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Competitive balance in football leagues when teams have different goals

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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
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  Competitive balance in football leagues when teamshave different goals Nicola Giocoli Published online: 18 September 2007 Ó Springer-Verlag 2007 Abstract In the standard two-team model of professional league sports it is shownthat if teams have different objectives (the maximization of, respectively, wins andprofits) the competitive balance conditions get worse with respect to the case whenteams share the same goal. A similar, though less clear-cut, result obtains in thethree-team setup. These outcomes call for policy measures to restore the balance.Three such measures are examined here: market-size-based revenue sharing, generalsalary 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. Keywords Team sports Á Competitive balance Á Revenue sharing Á Salary cap Á Asymmetric paternalism JEL Classifications D29 Á L21 Á L83 1 Introduction The paper presents a simple extension of the basic two- and three-team model of aprofessional sports league with the aim of capturing a peculiarity of European teamsports in general, and of Italian football in particular, which has so far beenneglected in the literature. The canonical model, as envisaged, for example by Fortand Quirk (1995) and Szymanski (2003), suggests two possible behavioral assumptions about professional teams: clubs are supposed to maximize eithertheir profits (profit-maximizing, PM, behavior) or the number of seasonal wins N. Giocoli ( & )Department of Economics, University of Pisa Faculty of Law, via Curtatone e Montanara 15,56126 Pisa, Italye-mail: giocoli@mail.jus.unipi.it  123 Int. Rev. Econ. (2007) 54:345–370DOI 10.1007/s12232-007-0022-5  (win-maximizing, WM, behavior). What matters most, behavior is assumed to behomogeneous, so that teams are either all PM or all WM: the former beingpredicated to mirror the reality of US professional leagues, the latter being viewedas better capturing the situation of European team sports.If we define the league’s competitive balance as the deviation from the ideal casewhere all teams win exactly the same proportion of matches during the season and if we accept the traditional assumption of sports economics literature that each team’srevenues are concave with respect to the team’s win percentage on account of thefans’ diminishing interest, and willingness to pay, for events whose outcome can beeasily predicted (so-called uncertainty of outcome hypothesis), the well-knownresult is that a league’s competitive balance is higher under the all-PM case thanunder the all-WM one. 1 This because rational, profit-oriented teams internalize thenegative effect on their revenues of an ‘‘excessive’’ number of wins and thus neverfully exploit any technical or athletic advantage that might stem from their financialstrength vis-a`-vis their weaker opponents; on the contrary, rich WM teams simplytry to extract as many wins as possible from such an advantage, eventually winningalmost all matches and thus earning so little revenues that they barely manage tobreak even or, worse, incur in (possibly huge) economic losses that owners arecalled to stand at the end of each season.What is suggested in the paper is that a more realistic characterization of European professional leagues is that of ‘‘mixed’’ leagues, namely, of anenvironment where, while some teams still pursue the traditional win-maximizinggoal, some others have modified their behavior in the direction of straightforwardprofit-maximization (so-called Americanization of European sports: see Hoehn andSzymanski1999). In particular, it is argued that this characterization may capturethe recent development in the main Italian football league: the Serie A: where, in theface of the dramatic financial imbalances caused to WM teams by the rising cost of the players’ talent, a few clubs seem to have shifted to a profit-oriented pattern of behavior. Hence, we propose a modified version of the standard model, where oneteam is PM, while the other(s) is (are) WM.The peculiarity of our simple comparative statics exercise is that the team that isassumed to embrace a profit goal is either the small (in the 2-team setup) or the medium (in the 3-team case) one in terms of revenue potential and market size(which in turn depends on, say, the team’s urban area of reference, the number of itsfans, the latter’s ability and willingness to pay, the team’s skills in exploiting itsmerchandising possibilities, etc.). The rationale is straightforward: starting from anall-WM situation, where the equilibrium competitive balance entails a larger win-percentage for the big team because of its higher capacity to purchase technical–athletic talent, the small or medium team’s owner may reasonably ask herself whatis the point of pursuing a sporting goal (say, winning the league’s title) she wouldnever achieve, while at the same time forfeiting the possibility to earn some profits. 1 See, however, Fort and Quirk (2004) who deny any direct relation between teams’ objective andcompetitive 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 comparativestudies of the two homogeneous cases; yet they still fail to address the more realistic ‘‘mixed’’ case. Thepresent work aims at filling this gap.346 N. Giocoli  123  Hence, there is a strong incentive for the small or medium team to shift to a PMbehavior, at the only price of a further—but possibly irrelevant from the end-of-season outcome’s viewpoint—reduction in its win percentage.This, again, seems to capture a feature of the Italian Serie A (Baroncelli and Lago2006). On one side, we have big teams’ owners who stick to a WM behavior,sometimes in the eventual pursuit of other, non-sporting goals (such as personalprestige and a positive spillover on their other business, or non-business, activities),and thus go on spending large amounts of money in the effort to secure wins, caringnot too much about end-of-season financial losses which they are always willing tofoot. 2 On the other side, we have some medium and small teams’ owners who arewell aware that they cannot really compete against the big clubs and who, above all,consider the management of a football club their main, and sometimes exclusive,business: these owners are led to adopt a PM behavior with the only constraint (notmodeled here, but see Giocoli2006) of not incurring in so many losses that theirteam risks being relegated in the league’s lower division.The outcome of our ‘‘mixed’’ model is a change in the league’s competitivebalance with respect to both the ‘‘pure’’ (WM and PM) cases. In short, starting froman all-WM league and having the small or the medium team shifting to PM behaviorshould produce an increase in the win percentage of all the other teams on accountof the reduction in the number of wins of the changing one. In the 2-team case thisleads to an obvious worsening of the league’s CB, while in the 3-team setup,provided the behavioral shift is made by the medium club, we witness a softening of the competition for the top places and a hardening of the struggle to avoid thebottom positions. In the case of the Italian Serie A, these outcomes seem indeed tocapture what emerges from casual observations (such as, say, the high frequencywith which a few teams occupy the league’s top spots to the almost completeexclusion of the others) as well as from more systematic ones (such as the timepattern of the commonest measure of competitive balance, the standard deviation of seasonal wins). 3 If this is so, what may be done to restore more balanced conditions on the playingfield? The paper suggests three policy measures that may lead to this result: (1)market-size-based revenue sharing, (2) general salary cap, (3) team-specific salarycap. Remarkably, all are shown to be potentially effective in promoting conditionsof more competitive balance in our ‘‘mixed’’ league. This goes against thetraditional wisdom that, with the only exception of a general salary cap, no suchmeasure may be capable of doing so (so-called invariance proposition, a cornerstoneof team sports economics since Rottenberg1956). Hence, the paper offers anormative, though idiosyncratic, justification for a change in the ‘‘rules of thegame’’ of the top Italian football league. Moreover, it is suggested that, though alleffective, the three measures may nonetheless be ranked in terms of either their 2 Note that this pattern of behavior is little affected by the club’s listing in the stock market as even acasual look at the financial statements of the very few Italian clubs who are actually listed immediatelyreveals: 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).Competitive balance in football leagues 347  123  actual enforceability or their conformity to the main principle of asymmetricpaternalism (Camerer et al.2003).The content of the paper is as follows. In the next section, we review the basicingredients of the standard team sports economics model. The so-called invarianceproposition, the traditional benchmark for any policy evaluation is introduced inSect.3. The 2-team model in its two ‘‘pure’’ versions, namely, when teams are eitherboth WM or both PM, is analyzed in Sect.4. The fifth section presents the ‘‘mixed’’model, where one of the teams—specifically, the small one—changes its behaviorfrom WM to PM. In Sect.6, we extend the analysis of the ‘‘mixed’’ case to the3-team setup, this time assuming that the behavioral shift is made by the mediumclub. The seventh section offers our policy exercises in the 2-team case, as well as aranking of the proposed measures. Section8concludes. 2 Team sports economics models: a review of the basic ingredients Most team sports economics (TSE) models share two general remarks and aspecific assumption. The remarks concern the peculiar character of the productiveprocess in that particular economic activity called ‘‘production of team sportsevents’’. First, this activity is characterized by the phenomenon of inverse jointproduction: in order to obtain a unit of output (here, a game or a tournament) twoor more production processes, i.e., two or more firms (here, the sport clubs), areneeded. It is still true that even in the case of team sports a firm is willing tooutcompete its rivals because its revenues are increasing in the outcome of itsproduction process (here, the results obtained on the game field, as each unit of output, viz., a game, is always assigned to one or the other of the firms who havecontributed to its production). 4 Yet, it is also true that the firms’ productionfunctions exhibit a strong degree of complementarity, so much so that were a firmcapable of conquering the whole market, ‘‘eliminating’’ all its rivals, it would seeits revenues falling to zero on account of the impossibility to produce even a singleunit of output on its own.Secondly, the outcome of a single firm’s production process in such a peculiareconomic activity is summarized by an index, the performance on the field, which issubject to a tight aggregate constraint. Measuring each club i ’s performance with thepercentage w i [ [0,1] of games won with respect to games played in a given interval(say, a league’s season) the constraint is: X ni ¼ 1 w i ¼ n 2 ð 1 Þ (so-called adding up constraint  ), where n is the number of clubs in the given league.Thus, given the peculiar ‘‘rules of the game’’ of this particular economic activity, 4 In other words, while from the league’s viewpoint the output is the number of games played, from theclub’s perspective, it is the number, or share, of games won. This assuming that each game has a winnerand a loser. In case draws are admitted, they are considered as half win each.348 N. Giocoli  123  the overall output (the number of games, i.e. of wins) 5 is predetermined and the onlyissue is how it will be divided among the firms (the league’s clubs).The assumption is about the consumers’ choice with respect to the outcome of this economic activity, that is, about the fans’ preferences for the games of a giventeam sport. First formulated by Rottenberg (1956) and Neale (1964), this assumption is known as uncertainty of outcome hypothesis (UOH) and claimsthat, generally speaking, the fans’ interest in any sport contest (not necessarily ateam sports one) dwindles when its outcome is certain or, in any case, too easilypredictable. In team sports, this amounts to saying that if  w i ? 1, i.e. if it is almostsure that team i is going to win all its league games, consumers will reduce theirdemand for the ‘‘product’’, i.e. they will be less willing to spend their time andmoney to watch the games either live or in TV. 6 From the club’s viewpoint, theUOH means that the revenue function is concave with respect to the winpercentage:  R i ¼  R i Z  i ; w i ð Þ ð 2 Þ where Z  i is a vector of the other determinants of the club’s revenues, and o  R i o w i [ 0 ; o 2  R i o w 2 i \ 0 : The assumption strengthens the cooperative element of the production process:not only it is impossible for a single club to produce the output ‘‘games won’’, but itis not even profitable to ‘‘produce’’ a w i too close to unity. It follows that the mainnotion in TSE literature is that of  competitive balance (CB), namely, the degree of closeness in the win percentage of the different teams taking part in a given league.The highest CB is when w i ¼ 12 for each i , to indicate that each team wins exactlyhalf of its games. In such a situation, we have the maximum uncertainty on a game’soutcome and thus, provided the UOH holds, the fans’ maximum willingness todedicate their time and money to the event. The larger the deviation from such anideal situation, the lower the degree of CB in the league, and thus the smaller theconsumers’ demand and the clubs’ revenues.While basically sharing both the remarks and the UOH, TSE models may differunder several other respects. Let’s start from a hypothesis which is now standard inthe literature, namely, that of considering the output ‘‘percentage of games won’’ asunivocally determined, through a contest success function (CSF), by each club’samount of technical and athletic talent. Indicating team i ’s talent with x i andassuming that talent is measurable in homogeneous units, so much so that we cansay that athlete a has more talent that athlete b if  x a [ x b , we have x i ¼ P Xa ¼ 1  x a ; where X is team i ’s number of athletes. Taking X  ¼ P i  x i as the total talent availablefor all the clubs in a given league, a logit CSF is: 5 See the previous footnote. 6 For a more sophisticated analysis, dividing consumers into committed supporters and uncommitted TVwatchers, with only the latter subject to the UOH, see Szymanski (2001).Competitive balance in football leagues 349  123
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