitted TV watchers, with only the latter subject to the UOH, see Szymanski (2001).

  7. At least, static models. It is curious to observe that the work pioneering most of the recent static literature, that of El-Hodiri and Quirk (1971), actually contained a dynamic analysis. For fully-fledged dynamic models see Palomino and Rigotti (2000), Szymanski and Valletti (2005).

  8. See, e.g. Quirk and Fort (1992), Fort and Quirk (1995) and Vrooman (1995).

  9. See Szymanski and Kesenne (2004) and Kesenne (2005).

  10. See Hoehn and Szymanski (1999), Fort (2000) and Sanderson and Siegfried (2003). For a historical explanation of these peculiarities, see Cain and Haddock (2005).

  11. Defined by the European Commission as a distinctive trait of European sports: see European Commission (1998).

  12. Hoehn and Szymanski (1999) and Fort (2000). But also see the skeptical remarks in Baroncelli and Lago (2006).

  13. In the Italian case, a recent authoritative rating of Serie A clubs based on criteria of good management and financial performance assigns just one star, out of a maximum of five, to two of the three listed clubs, S.S. Lazio and A.S. Roma. See Il Sole–24 Ore, 24 June 2007, p. 22.

  14. Modern behavioral economics has focused on this possibility: see Rabin (2002). For example, the owner might exhibit so-called present-biased preferences when comparing overspending now, in order to win next season’s title regardless of budgetary equilibrium, to a similar behavior in the future.

  15. There are models where talent is differentiated between high-quality and standard-quality: see Kesenne (1999). The assumption is that only the former’s supply is fixed, while the latter’s is perfectly elastic.

  16. More exactly, each player should be hired by the club where the value of her talent’s marginal product is highest and should be paid an amount equal to the second highest value of marginal product, the latter being the opportunity cost for any rational player. See Fort and Quirk (1995, p. 1272).

  17. See El-Hodiri and Quirk (1971) and, more recently, Quirk and Fort (1992) and Fort and Quirk (1995).

  18. For a formal proof of the proposition see the works quoted in the previous footnote.

  19. For the details, see again Fort and Quirk (1995). Also see Kesenne (2000a) and below, Sect. 7.

  20. See Kesenne (2000b, 2004).

  21. Note that m i could be viewed as team i’s share of the total market of a given league sport. In such a case, we would have m 1 + m 2 = 1 and the analysis would be further simplified. I thank Raul Caruso for this suggestion.

  22. Note that this normalization is different from the adding up constraint w 1 + w 2 = 1. While the latter holds in any TSE model, the former stems from having taken as fixed the total talent supply and as fully internalized any change in its distribution.

  23. Nothing would change in case we set a maximum amount of money losses that the club may bear: see next section.

  24. As shown by Kesenne (2004), the counterintuitive result in Fort and Quirk (2004) (namely, the possibility of a better CB in the both-WM case) crucially depends on assuming a league where, for some unspecified reasons, it is the small team which actually dominates.

  25. The most recent data available on Italian Serie A clubs’ financial performances give some support to this assumption: of the six clubs closing 2005–2006 season with a non-negligible profit, four were relatively small ones (Udinese, Parma, Livorno and Ascoli: see Il Sole–24 Ore, 24 June 2007, p. 22). Note however that in the European environment, characterized by the promotion and relegation system, even a small club may rationally stick to WM behavior in order to avoid relegation. This is why in the next section we assume that in a 3-team model the shift to PM is made by the “medium” club, that is, one which is neither so small to risk relegation by reducing its win percentage nor so big to be a realistic title contender by sticking to WM behavior.

  26. The tilde and the hat over c indicate the mixed nature of the solution.

  27. Going back to the data in footnote 25, Udinese Calcio is a typical medium club (ninth in terms of revenues among Serie A 20 clubs) which ranked first for profits in 2005–2006.

  28. In case this condition is violated, i.e., m 2−m 3 = 1, we get \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{x}_{3} = 0:\) the small club wins no games at all. But see above, footnote 21.

  29. This under the further condition that m 2−m 3 < 2 (which however is encompassed by the previous one that m 2−m 3 < 1). In case the difference between the medium and the small clubs’ market sizes exceeds 2, the small club never wins: \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{x}_{3} = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{x}_{3} = 0.\) Finally, if (m 2 − m 3 ) ∈(1,2 ), we have \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{x}_{3} = 0\) and \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{x}_{3} > 0,\) i.e., the small club manages to seize a few games only after the medium club has loosened the competitive conditions by shifting to PM.

  30. An empirical analysis along these lines for the case of the Italian Serie A is in Giocoli (2006).

  31. The implicit assumption is that a team’s choice to be either PM or WM is given. Alternatively, we might envisage policies aimed at pushing teams towards either a PM or a WM behavior (whichever is considered more desirable from the league’s viewpoint). See on this Fort and Quirk (2004).

  32. For example, the rule might require that revenues be redistributed from the clubs with a larger-than-average number of pay-TV subscribers to those with a smaller-than-average number.

  33. In US professional sports, the share λ is bargained by the players’ and the club owners’ associations.

  34. This, of course, only in case the WM behavior depends on a less-than-fully rational evaluation of present and future alternatives. Such is not the case when the owner rationally chooses to be WM because, say, this improves her non-sports business. On the limits of a general cap with respect to asymmetric paternalism, also see below in this section.

  35. See, respectively, Fort and Quirk (1995) and Kesenne (2000a).

  36. The second inequality holds provided the equilibrium cost is positive.

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Acknowledgments

I thank Raul Caruso and an anonymous referee for their useful suggestions. The usual disclaimers apply.

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  1. Department of Economics, University of Pisa Faculty of Law, via Curtatone e Montanara 15, 56126, Pisa, Italy

    Nicola Giocoli

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Giocoli, N. Competitive balance in football leagues when teams have different goals. Int. Rev. Econ. 54, 345–370 (2007). https://doi.org/10.1007/s12232-007-0022-5

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