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Journal of Economic Literature Vol. XLI (December 2003) pp. 1137–1187

The Economic Design of Sporting Contests

STEFAN SZYMANSKI1

1. Introduction television viewing of sports events is esti- mated to be 77 billion hours per year.2 One hat is the optimal number of entrants might add to this several hundreds of mil- in a race, or the optimal number of W lions of hours spent in discussion at the teams in a baseball league? What is the opti- water cooler. Designing an optimal contest is mal structure of prizes for a golf tournament, both a matter of significant financial concern or degree of revenue sharing for a football for the organizers, participating individuals, championship? How evenly balanced should and teams, and a matter of consuming per- the competing teams be in the NASCAR or sonal interest for millions of fans. Not sur- Formula One championships? What is the prisingly, many lawyers and politicians maximum number of entrants per nation to express close interest in the way that sport- the Olympic Games that should be permit- ing contests are run. ted? What quota of qualifying teams to the Economists have something to offer as soccer World Cup should be allocated to the well. The design of a sporting contest bears developing nations? a close relationship to the design of an auc- These are all examples of design issues in tion. In both cases, the objective of the sports. Sporting contests are one of the most organizer is to elicit a contribution (a bid, an significant branches of the entertainment investment, or some effort) from contestants industry, measured by the amount of time who may as a result win a prize. The anal- that consumers devote to following them. ogy between an auction and a contest/tour- According to the U.S. Census Bureau, annu- nament3 is already well known (see e.g. Arye al attendance at spectator sports in 1997 Hillman and John Riley 1979). Given the totaled 110 million (equivalent to 41 percent objective function of the organizer and the of the population), while annual household

2 Kagan Media estimates that sports accounts for 25 1 The Business School, Imperial College, London. I am percent of all TV viewing, while Nielsen Media Research grateful to Jeff Borland, Braham Dabscheck, David estimates the average U.S. household views 2738 hours of Forrest, Bernd Frick, Philippe Gagnepain, Brad TV per year (7.5 hours per day). This significance to con- Humphreys, Erik Lehmann, Stefan Késenne, Gerd sumers is not reflected in dollar spending. The Census Muehlheusser, Steve Ross, Rob Simmons, Peter Sloane, Bureau reported in 1997 that spectator sports generate a Paul Staudohar, Tommaso Valletti, Andy Zimbalist, the direct income of only $14 billion domestically (0.17 per- editor, and two anonymous referees for valuable com- cent of GDP). The annual value of U.S. major league ments. I also thank seminar participants at the ESRC study sports broadcast rights is in the region of $4 billion group on the Economics of Sport, Arts and Leisure, the (Soonhwan Lee and Hyosung Chun 2001). Stockholm School of Economics, and Glasgow University 3 The words “contest” and “tournament” are used inter- for their observations. Errors are of course my own. changeably throughout.

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technology of the auction/contest it is possi- directions in which the literature may de- ble to design an optimal prize scheme con- velop. A unifying theme of the paper is that tingent on the distribution of contestant the empirical literature can do much to shed abilities/willingness to pay. While there have light on the issues raised by the theoretical been a number of reviews of the economics literature.5 of sports in recent years (e.g. John Cairns, The classification of sports is a subject Nicholas Jennett, and Peter Sloane 1986; that has exercised the minds of sociologists Rodney Fort and James Quirk 1995; and economists alike. One distinction that Lawrence Kahn 2000; John Vrooman can be made is between modern sports that 2000),4 none of these has attempted to have been formalized, quantified, and regu- explore systematically the design of sporting larized on the one hand, and traditional contests. sports that are often informal and only The contest design approach may seem an semi-structured on the other hand. unusual way of thinking to those who use Examples of the latter might include baseball or soccer as their sporting para- medieval football in Europe or the Aztec digm. In these and other team sports we are Ball Game (see Allen Guttman 1998 for accustomed to thinking of teams as inde- further examples). This paper deals prima- pendent entities that come together to agree rily with the commercialized modern on rules of the competition. In their review sports, almost all of which were formalized for this journal, Fort and Quirk (1995) state, somewhere between 1840 and 1900—e.g., “Professional team sports leagues are classic, baseball (1846), soccer (1848), Australian even textbook, examples of business cartels.” football (1859), boxing (1865), cycling Members of a sports league certainly have (1867), rugby union (1871), tennis (1874), common interests and may benefit from a American football (1874), ice hockey reduction of economic rivalry between the (1875), basketball (1891), rugby league teams. Many sporting contests are centrally (1895), motor sport (1895), and the coordinated, however, with little or no input Olympics (1896).6 from the teams or individual contestants; Historians (see, e.g., Tony Mason 1980; examples include the Olympic Games, the Wray Vamplew 1988) have argued that the soccer World Cup, the New York Marathon, process of formalization of sports mimicked and the U.S. Open Golf Championship. the formalization inherent in industrializa- What all these contests have in common is tion and urbanization (time-keeping, rou- the need to provide contestants with the tinization). Indeed, the commercialization of appropriate incentives to participate and sport was initially an urban phenomenon, perform. Joint decision-making through a since industrial towns and cities were capa- cartel is simply one (possibly inefficient) ble of supplying large paying audiences. It is mechanism to achieve this end. probably for this reason that most modern This review attempts to systematize the sports were formalized either in Great contribution of economic thinking to design Britain (the first industrialized nation) or the issues in sports, and to relate this research to the growing empirical literature on sports. This is an enterprise still in its infancy, how- ever, and much remains to be done to under- 5 This paper can thus be distinguished from fields such stand fully the interaction of contest design as “sabermetrics”—the study of baseball statistics for their own sake—which has little to do with empirical testing of and outcomes. The review will suggest new economic theory. 6 All of these dates, associated with early rulebooks, are subject to controversy. By contrast, golf, cricket, and 4 See also Andrew Zimbalist (2001) for a useful collec- horse racing had established rules and clubs from the tion of seminal articles in the sports literature. mid-eighteenth century. dec03_Article 2 12/4/03 11:17 AM Page 1139

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United States (the most rapidly industrializ- atively simple. Players perform and agree to ing nation of the late nineteenth century).7 abide by the tournament rules in order to In this paper we draw the distinction compete for a prize which is usually meas- between individualistic sports (such as ten- ured in terms of both status and money. nis, golf, and boxing) and team sports, such Players make little long-term commitment to as soccer and baseball.8 The distinction rests the organizers, even if it is an annual event, on the unit of competition and the nature of and select among available competitions to the demand for the contest. In team sports, maximize their own utility. Likewise, the the players act as agents on behalf of the organizers make few commitments to the team—which may be an actual employer athletes, and typically offer places to the best (e.g. a club) or some delegated authority players they can attract. The demand for an (e.g. a national team).9 In individualistic individualistic contest depends to a signifi- sports the player acts as a sole trader; typi- cant degree on the quality of the contestants cally in these sports, the athletes/players participating and the amount of effort they enter competition in order to establish who contribute to winning. Thus an individualis- is the best, because this is what interests the tic sporting contest conforms naturally to the spectators. The relationship between the standard contest model, outlined in the next tournament organizer and the players is rel- section. Section 3 reviews the contribution of the empirical literature to testing the pre- dictive power of contest models. 7 The other great industrial nation of the period, Germany, also developed its own sporting activity during The demand for team sports is more com- this period, the gymnastic “Turnen” movement. This plex. Firstly, while the organizational struc- movement eschewed competition between individuals in ture of individualistic sports is fairly uniform favor of the development of a disciplined athleticism with military purposes in mind, and was ultimately ousted by (for example, there is little difference the Anglo-Saxon sports (see Guttman 1998, ch. 7). between the organization of the New York 8 Like all classifications, this one is at best imperfect. Marathon and the Berlin Marathon, or that For example, the competitors in motor racing are teams of mechanics, but much of the spectator interest focuses on of the U.S. and the British Open Golf the individual exploits of the drivers. Rowing involves Championships), the organization of profes- teams of rowers competing in a format that is very similar sional team sports differs substantially on to most individualistic athletic contests, and horse racing is based on a distinctive form of cooperation between horse, either side of the Atlantic. Section 4 discuss- trainer, and jockey. One difference is that in individualistic es the major differences and considers how sports each contestant’s marginal productivity depends these differences emerged from the differ- only on their own effort, while in team sports it also depends on the marginal productivity of other team mem- ent institutional settings that ruled at the bers. While this makes individual productivity difficult to foundation of baseball (the archetypal North measure, its economic significance may not be all that American team sport) and soccer (the arche- great. In many team sports such as baseball and cricket, team members’ marginal products are almost entirely typal European team sport) at the end of the independent. Even where interactions are more impor- nineteenth century. tant, the economic implications are unclear and their Secondly, while consumers of team sports importance unproved. For example, if interaction terms were truly of economic significance in some team sports, resemble those of individualistic sports in one might expect to see players offering themselves to the wanting to see the best players, the nature market as partnerships, as happens, for instance, with of team sports “fandom” is that supporters teams of bond traders or teams of consultants. Even in team sports where the labor market is open to such possi- tend to attach themselves to teams rather bilities (e.g. soccer, rugby, or cricket), player partnerships than players, and teams identify themselves are almost unknown. The substantial empirical literature with particular locations.10 In practice this concerning the estimation of sports team production func- tions (see e.g. Kahn 1993) lies beyond the scope of this review. 10 While it is possible to be a fan of an individualistic 9 In amateur sports the team is a kind of partnership, competition (e.g. Wimbledon tennis) or event (e.g. the and early professional baseball and cricket teams were also Olympics), this tends to happen only in the case of a small organized on this basis. number of elite contests. dec03_Article 2 12/4/03 11:17 AM Page 1140

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can mean that fans attach themselves to the implications of the most commonly pro- perpetually weak teams that do not hire the posed alternative to the profit-maximizing best players, and maintain such attachments hypothesis, namely, win maximization. While over an entire life. However, contest organ- the controversy over the proper specification izers often express the concern that fans of the objective function of privately owned will lose interest in perpetually weak teams clubs is unlikely to be settled in the near and that when this happens they will desert future, this section also highlights the paral- the sport altogether. To prevent this from lel development of ostensibly not-for-profit happening, they argue, it is necessary to international sporting organizations offering design the contest in such a way that all international contests based on national rep- teams have roughly equal chances of win- resentative teams (e.g. the IOC and the ning, or that at least all teams win occasion- Olympics; FIFA and the soccer World Cup). ally.11 The competitive-balance issue has The section concludes with a discussion of tended to dominate the analysis of team the growing rivalry in the soccer world sports, and section 5 sets out some empiri- between club-based and national-team- cal evidence on competitive balance and based competition. related issues in North American and Most sports are governed hierarchically, European team sports. with a committee or commissioner at the Section 6 considers possibly the most apex of a pyramid possessing the right to important theoretical contribution to the change rules and arbitrate disputes. As analysis of team sports: the so-called invari- sporting governments, these have found ance principle. This states that (a) changes their authority challenged by the courts in ownership rights over player services when dealing with matters that have an (such as the introduction of free agency) economic or commercial dimension. and (b) certain types of income redistribu- Section 8 provides a brief review of tion (such as gate revenue sharing) will antitrust issues on both sides of the have no effect on competitive balance. Atlantic. Section 9 concludes. Empirical evidence on the first of these propositions is discussed in section 6.1, while section 6.2 considers the theoretical 2. The Design of Individualistic basis of the second. Sporting Contests Section 7 discusses other mechanisms It is relatively straightforward to apply used to promote competitive balance, such as contest theory to the design of an individual- prizes, salary caps, luxury taxes, promotion istic contest. Consider a simple footrace, and relegation. The role of exclusive territo- organized by a profit-maximizing entrepre- ries and its implications for optimal league neur (e.g., the owner of a racetrack).12 The size are also discussed in that section. The organizer may generate a profit by selling underlying objectives of organizers of team tickets, broadcast rights, refreshments, or sports have been a consistent source of con- merchandise, or some combination of these. troversy over the years. Section 7 discusses The organizer expects that spectators will be

11 The Blue Ribbon Panel on Baseball Economics (Richard Levin et al. 2000), which was formed by the com- 12 In some sports it is frequently argued that profit max- missioner to investigate whether revenue disparities imization is not the objective of the organizers (most among the teams in Major League Baseball were under- notably, see Sloane 1971). This may not make much dif- mining competitive balance, defined a proper level of ference to the design of a competition. For example, ama- competitive balance as a state where “every well-run club teur sporting associations frequently seek to maximize has a regularly recurring hope of reaching postseason play” income from a popular sporting event, which is then used (p. 1). to develop the grass roots. dec03_Article 2 12/4/03 11:17 AM Page 1141

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attracted by the quality of the field entering multiplied by the value of the prize (V), less the race and the effort the entrants con- the cost of effort. It is assumed that the tribute. Thus the objective is to design an contestants are risk neutral.14 incentive mechanism to maximize the effort The probability of success is defined by contribution of the selected entrants. the technology of winning—the Contest Success Function (CSF)—which depends 2.1 The Symmetric Winner-Take-All on both the effort contribution of the ath- Contest letes and their inherent abilities. For the The winner-take-all contest has been time being, we assume that all contestants applied to a number of economic problems have equal ability (symmetry). A natural and originates with Gordon Tullock’s (1980) form for the CSF is the logit function model of a rent-seeking contest.13 γ = ei The organizer’s program can be written as pi n , (3) γ n   ∑ ej π = − = Max R∑ ei  V (1) j 1 V  =  i 1 where γ is a measure of the discriminatory subject to power of the CSF. A high γ implies that ∗ ∗ pi (ei ) V ei p (ei) V ei , for all ei even slightly higher effort than one’s rivals (incentive compatibility) ensures a high probability of winning the ∗ ∗ γ pi (ei ) V ei 0 prize, while a low value of implies that (individual rationality) (2) differences in effort have little impact on outcomes. where R(.) is a strictly concave revenue func- This winning technology differs funda- tion that depends upon the sum of contribu- mentally from that assumed in an auction, tions e of each contestant, which can be i where the highest bidder wins with proba- interpreted in a number of ways (e.g. effort, bility one (the contest is perfectly discrimi- investment, bids, ability) dependent on the nating). Here, the technology does not dis- context—for the remainder of this section it criminate perfectly between effort levels, is labeled “effort.” The cost of effort is and the highest bidder can only be certain of assumed to be linear with marginal cost winning if all other contestants contribute no equal to unity. Equation (2) states that each effort at all, except in the limiting case as γ contestant selects their optimal effort goes to infinity, when the logit contest (incentive compatibility) and that all contest- becomes perfectly discriminating.15 That ants willingly participate (individual rational- contests are in fact imperfectly discriminat- ity). The total payoff to each contestant ing, yielding uncertainty of outcome, was depends on the probability of success (p ) i recognized by Walter Neale (1964) in his seminal paper. 13 The analysis of rent-seeking contests has been applied to, inter alia, labor markets (e.g. Edward Lazear and Sherwin Rosen 1981), competition for innovation (e.g. Glenn Loury 1979) and competition for research contracts 14 Risk aversion is a natural assumption in many exam- (e.g. Curtis Taylor 1995). There is also a substantial relat- ples of labor-market contests, but in sporting contests ed literature on all-pay auctions (see e.g. Michael Baye, involving professional athletes risk neutrality seems less Dan Kovenock, and Casper de Vries 1996). Theoretical objectionable. The very fact of investing the time and research on the implications of rent-seeking contests effort from an early age to become a professional athlete, includes Baye et al. (1999), Ani Dasgupta and Kofi Nti when the probability of substantial earnings is very low, (1998), Avinash Dixit (1987), Jerry Green and Nancy would seem to suggest selection in favor of those with Stokey (1983), Richard Higgins, William Shughart, and negligible risk aversion. Robert Tollison (1985), Barry Nalebuff and Joseph Stiglitz 15 Lazear and Rosen (1981) and Dixit (1987) use the (1983), Shmuel Nitzan (1994), Nti (1997), and Stergios probit model, but as yet this has not been applied to the Skaperdas (1996). analysis of a sporting contest. dec03_Article 2 12/4/03 11:17 AM Page 1142

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Solving the contestants’ first-order condi- Having identified the incentive-compati- tions, we find the optimal effort level in the ble investment level, it is then trivial for the symmetric case16: organizer to select the prize fund to maxi- − ∗ γ Vn()1 mize the difference between revenues and e = , (4) 18 i n2 costs. from which it is apparent that 2.2 Multiple Prizes in Symmetric Contests (i) individual and aggregate effort is In practice, most organizers of sporting increasing in the value of the prize; contests do not offer a winner-take-all prize: (ii) individual and aggregate effort is in addition to gold medals, there are silver increasing in the discriminatory and bronze. Benny Moldovanu and Aner power of the CSF; Sela (2001) show that multiple prizes can be (iii) individual effort decreases with the optimal in a perfectly discriminating all-pay number of contestants; auction, depending on the cost structure of (iv) aggregate effort increases with the the bidding technology—if the cost of bid- number of contestants. ding is linear or concave, a single prize These results are intuitive, although per- dominates any other prize structure. If costs haps the third might surprise nonecono- are convex, however, a second prize can be mists. Large fields of contestants are usually optimal. Szymanski and Valletti (2002) associated with highly prestigious contests extend the analysis of the problem to an such as the Olympics, so there may be a cor- imperfectly discriminating (logit) contest. relation between the value of a prize and the They show that if contestants are symmet- number of entrants, which obscures the dis- ric, a first prize always dominates, while if couragement effect of large fields on effort. contestants differ enough in ability then a However, organizers of individual race second prize can be optimal. In an imper- meetings typically do seek to limit the field fectly discriminating contest offering a prize so as not to dilute the incentives of the par- fund to be divided between the first and the ticipants. The result is very similar to the second prize, the return to contestant i can standard Cournot-Nash oligopoly result that be written as equilibrium output choices for individual +− − − firms decrease in the number of competitors ()pkiiii112()()11 p p k V e (5) but the aggregate output increases.17 If the where k is the fraction of the prize fund allo- organizer is interested in obtaining the max- cated to the first prize, p is the probability imum winning effort then the optimal num- i1 of contestant i winning the first prize, and p ber of contestants is two (see e.g. Richard i2 is the probability of i winning the second Fullerton and Preston McAfee 1999). If the prize (contingent on not having won the first organizer is interested in a specific level of prize). Note that when the contest is sym- performance then the reward function may metric the probability of winning the second look more complicated than a simple con- prize in equilibrium is the same whoever test: e.g., a bonus based on the race time wins the first prize (other than contestant i). plus a prize for winning. For a logit contest pi1 is still defined by (3), while pi2 is the equivalent expression for the 16 Here we focus on pure strategy equilibria. A mixed probability of winning second prize, the only strategy may exist even if a pure strategy equilibrium does not (see e.g. Baye, Kovenock, and de Vries 1994). Note difference being that the contest for second that the equilibrium described here will not be symmetric prize involves n1 contestants rather than if there are some contestants who decide not to enter the n. Hence, in general: race; we ignore this possibility here. 17 Nti (1997) shows that the result on aggregate effort is sensitive to the type of winning technology selected. 18 The first order condition is R' γ(n1)/n1. dec03_Article 2 12/4/03 11:17 AM Page 1143

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γ Asymmetry has been little studied in the = ei pi2 n−1 . (6) contest literature (two notable exceptions γ ∑ eh are Dixit 1987 and Kyung Baik 1994), even h=1 though this is a fundamental characteristic of hj≠ many contests, not least in sport. Asymmetry In the symmetric case, the first-order can be modeled either as a difference in the condition for contestant i can be rearranged cost of effort required to achieve a given to show that winning probability or as a difference in the  − −  ∗ ()()n 11k winning probability for any given level of eV= γ  −  (7)  n2 nn()− 1  effort. Taking the first of these approaches, the payoff functions in a two-person contest from which it follows that an increase in the can be written as weight attached to the second prize (reduc- ing k) will lead to a reduction in effort. In a π β 1 p11kV (1 p11) p12 (1 k)V (1 )e1 two-person contest, effort falls to zero when β 1 (2k 1) p11V(1k)V (1 ) e1 k 2 (the second prize is identical to the first prize) but will be positive for all values of π (2k 1) p V(1 k)V (1β) e . (8) k ∈ [0, 1] for n 2. 2 21 2 2.3. Asymmetric Two-Person Contests Asymmetry has two effects on the contest. Most obviously, it will create a competitive Although symmetric contests should only imbalance—the greater is β the larger the ever have first prizes, most sporting contests low-cost player’s winning probability—and if are in practice asymmetric: there are asymmetry gets large enough the participa- favorites and long shots. This complicates tion constraint of the weak contestant will be the issue in two ways. First, in a symmetric violated. Secondly, it can affect total effort. contest there is no trade-off between win- Faced with two asymmetric contestants, the ning effort, average effort, and the variance usefulness of a second prize as an instrument of effort. In an asymmetric contest the of the contest organizer is relatively limited. organizer must decide the appropriate Total effort increases in the size of the prize objective. Maximizing winning effort is often fund and the share awarded to the winner. important (e.g. breaking the world record). The two first-order conditions for effort On the other hand, a close contest (compet- derived from (8), assuming the logit CSF (3), itive balance) may be valued if consumers imply that the effort ratio in equilibrium is like to see an even contest,19 and the organ- − β izer may be keen to maintain the overall e2 = 1 + β . (9) quality of the contest (average effort). e1 1 Providing greater incentive for winning This tells us that while the contest effort may reduce the effort of weaker con- becomes less balanced as the difference in testants and so reduce average effort. Even the cost of effort increases, the prize struc- if average effort does not decline, the vari- ture has no effect on relative effort: a second ance of effort may increase. Secondly, in an prize does nothing to improve the balance of asymmetric contest the existence of a second the contest. This suggests two policy options prize may not only increase the average for the organizer if competitive balance mat- and/or reduce the variance of effort, it may ters: (a) screen for ability to ensure balanced also increase the winning effort. contests and (b) handicap the strong player, i.e., increase the strong player’s (marginal) 19 Competitive balance is discussed in more detail in cost or subsidize the weak player’s (marginal) section 5. cost. Fullerton and McAfee (1999) consider dec03_Article 2 12/4/03 11:17 AM Page 1144

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the case where ability is not observable and Consider a three-person race with two weak show that by both setting the prize and contestants and one strong one. If the play- charging an entry fee the organizer can ers are more or less evenly matched, then it ensure that the best contestants enter and pays to put all the weight on first prize as in offer first-best effort either in a homogenous a symmetric contest. But the motivation contest with fixed costs or a heterogenous effect of the first prize is dulled if the two contest. This may explain, for instance, why weak contestants are very weak, because it is common to observe that entry to races however much effort they make they have with large financial prizes is by invitation little chance to win. It follows that if two out only to an exclusive group of athletes. of three contestants give up then even the Defining z(1β)/(1β), total effort is strong contestant is unlikely to make any given by effort. By introducing a second prize, the two weak contestants are given something to γ − +=221Vk() z ee . (10) play for, and as a result of their effort even 12 +−22β ()()11z the strong contestant cannot coast along γ When 1itisclear that e1 e2 quite so easily and is provoked into supply- V(2k1)/2, so that total effort is independent ing more effort. This observation suggests of β and any increase in asymmetry yields off- that large prize spreads should be observed setting increases and decreases in effort from when contestants are relatively evenly the strong and weak players respectively. matched but narrower spreads should be When γ 1 (the contest is relatively discrim- offered when there are large differences in inating) increasing asymmetry reduces total ability.20 effort since the discouragement effect for the A second prize may also improve compet- weaker player outweighs the encouragement itive balance, but at this stage a problem of effect for the stronger player. On the other definition arises. It is natural to think of bal- hand, when γ 1 the reverse is true and ance in terms of the variance of contribu- increasing asymmetry increases effort (when tions, but with three or more contestants it is the contest is not very discriminating no one possible for different combinations of effort is very motivated to supply effort, but asym- to produce the same variance, while in re- metry provides an encouragement to the ality the organizer may not be indifferent strong player to secure the prize). Lazear and among them. For example, consider a three- Rosen (1981, p. 858) demonstrate similar person contest where only effort matters. If results in a rank order labor tournament contestant 1 contributes three units of effort, where the CSF is asymmetric, but in their contestant 2 contributes two units, and con- model the effect on total effort depends on testant 1 a single unit, the variance of effort the concavity or convexity of costs. (equal to one) would be the same as an alter- native case where the first contestant sup- 2.4 Asymmetric Contests With More Than plied 2.732 units and the other two supplied Two Players a single unit each. In the first case there is an With more than two players a second equal gap between each contestant, while in prize can be a useful instrument for the the second case there is a larger gap organizer. For instance, a second prize can now be a motivational device. Szymanski 20 The modern practice in schools and elsewhere of and Valletti (2002) develop a formal model offering almost all competing students a prize of some of a three-person contest to show that sec- sort for participating in sporting contests is often criti- ond prizes may not only improve competi- cized as an excess of political correctness—but in this context it might be viewed as simple recognition of the tive balance, but also increase total effort. need for motivation for all contestants when abilities are The intuition is quite straightforward. heterogenous. dec03_Article 2 12/4/03 11:17 AM Page 1145

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between the strong player and two equally where a single prize is awarded to the ulti- weak players. The race for first place may be mate winner of the contest. They showed more exciting in the first case, but even then that in a symmetric contest where the the strong player has a big lead (in terms of object is to ensure dissipation of all the effort). By contrast, the second case will at rents (i.e. so that total effort expended least produce a close race for second place, equals the value of the prize), an S-contest which may compensate for a lack of tension is preferred for γ 1 (high discriminatory in the race for first place. An argument can power), while for γ 1 a T-contest is pre- be made for either case being more attrac- ferred, and for γ 1 the choice makes no tive. The problem is that there is no natural difference. The intuition behind this result metric for competitive balance when n 2, is that when discriminatory power is high a and thus it may be difficult to rank different single simultaneous contest is enough to incentive schemes. ensure that all rents are dissipated. But when the discriminatory power of each 2.5 Match Play individual contest is low a single contest In many sporting contests the organizers cannot dissipate all rents, whereas a multi- must make a structural choice between stage contest, in which contestants have to match play and simultaneous play by many put in additional effort at each stage, can contestants. For example, a golf tournament dissipate rents.21 could be organized by pairing contestants 2.6 Dynamic Contests and allowing the winner from each pairing to enter the next stage until a winner emerges The contests described so far have been from the final pairing, or all players could one-shot games or, in the case of sequential play simultaneously and the player with the contests, it has been assumed that the con- lowest score would be declared the winner. testants compete in every round until elimi- Some sports, such as tennis, cannot realisti- nated. However, if contestants acquire infor- cally be organized as simultaneous contests, mation about the state of play as the game while others, such as Olympic track and progresses, they may decide to drop out alto- field, typically have elements of both (e.g., gether. There are a number of models in the eight lanes of runners and the fastest go economics literature that examine contests through to the next round). in a dynamic context, most notably the war Rosen (1986) specifically used the exam- of attrition and competition for monopoly, ple of a tennis tournament to consider the preemption games associated with patent optimal prize structure in order to maintain races (both types of game are reviewed in effort over a match play tournament. He Drew Fudenberg and Jean Tirole 1991) and showed that if the reward for winning market share attraction games in the adver- increases linearly as the tournament pro- tising literature (see George Monahan and gresses, then effort will decrease, since the Matthew Sobel 1994). These have some added spur of reaching higher and higher implications for contests that involve a prizes is diminished. This, he argued, ration- sequence of competitions such as the T-con- alized the observation that rewards are often tests described above. Many of these types heavily skewed toward the top end of a con- of contest are found in team sports, but indi- test, since this prize structure will ensure vidualistic contests can also involve a dynam- that effort is nondecreasing. ic element, either because the contest itself Mark Gradstein and Kai Konrad (1999) compared simultaneous contests (which 21 See also Moldovanu and Sela (2002) for discussion they labeled S-contests) and match play of different contest architectures in all-pay perfectly contests (which they labeled T-contests) discriminating auctions. dec03_Article 2 12/4/03 11:17 AM Page 1146

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is drawn out (e.g., a marathon or a five-set to “leapfrog” ahead of the leader (e.g. tennis match) or because players compete Harris and Vickers 1987).22 throughout a season for rankings. As far as a contest organizer is concerned, In the war of attrition, competitors sup- these types of games are degenerate, in the ply effort in the expectation of winning a sense that spectators typically expect to prize at some future date when all rivals watch a full contest and might ask for their have dropped out of the contest. If contest- money back if one of the contestants pulled ants are symmetric then a pure strategy out.23 However, in contests where the cost of equilibrium (in which each contestant is effort is extremely high (e.g. marathon run- indifferent between staying in and drop- ning and heavyweight boxing) it is not ping out of the game) does not exist. A uncommon for an out-of-contention player mixed strategy equilibrium does exist to pull out. Contest organizers may try to where each player exits with some proba- create some uncertainty about performance bility and the probability equates the levels (perhaps even changing the rules) in expected value of remaining with the order to prevent this from happening. expected gain from quitting. However, asymmetric pure strategy equilibria also 3. Empirical Research on Individualistic exist, and if the contestants have different Sports abilities the game may be degenerate with The research agenda discussed in the pre- weaker contestants withdrawing instantly vious section can be summarized under four (see e.g. Jeremy Bulow and Paul main headings: Klemperer 2001). (i) The impact of prizes on incentives to In the war of attrition, contestants learn perform (depending on discriminatory nothing from their continued participation power, effort functions, and the size of in the game (the game is memoryless). In the prize fund); preemption games (e.g. Christopher Harris (ii) The impact of the distribution, or and John Vickers 1985; Fudenberg and spread, of the prize fund (second Tirole 1985) the players acquire experience prizes, third prizes, and so on); (e.g. know-how in a patent race), and expe- rience increases the probability of success, 22 “Consider a foot race between two athletes. Assume so that at any point the perception that one that it is common knowledge that the two athletes are player has an established lead may cause all equally good, and that they prefer to reserve themselves the other players to withdraw. In particular, (run at a slow pace) rather than exhaust themselves by running at a fast pace. Suppose further that the leader has if one player is known to enter the race eyes in the back of his head and can monitor whether the with an established advantage, no other follower is catching up. Because the leader can keep his contestants will enter (or, if they enter, will lead by speeding up if the rival does so, there is no point ∈ for the rival in even engaging in the race. The leader can supply zero effort), a result known as - thus proceed at a slow pace without fear of being preemption (see Fudenberg et al. 1983). leapfrogged. But the picture changes dramatically if the This kind of first-mover advantage can thus two athletes run on tracks separated by a wall. Suppose that the wall has holes, so that from time to time each ath- undermine the incentive of contestants, lete can check his relative position. Now the leader can no especially weaker ones, to supply effort, longer run at the slow pace; if he did, the follower could effectively handing success to the domi- run fast, leapfrogging the leader without his noticing it, and force him to drop out of the race at the next hole. Thus nant players “on a plate.” This extreme lags in information (or in reaction) engender competition” result is sensitive to assumptions about Tirole (1988). 23 information sets, however, and if there is Of course, if a championship is decided as a “best of n matches” like the seven-match World Series, the organ- some uncertainty about the state of play izers are keen to see the contest go to the wire. This is yet then the follower might have an incentive another reason for wanting competitive balance. dec03_Article 2 12/4/03 11:17 AM Page 1147

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(iii) The impact of the structure of the sumably reflects the notion that a laggard contest (number of contestants, will be discouraged as in a war of attrition). simultaneous or sequential contests This prediction is also strongly confirmed and so on); by the data.26 (iv) The impact of pre-screening and Another important issue that Ehrenberg handicapping. and Bognanno address is the relationship Researchers in the field of contest theory between performance in a given tournament have set out to explain the widespread use and entry. If larger prizes attract better con- of prizes as an incentive device in labor and testants then the observed improvement in product markets.24 The claim that sports scores may be attributable to the “sorting” provides a natural laboratory for testing effect rather than the tournament incentive hypotheses from the economics literature is effect. In fact, they found no evidence that widely made (e.g. Kahn 2000). While that their prize results were due to sample selec- paper focused primarily on team sports, it tion bias. This issue has also been addressed pointed out that “some of the most intrigu- in James Lynch and Jeffrey Zax (2000), who ing evidence on the links from incentives to examine data on nearly two thousand con- performance comes from sports … like golf testants covering 135 different road races in and marathon running.” In these sports it is the United States ranging between five kilo- possible to gather data on individual per- meters and a full marathon (42 km). They formance and relate that data to the prize were able to construct a measure of pre-race structure offered in individual tournaments. expected rank, based on an athlete’s previous Perhaps the best-known results are those of history, and then to construct a measure of Ronald Ehrenberg and Michael Bognanno the incentive to supply effort based on the (1990a,b) who examined scores in American difference between the prize for achieving and European PGA golf tours.25 Their prin- his or her pre-race rank and one rank lower cipal finding is that scores tend to be lower than this (presumably the asymmetry of the (so performance is better) when the prize race is thought to be large enough that mul- fund is larger, which seems to be a striking tiple prizes are required to increase total endorsement of tournament theory. They effort). They find on this basis that recorded also considered the effect on the final round times are decreasing in the prize difference, score of an individual’s current position in apparently suggesting higher effort in the contest. Since the prize spread decreas- response to larger prize spreads. However, es with rank (the difference between the once the pre-race ranking variable is includ- first and second prize is much larger than ed in the regression, to account for the qual- the gap between the tenth and eleventh ity of the field entering the race, the impact prize) it is predicted that effort will be of the prize spread disappears. The authors higher and scores lower in the final round thus attribute the impact of prize spreads to when a player has a higher placing at the the sorting effect rather than the tourna- beginning of the round (this hypothesis pre- ment incentive effect. Michael Maloney and Robert McCormick 24 This research agenda is therefore primarily positive (2000) use data on 115 footraces ranging rather than normative. However, the adoption of procure- between one mile and a full marathon ment auctions by governments has introduced a normative element to this literature. 25 “The Ehrenberg and Bognanno work is perhaps the 26 Michael Orszag (1994) was unable to replicate these best test of tournament theory, not because it is easily findings using data on the 1992 U.S. PGA tour. He argues generalizable to the corporation but rather because the that this may be due to increased media pressure since data are so well suited to testing the model” (Lazear 1995, the 1980s causing more randomness (e.g. nerves) in the p. 33). relationship between effort and performance. dec03_Article 2 12/4/03 11:17 AM Page 1148

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involving nearly 1500 athletes. They identify performance deteriorated.28 Higgins and the sorting effect with the total size of the Tollison (1990) examine the impact of the prize fund and the incentive effect with the number of contestants on the average dis- prize spread, and find that both effects are tance of contestants behind the winner in statistically significant and have the expected the Kentucky Derby and find that larger sign. Although on average the prizes seem fields tend to fall further behind the winner, quite small (about $400), their impact is sig- which they equate with a slower race, con- nificant since doubling the prize spread sistent with contest theory. However, they reduces race times by 4 percent. One weak- also find that larger prizes do not appear to ness of these footrace studies is that the con- produce systematically faster times. testants do not include a significant fraction Michael Maloney and Kristina Terkun of the world’s best, which is reflected in the (2002) address an issue that has generally average times of the sample. Bernd Frick, been neglected in the literature, notably the Joachim Prinz, and Alexander Dilger (2001) competition between prize-givers and the consider a sample of 57 marathons run impact of this competition on prize spreads. worldwide and involving much larger prize They point out that if prize-givers compete money ($135,000 per race in 1993 dollars). to attract contestants, as is the case with They examine the impact of the total prize motorcycle racing sponsors, who are the fund, its distribution, and bonuses paid for subject of their study, then if the prize fund achieving a fast time. They find that (a) dou- offered by rival sponsors increases, all else bling the average prize reduces average equal, a given sponsor must reduce the prize times by 1 percent; (b) doubling the spread spread in order to attract the same contest- improves average times by 2 percent; (c) ants. They find that this prediction, which doubling bonus payments improves average they derive from Lazear and Rosen, is times by around .75 percent; (d) increasing indeed supported by the data on prize funds the prize fund, spread, and bonuses increas- and spreads in a sample of 112 sponsors of es the closeness of the race, measured as the motorcycle races. time difference between the winner and One concluding comment on individual other finishers; and (e) race times are contests concerns cheating. Thus far we have decreasing in the number of “in the money” assumed that all efforts contributed are ranks (i.e. the number of prizes). equally valid, while in reality certain kinds are Apart from footraces and golf, almost the proscribed (e.g. bribery and performance- only other individualistic sport to have pro- duced some empirical research is horse rac- 28 Brian Becker and Mark Huselid (1992) analyzed 27 ing. Susan Fernie and David Metcalf driver performance in NASCAR races and found that prize (1999) examined the effect of a change in spread improved race times. While much of the interest of the fans is focused on the drivers in this sport, there is the compensation of British jockeys which clearly a very strong team element in the preparation of involved replacing performance-related the car. Rafael Tenorio (2000) considers the practice in payments with noncontingent retainers. boxing of providing a “purse” for title fights that depends not on current but rather on past performance. He points Their evidence shows that individual out that this may lead to inadequate effort supply in these matches. However, this phenomenon has much to do with the risk attached to boxing. Because of the fragmentation of governing bodies in boxing, promoters compete to offer boxers the best terms to stage a fight. A similar situation applies in the world of chess, where payments for the 27 Ignoring the possibility that horse and jockey oper- appearance of champions also tend to be high and inde- ate as a team. Team elements might also be identified in pendent of performance, but in this case the personal risks golf (player and caddie) and foot races (e.g. runner and are not so great and so the temptation to “take the money trainer). and run” (or rather, fall over) is not so great. dec03_Article 2 12/4/03 11:17 AM Page 1149

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enhancing drugs). Little has been written on per nation has a significant influence on the the economics of cheating in this sense, outcome of competition.29 although a recent paper by Mark Duggan and Steven Levitt (2002) illustrates the 4. The Comparative Economics of potential for research in this area. A related Team Sports point, raised by Lazear (1989), is that tourna- 4.1 Peculiar Economics ments create an incentive to undermine the performance of rivals in order to increase The analysis of team sports has been pri- one’s own probability of winning—i.e. sabo- marily motivated by normative issues.30 tage. Luis Garicano and Ignacio Palacios- Economic analysis has been used to advise Huerta (2000) have examined this proposi- team owners and player unions when nego- tion for the case of soccer, where a change in tiating wage deals, as testimony in antitrust the points system appeared to lead both to cases, as testimony in congressional hearings more creative effort and more sabotage on legislation, and other proposed public (fouls, in the case of soccer). interventions in the organization of sporting Despite the enthusiasm of theorists for contests. Economists and lawyers have also sports as a laboratory for testing contest the- used economic analysis to propose alter- ory, it is apparent that there remains a great ations to the design of sporting contests (see deal more work to be done in this field. e.g. Fort and Quirk 1999; Zimbalist 2003; Almost the only issue considered thus far has and Stephen F. Ross 1989). been the impact of the size and spread of the The analysis of normative problems in prize fund. While most research seems to sports, as in many activities, is often made confirm the most basic economic proposi- more difficult by the role of culture. A con- tion that bigger prizes produce more effort, test design that is optimal for a particular even this result is subject to dispute due to group of consumers may not be to the taste the simultaneity of sorting and incentive of another. A good example is the attitude effects. Larger prize spreads seem to elicit toward player trading in team sports. In more effort, but the pure winner-take-all North America most fans seem to frown contest appears to be a purely theoretical upon player mobility and place the greatest possibility. value on players who remain loyal to the Issues deserving further attention include same team over their entire career. In the value of screening, the role of handicap- Europe, however, player trading has always ping, contest structure (match play and been an accepted part of the soccer system. simultaneous contests) and discouragement While most fans would prefer that good effects, the impact of penalties (e.g. failing players remain on the team, mobility is to make the cut in golf), the impact of qual- accepted as a fact of life and fans do not ifying races, cheating, sabotage, and possibly other issues. None of the papers discussed 29 This is also an important issue in team sports. For examined in any detail the objectives of the example, until the 1970s, European and South American teams were awarded a disproportionate share of qualifying organizer, which are clearly critical in deter- places in the soccer World Cup, while after that period the mining the optimal design. For example, policy was reversed by the governing body (FIFA). Since rules on qualification for the Olympic the 1970s the African teams were given an increased share and have (therefore?) been increasingly successful in the Games reflect the values of the founders of tournament (John Sugden and Alan Tomlinson 1999). the Olympic movement, and are not simply 30 Perhaps the main exception, to this has been in the intended to find the fastest runner or swim- field of labor economics where data on earnings in team sports has been used to develop tests of discrimination mer. Discrimination against stronger (reviewed in Kahn 2000 and Sherwin Rosen and Allen nations by restricting the number of athletes Sanderson 2001). dec03_Article 2 12/4/03 11:17 AM Page 1150

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seem to express opposition to player trading attract support as long as they are winning in principle.31 and then collapse when they lose (a rational It is possible that different attitudes may bubble); (b) team owners dissipate all the reflect broader cultural differences, while rents in competing to hire the best talent; historical accident and path dependency may and (c) the opportunities for gambling on also account for different practices. Clearly, the records of individual teams generate tradition and folk memory are an important match fixing. aspect of sports fandom—but are all tradi- The founders of the National League set tions equally likely to stick, or are some more out to create a new kind of equilibrium, likely to hold in some cultures than in oth- more satisfactory for team owners. The ers? For example, Americans and Europeans National League was a deliberately elitist seem to enjoy the same kinds of individualis- affair. Its exclusivity invested members with tic sports (Olympic sports, golf, tennis, box- a stake in its long-term success (to combat ing, etc.) but most are attracted to quite dif- short-run incentives for match fixing); its ferent team sports. Moreover, as pointed out granting of exclusive territories guaranteed in the introduction, while the design of indi- a local monopoly (providing an incentive to vidualistic contests seems to be relatively invest in the local market); and its reserve similar throughout the world, there are clause established monopsony rights over some substantial organizational differences the players (ensuring that the income between North American and European stream from matches accrued principally to team sports. It is useful therefore to begin the owners). The extraordinary success of the analysis of team sports by some compar- this model made it not only the basis for the isons in the development of the archetypal national sport of the United States, but also American team sport, baseball, and the for the other North American team sports archetypal European team sport, soccer. (football, basketball, and ice hockey). American sports played in other countries 4.2 Baseball adopted this model (e.g. baseball in Japan Harold Seymour (1960), the authoritative and Mexico, basketball in Australia), as have historian of early baseball, made it clear that some other sports in other countries influ- the structure of the National League, creat- enced by the United States. (e.g. Australian ed in 1876, and the foundation of organized Rules Football in the 1970s). While other baseball emerged as a consequence of the team sports in the United States developed free-for-all that was undermining interest in new organizing principles (e.g. the draft in the new national sport. From the end of the football or the salary cap in basketball) Civil War, interest in the game spread rapid- these principles were largely integrated into ly across the United States, with teams and a common framework that characterizes competitions proliferating and vying to each of the major sports. These common attract spectators. The barnstorming teams elements include: of this era crossed the country in search of 1. organizational independence of the opponents, relying on reputations driven by domestic major leagues; winning records to generate income. The 2. a fixed number of teams; natural equilibrium of this free-entry 3. entry through the sale of expansion dynamic game is (a) barnstorming teams franchises; 4. exclusive territories and franchise 31 Leo Kahane and Stephen Shmanske (1997) found mobility; that teams with more stable team rosters enjoyed higher 5. draft rules giving teams monopsony attendance, all else equal. Fans appear genuinely to prefer team stability. There is no evidence of any such preference rights in player acquisition; among European soccer fans. 6. roster limits; dec03_Article 2 12/4/03 11:17 AM Page 1151

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7. low player mobility and limited player worked inside them. This meant that (a) the trading for cash, especially for top stars; Football League never attempted to become 8. collective bargaining over player condi- an exclusive institution, but intended from tions; the start to admit, eventually, all the major 9. collective sale of national broadcast teams into its ranks, and (b) League teams rights (exempted from antitrust); accepted from the beginning the practice of 10. collective sale of merchandising; releasing star players to represent their 11. restrictions preventing the stock mar- country in international competition without ket flotation of clubs. compensation (although this has become Each of these arrangements has been increasingly controversial). adopted to a greater or lesser extent, but is As soccer spread rapidly around the globe present in all the major leagues.32 Some other and other nations adopted the British system, types of agreement, such as gate-revenue there evolved a distinctive organizational sharing (MLB33 and NFL) and salary caps structure involving (i) an overarching govern- (NBA, NFL) have not been universally ing body responsible for the rules and organ- adopted, but are not inconsistent with the izing highly successful competitions (e.g. the structure of the non-adopting leagues (which World Cup, the European Championship) have considered adoption and may yet adopt). independently of domestic league authori- These structures are quite distinct from those ties; (ii) a domestic league system incorporat- found in sports leagues outside of the United ing promotion and relegation35; and (iii) a States, most notably in the case of soccer, system where star players are paid employees arguably the world’s most popular team sport. of clubs and play for them (primarily) in league competition, and are also representa- 4.3 Soccer tives on the national team, whose success is The creation of the Football League in usually seen as even more prestigious. This England in 1888 had similarly momentous system has also been applied to a number of implications for the national pastime of other team sports, usually in countries where nations that adopted the British model of the soccer system is dominant (e.g. rugby league organization (see Simon Inglis 1988 union and basketball in Europe36). Common for full details). The Football League was elements of the “soccer system” include: formed by a group of teams that belonged to 1. integrated governance structure within an all-encompassing governing body, the a global hierarchy and national leagues Football Association (FA), founded in 1863. subordinate to national associations that As well as laying down the rules, the FA participate in international competition administered its own successful club compe- using league players; tition, the FA Cup, and organized interna- 2. mobility of teams through the system of tional representative matches against other promotion and relegation; countries using club players.34 Unlike the 3. free entry for new teams at the bottom founders of the National League, the 35 founders of the Football League did not This is a structure in which clubs affiliated with the governing body are promoted from a given league division break away from the existing structures, but to its immediately senior division on the basis of league ranking at the end of each season, and subject to relegation 32 Here meaning Major League Baseball (MLB), the to the immediately junior division on the same grounds. National Football League (NFL), the National Basketball 36 There are exceptions: in the United Kingdom, Rugby Association (NBA), and the National Hockey League League has adopted many American-style restrictions. The (NHL). case of Australian team sports is interesting, since these 33 In the 1990s MLB ceased sharing gate revenues only had structures resembling European sports until the 1980s in favor of local revenue sharing (including TV income). but since then a number of American institutions have 34 The first FA Cup final and the first international been adopted (see e.g. Braham Dabscheck 1989; Rob match (Scotland v. England) both took place in 1872. Hess and Bob Stewart 1998). dec03_Article 2 12/4/03 11:17 AM Page 1152

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of the hierarchy, but promotion on seen as only imperfect substitutes, and while sporting merit only; competition for player services is intense, it 4. nonexclusive territories; has not brought about league bankruptcy or 5. competitive labor markets at the entry mergers (even for relatively small European stage, no draft; nations such as Belgium, Denmark, or 6. no roster limits; Greece). This issue is discussed in more 7. high player mobility and trading for detail below. cash, especially for top stars; Some commentators, most notably Fort 8. limited unionization or collective bar- (2000), have argued that these institutional gaining over player conditions;37 differences have given rise to structural dif- 9. limited collective sale of national broad- ferences that are more apparent than real. cast rights (no antitrust exemption); For example, he argues that the difference 10. no collective sale of merchandising; between the closed, North American 11. limited restrictions on the stock mar- leagues and the open soccer leagues of ket flotation of clubs. Europe (i.e. open to new entry through pro- These are material differences from the motion and relegation) has little practical “baseball system” described above. A fur- effect, since both systems ensure that the ther institutional difference lies in the plu- best teams and talents migrate to where they rality of major soccer leagues compared to are most valued, whether it be through fran- the North American major leagues. While chise expansion or promotion. The proposi- competition among rival leagues has charac- tion that institutional differences have no terized part of the history of North implications for the attractiveness of sport- American sports, in most cases competition ing contests is a natural starting point for at the level of the league has not survived both theoretical and empirical analysis of long. Fans are drawn to the best competi- team sports, as has been shown by much of tion; competing head to head to attract tal- the comparative analysis of team sports ent drives down profits to the point where inside the United States (e.g. Quirk and Fort either leagues have folded or the incentive 1992; Gerald Scully 1995). to reestablish monopsony has led to merg- Moreover, some proposals for the reform ers. The close substitutability of rival major of North American leagues have a distinct- leagues in the eyes of consumers has thus ly European flavor. For example, the pro- been the driving factor toward establishing posal to break up the major leagues into dominant major leagues in each of the competing entities (Ross 1989; Quirk and North American team sports, particularly in Fort 1999) would create a structure in the television age. In European soccer, how- which independent leagues competed ever, the more rigidly defined regional loyal- among themselves in the regular season and ties associated with national territories has came together for the play-offs. This is sim- meant that the national leagues of Italy, ilar to the European model where teams Spain, Germany, and England have been compete in national leagues as well as a pan-European Champions’ League. Roger 37 It is perhaps more historically accurate to say that Noll (2002) and Ross and Szymanski (2002) unions were relatively weak both in North America and in have proposed the adoption by the major Europe until the 1950s. On both continents, union power leagues of the European promotion and rel- started to grow at this time, and had some notable suc- cesses in Europe (e.g. the abolition of the maximum wage egation system (see section 7.5). Extending and the retain-and-transfer system in England; Szymanski the analysis of team sports to assess the and Kuypers 1999, ch. 4). However, in North America the effect of the strikingly different institutions role of the unions has grown significantly over the past forty years, while in Europe they remain relatively weak to of soccer offers a rich laboratory for this day. researchers. dec03_Article 2 12/4/03 11:17 AM Page 1153

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5. Team Sports, Uncertainty of Outcome, exists. If the rate of exploitation is common and Competitive Balance across players, then at the level of the team, The justification for the striking range of contest success should be closely correlated restrictions utilized in the baseball system with player salaries. (fixed number of teams, exclusive territories, Aggregate data for total player wage bill draft rules, roster limits, limited player trad- per team provides a more direct test of the ing, especially in relation to cash sales, col- hypothesis. Table 1 reports a simple regres- lective selling of national broadcast rights sion of regular season winning percentage and merchandising, restrictions on owner- (wpc) upon team wage bill, expressed relative ship) has been based on the nature of com- to the average of all teams’ wage spending in petitive team sports. The argument, which the season (RW), for the four North has formed the basis of numerous antitrust American major leagues and the four leading defences in the U.S. courts, can be reduced soccer leagues in Europe. These results sug- to three core claims: gest a fairly close correlation between success 1. Inequality of resources leads to unequal and relative wage spending. Since the aver- age of RW is unity, by construction the coef- competition. α β 2. Fan interest declines when outcomes ficients and must sum to 0.5 for a repre- sentative sample (i.e. average wpc). A larger become less uncertain. β 3. specific redistribution mechanisms pro- estimate of implies a larger pay-perform- duce more outcome uncertainty. ance sensitivity. Thus the pay-performance These propositions have defined both the sensitivity of the two baseball leagues is much empirical and theoretical research agenda of smaller than that of the NFL. However, this team sports economics. This section reviews does not make baseball more balanced, since the empirical literature on the first two of the variance of relative wage spending is these propositions. Section 6 will consider much greater. Moreover, the explanatory power of the regression, as measured by the individual measures to improve competitive 2 balance. R ,isalso larger, most notably in the American League (home of the Yankees).38 5.1 Inequality and the Sensitivity of Success The apparent explanatory power of the to Resources regression for the European soccer leagues The starting point for empirical analysis is of England, Italy, Germany, and Spain is that better players produce more success, greater than for the North American and acquiring better players costs more leagues, even though the pay-performance money. In other words, we can substitute sensitivity is not significantly larger. Given a “cash” for “talent,” and talent plays the same much larger variation in wage payments, the role as “effort” in the CSF. Implicit in this same pay-performance sensitivity can notion is a functioning labor market, account for much more of the variation of notwithstanding any constraints upon initial win percentages. In that sense European endowments or trading rights within that leagues appear more predictable. It is strik- market. Direct testing of this hypothesis is ing, given the widespread concern in the relatively sparse in the literature. One United States about growing imbalance in implicit test is contained in the literature on 38 monopsonistic exploitation, following the The degree of sensitivity reported here seems much greater than that reported by other authors (e.g. James methodology of Scully (1974). Even if play- Quirk and Mohamed El-Hodiri 1974; Fort and Quirk ers do not receive their full marginal revenue 1999); this may be in part a consequence of choice of products, in an efficient market the rate of specification and using a larger and longer panel of data. Zimbalist (1992) reports a similar R2 for baseball and con- exploitation per unit of talent should be the cludes that “average team salary has been related only same—otherwise an arbitrage opportunity tenuously to team performance.” dec03_Article 2 12/4/03 11:17 AM Page 1154

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TABLE 1 PAY-PERFORMANCE SENSITIVITY ESTIMATES

αβσσ∗ σ 2 League wpc wpc RW R Period Obs North America Baseball NL .42 .08 .07 .04 .27 .11 80–96 208 Baseball AL .40 .10 .07 .04 .33 .26 80–96 238 NFL .19 .31 .19 .13 .13 .05 89–00 350 NBA .21 .29 .16 .06 .22 .16 86–00 351 NHL .35 .15 .10 .06 .23 .11 90–98 218 European soccer Premier League (England) .33 .19 .11 .08 .34 .34 74–99 339 Serie A (Italy) .34 .15 .13 .11 .63 .56 88–99 214 Bundesliga (Germany) .39 .12 .11 .09 .47 .28 82–96 244 Primera Liga (Spain) .43 .07 .11 .08 .87 .32 97–02 111 αβ ε Notes: Estimated equation: wpcit RWit . RW is wage bill of a team relative to average wage bill for the σ∗ league in that year. All estimates significant at the 1% level. wpc is the idealized standard deviation if teams had an equal chance of winning each match they played ( .5/√m, where m is the number of matches played by each team). European data refers to the top division only.

baseball, that the variation of wages and the One interpretation of this result is that in R2 of the regression are only noticeably larg- English soccer there is an unrestrained mar- er in the American League compared to the ket for players so that there is no barrier to other North American sports and even then the operation of an efficient market (for these do not reach the levels found in the details of its operation, see Szymanski and European leagues. In more recent years, Kuypers 1999). In MLB, player contracts are however, there may have been a trend much more restrictive, both for players and toward increasing predictability (see owners, and this gives rise to bargaining over Stephen Hall, Szymanski, and Zimbalist team rents, the outcome of which is likely to 2002). depend on past performance. Testing this Correlation does not imply causation. An hypothesis, which requires the collection of implicit assumption in the regression specifi- a wider range of potential explanatory vari- cation is that wages cause performance—but ables for MLB, is an important subject for it could be argued that causality runs in the future research, as is the nature of causality opposite direction, from performance to in other leagues.39 wages. For example, it is usual for winning One feature of table 1 that might strike a teams to be paid bonuses, and it is sometimes North American reader is the combination said that team owners would rather come of relatively low standard deviation of win- second than win a championship in order to ning percentages, often considered an indi- avoid excessive bonus payments (an example cator of competitive balance, in the of the limited role of prizes in rewarding European leagues, combined with relatively team, as opposed to player, performance). high standard deviation of wage payments Testing for the direction of causality is fea- (see also Ingo Kipker 2000, and David sible. Hall, Szymanski, and Zimbalist (2002) tested for Granger causality from wages to 39 There have been relatively few attempts to analyze performance and from performance to causality empirically in the sports literature. Brian Davies, wages, and found that they could reject the Paul Downward, and Ian Jackson (1995) and Stephen Dobson and John Goddard (1998) look at the relationship latter direction of causality for English soc- between income variables (attendance and revenues) and cer but not for major league baseball (MLB). success in English rugby league and soccer. dec03_Article 2 12/4/03 11:17 AM Page 1155

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Forrest and Robert Simmons 2002b for Luigi Buzzacchi, Szymanski, and Valletti detailed comparison). Given a reasonable (2003) develop a dynamic measure based on degree of sensitivity of performance to estimating the number of teams entering the wages (which does appear causal, at least in top k ranks of a league competition over T the English case) one might have expected a years (they look at the top rank and the top relatively high standard deviation of win per- five ranks over the ten-year intervals from centage reflecting a high degree of competi- ten to fifty) relative to the idealized number tive imbalance.40 of teams that would have entered these The standard deviation of winning per- ranks under an equally balanced contest. centage, however, may be a relatively poor Note that in an open system where the prob- measure of competitive balance, largely ability of success is identical for each team, because it only considers performance with- there will be a very high turnover at the top in a season. Performance in the open over a twenty-year period, since so many European leagues tends to be relatively more teams have access compared to a bunched together, since teams near the bot- closed league. They compare three North tom keep competing right to the end in American leagues (MLB, NFL, and NHL) order to avoid relegation (see section 7.5). with three national soccer leagues (Italy, Yet over a number of seasons the same big England, and Belgium) and find that the teams tend to dominate European competi- number of entrants to the top ranks is tion, so there is little turnover at the top. slightly higher in North America, but that Relatively little attention has been paid to relative to potential entrants the number of measuring this notion of competitive bal- actual entrants is very small in the European ance, although this is clearly the aspect that leagues. They suggest that an open system figured heavily in the Blue Ribbon Panel’s can be characterized as one that produces investigation into baseball (notably the equality of opportunity, while closed leagues dominance of the Yankees) and has been are more successful at producing equality of raised by some critics of static measures outcome. More research is required into the (e.g., Ross and Robert Lucke 1997; causes of these differences. Woodrow Eckard 1998).41 5.2 Demand and Uncertainty of Outcome 40 A number of authors have used the standard devia- Whatever the causes of inequality, the tion of winning percentage relative to the idealized stan- dard deviation (assuming winning probabilities) as an lynchpin of team sports organizers’ defense alternative measure (see e.g. Scully 1989; Quirk and Fort of restrictive agreements has been the claim 1992; Vrooman 1995). Other static measures include the that such measures are required to combat Gini coefficient (Quirk and Fort 1992), relative entropy (Ira Horowitz 1997), and the Hirschman-Herfindahl index the threat of uneven contests that will (Craig Depken 1999). reduce the interest of the fans. This proposi- 41 Eckard (1998) proposes a decomposition of the vari- tion was first fully enunciated in the eco- ance of winning percentages into a cumulative and time- varying component. For a given total variation a decrease nomics literature in a celebrated paper by in the variation through time implies greater cumulative Neale (1964). As a testable hypothesis it has variation; in other words, from season to season there is now generated a substantial literature of its less turnover in team standings (competitive imbalance). Brad Humphreys (2002) proposes a similar measure. Alan own. To begin with, it is useful to differenti- Balfour and Philip Porter (1991) and Vrooman (1996) have ate three types of uncertainty: estimated first-order autoregressive processes for win per- 1. match uncertainty, cent as a way to search for possible structural breaks asso- ciated with free agency (see below). In other words, they 2. seasonal uncertainty, consider the degree of persistence, which might be 3. championship uncertainty. thought a natural measure of dynamic competitive bal- The meaning of match uncertainty is obvi- ance. Szymanski and Ron Smith (2002) adopt this approach to compare persistence across North American ous. Seasonal uncertainty means a close and European leagues. championship race within a season, while dec03_Article 2 12/4/03 11:17 AM Page 1156

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championship uncertainty means there is a Finally, championship uncertainty has variety of champions over a period of years, hardly ever been tested, although the evi- rather than domination by one or two teams. dence comparing the relative long-run Table 2 summarizes the research in this imbalance of European soccer to the North area. In recent years, research on match American leagues suggests that this is an uncertainty has focused on the use of pre- issue worthy of investigation.42 On the face match betting odds as a means of measuring of it, European soccer is every bit as popular uncertainty. There seems to be an emerging with Europeans as the North American consensus that demand for match tickets leagues are with Americans, despite long- peaks at the point where a home team’s run domination by a much smaller subset of probability of winning is about twice that of teams. the visiting team, i.e., a probability of around Overall, of the 22 cases cited here, ten 0.66. (See e.g. Glenn Knowles, Keith offer clear support for the uncertainty of Sherony, and Michael Haupert 1992; outcome hypothesis, seven offer weak sup- Forrest and Simmons 2002a summarizing port, and five contradict it. Given that even the work of David Peel and David Thomas supportive studies on the issue of match (1988, 1992, 1997), and Dan Rascher 1999). uncertainty seem to imply that attendance is Several reviewers have commented upon maximized when the home team is about just how unbalanced a contest characterized twice as likely to win as the visiting team, the by this probability would be, and in most empirical evidence in this area seems far datasets there are relatively few observations from unambiguous. This is remarkable given involving such extremely unbalanced con- the weight that is placed on this argument in tests. Whether this imbalance is optimal policy making and in antitrust cases. Given from the point of view of the league is not that even quite unbalanced matches, cham- something that these studies address, but it pionships, and leagues can be attractive to seems reasonable that the optimal balance consumers, a more nuanced approach is for the league may be greater than that for called for.43 the home team. Less work has been done on the issue of 6. The Invariance Principle seasonal uncertainty. The key problem in In this section we turn to the considera- this area is controlling for all the other rele- tion of specific rules and restrictions that vant factors that might influence demand. might be designed to increase uncertainty of For example, Martin Schmidt and David outcome and enhance competitive balance. Berri (2001) find that attendance is positive- Because of the cartel-like organizational ly affected by uncertainty, using nearly a structure of most team sports leagues, these century of MLB data, but with no other rules and restrictions have often been debat- explanatory variables. When they examine a ed in the antitrust courts. On the one hand, shorter panel including influences such as price data, they find that, for the National 42 One exception is Szymanski (2001), who exploits the League, attendance is significantly decreas- fact that, in soccer, teams participate in two national com- ing in uncertainty. While it is plausible that petitions at once, one of which contains a much less bal- fans prefer a close championship race, a run anced selection of contestants than the other. By pairing the subset of matches in each tournament that involve the of success by a single team may itself spark same teams he is able to infer the effect of the balance of interest (like the old barnstorming teams). It each tournament taken as a whole. 43 may be that the causal relationships are too Paul Downward and Alistair Dawson (2000) reach a similar conclusion: “the evidence suggests that uncertain- complex to isolate a single influence such as ty of outcome has been an overworked hypothesis in uncertainty of outcome. explaining the demand for professional sports.” dec03_Article 2 12/4/03 11:17 AM Page 1157

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TABLE 2 OUTCOME UNCERTAINTY IN THE LITERATURE

Authors Testing Uncertainty measure Data Result

Noll (1974) seasonal - whether team in contention ice hockey weak support for playoff - whether championship race baseball weak support close

Hart et al. match - log difference in league 4 English football weak support (1975) positions clubs 1969/70– 1970/71

Jennett (1984) seasonal - championship/relegation Scottish League Support significance of each game Football 1975–81

Borland (1987) seasonal -diff. in games won between Victorian Football weak support first and last League (Australian -sum of coefficients of Rules) 1950–86 variation of game won -average no of games behind the leader championship -number of teams in contention no support

Cairns (1987) seasonal dummy of contention in 4 Scottish football support championship clubs 1969/70– 1979/80

Jones and match dummy for top of the table NHL Season no support Ferguson(1988) and bottom of the table matches 1977/78

Whitney seasonal average expected probability baseball 1970–84 weak support (1988) of winning

Peel and match betting odds (probability of 1981/82 English weak support Thomas home win) football league (1988) matches

Knowles et al. match betting odds (probability of MLB 1988 support (1992) home win)

Peel and match betting odds (probability of English Football weak support Thomas (1992) home win) League matches

Borland and seasonal sum of matches required to Australian Rules no support Lye (1992) qualify for the finals

Kuypers (1996) match betting odds (difference in 1993/94 no support max and min) individual English seasonal points and games left Premier League support matches

Peel and match betting odds (points spread) Rugby League support Thomas (1997) 1994/95 dec03_Article 2 12/4/03 11:17 AM Page 1158

1158 Journal of Economic Literature, Vol. XLI (December 2003)

TABLE 2 (cont.)

Authors Testing Uncertainty measure Data Result

Baimbridge et seasonal dummy when both teams in 1993/94 no support al. (1996) top (bottom) four positions Individual English Premier League Matches

Rascher (1999) match betting odds (probability of MLB 1996 support home win)

Szymanski championship competition type (with English League support (2001) identical contestants) and FA Cup matches 1977–98

Schmidt and seasonal gini coefficient MLB 1903–98 support Berri (2001) (Gini only) MLB 1975–88 (Gini plus other support for AL variables) no support for NL

Forrest and match odds ratio (accounting for Football League support Simmons (2002a) favorite-longshot bias) matches 1997/98

Source: Adapted from Szymanski and Kuypers (1999).

economists can try to shed light on whether to establish monopsony rights. Thus the specific restrictions achieve their stated aim reserve clause of baseball (see e.g. Quirk and (and whether they were strictly necessary to Fort 1992 for an explanation) functioned in achieve it); on the other hand, they can also much the same way as the Retain and identify other consequences arising from a Transfer System of English soccer (see e.g. given restriction. These may be conse- Sloane 1969).44 This inevitably led to chal- quences for profits (the owners’ interest); lenges in the courts by the players claiming prices, quality, and choice (the consumers’ the right to move freely between employers. interests); and employment conditions and Simon Rottenberg’s celebrated (1956) article remuneration (the players’ interests). examined this issue and presented the team Economic analysis of these issues is usually owner’s rationale: both theoretical and empirical, and the bal- ance between the two often depends on the “The defense most commonly heard is that the nature of the restriction and the availability reserve rule is necessary to assure an equal distri- of data. bution of playing talent among opposing teams; that a more or less equal distribution of talent is 6.1 The Invariance Principle and Talent necessary if there is to be uncertainty of outcome; Allocation Rules and that uncertainty of outcome is necessary if the consumer is to be willing to pay admission to the One common characteristic of team sports as they developed on both sides of the 44 Atlantic has been the desire of the owners of In fact, the two systems were so similar that it is hard to believe that the Football League did not copy the teams belonging to professional leagues to National League. However, no evidence to this effect has control the market for players, in particular ever been produced. dec03_Article 2 12/4/03 11:17 AM Page 1159

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game. This defense is founded on the premise that natural experiment.45 The owners claimed there are rich baseball clubs and poor ones and that, if the players’ market were free, the rich clubs that as a result of this limited free agency, would outbid the poor for talent, taking all compe- the best veterans would migrate to the big tent players for themselves and leaving only the city teams and competitive balance would be incompetent for other teams.” (p. 246) undermined. A number of studies have attempted to use this rule change to test the Rottenberg argued that (a) the reserve invariance hypothesis, and the findings from clause did nothing to prevent the migration these studies are reported in table 3. Most of of talent to the big city teams and so would the studies simply look at the standard devi- not affect the distribution of talent, and that ation of win percentages before and after (b) by establishing monopsony power over a 1976 (Scully 1989; Balfour and Porter 1991; player throughout his career the team own- Quirk and Fort 1995; Vrooman 1995; ers were able to hold down wages and raise Michael Butler 1995), while other measures profitability. Point (a) has since been identi- include persistence in win percent (Balfour fied as an example of the Coase Theorem at and Porter 1991; Vrooman 1996); entropy work: the initial distribution of ownership (Horowitz 1997); the Hirschman-Herfindahl rights should have no impact on the efficient index (Depken 1999); and analysis of vari- (here profit-maximizing) distribution of ance (Eckard 2001). Most of these studies resources. El-Hodiri and Quirk (1971) and find either no change (seven cases) or an Quirk and El-Hodiri (1974) took this analy- improvement in competitive balance (nine sis one stage further in a formal dynamic cases), contrary to the claim of the owners model showing that, if teams have differing that free agency would reduce competitive revenue generating potential, (i) profit max- balance (four cases only). However, this imizing behavior will not lead to an equal meta-data is hardly a ringing endorsement distribution of resources (playing talent) and for the invariance principle, since “no effect” (ii) revenue redistribution on the basis of is reported in only seven out of twenty cases. gate sharing will have no impact on the dis- Of course, it can be argued that many other tribution of playing talent. Points (a) and (ii) factors have altered competitive balance are both examples of the well-known invari- (e.g. the increasing dispersion of local TV ance principle. revenues), but in that case the data, without There have been two significant changes controlling for these factors, can hardly be in talent-allocation rules in North American said to represent a test at all. sports over recent years. Firstly, in 1976, Some other studies have approached the major-league baseball players won the right invariance principle as a direct test of the of free agency after completing six years of Coase Theorem and tried to establish service, and this practice rapidly spread to whether the distribution of talent in the the other sports. Secondly, the draft rules of league has been affected by the introduction the NFL, which allocated the right to hire of free agency. George Daly (1992) observes new talent entering the league on the basis that under the reserve clause, top line play- of the reverse order of finish of the previous ers were seldom traded, a situation that has season’s competition, were adopted by the been affected by free agency, where after six other sports (see Paul Staudohar 1996 for years the top stars have a choice, leading to more details on both of these innovations). increased mobility. Timothy Hylan, These changes can be studied to identify the impact of changes in talent allocation rules 45 on competitive balance. In this case the change was exogenous—i.e. not itself motivated by a desire to affect competitive balance Free Agency. The advent of free agency in (see Bruce Meyer 1995 for a discussion of natural MLB in 1976 for six-year veterans is a clear experiments). dec03_Article 2 12/4/03 11:17 AM Page 1160

1160 Journal of Economic Literature, Vol. XLI (December 2003)

TABLE 3 THE IMPACT OF FREE AGENCY ON COMPETITIVE BALANCE IN MLB

Study Measure of Competitive Balance Impact on Impact on Competitive Competitive Balance in NL Balance in AL Daly and Moore (1981) Movement of free agents to large (-) (-) market teams

Scully (1989) Standard deviation of win percent (+) (0) and Gini coefficient of pennant wins

Balfour and Porter (1991) Standard deviation of win percent, (+) (+) persistence of win percent

Fort and Quirk (1995) Standard deviation of win percent (0) (0) and Gini coefficient of pennant wins

Vrooman (1995) Standard deviation of win percent (+) (+) relative to idealized standard deviation

Vrooman (1996) Persistence of win percent (+) (+)

Butler (1995) Standard deviation of win percent (0) (0) and serial correlation of win percent

Horowitz (1997) Entropy (-) (0)

Depken (1999) Hirschman-Herfindahl index of wins (0) (-) relative to ideal

Eckard (2001) Analysis of variance of win percent (+) (+)

Maureen Lage, and Michael Treglia (1996) pendent leagues then it should be more in a study of pitcher movements finds that profitable to hire a player from the same these players have become less mobile since league than the rival league. Intra-league free agency, a surprising result and one that trade raises the winning probability of the they claim does not support the Coase buying team by more than an inter-league Theorem. However, Donald Cymrot, James trade, since in the former case not only does Dunley, and William Even (2001) examine the buyer have a larger share of talent, but player mobility in 1980, controlling for pos- the seller now has a weaker team. Under the sible selection bias and find that, for that reserve clause this effect will be built into season at least, there was no evidence that the seller’s price, but under free agency it restricted players (with less than six years of will not, since the free agent is indifferent to service) enjoyed more or less mobility than the adverse effect on the team he is leaving. unrestricted free agents after controlling for Thus with free agency the relative price of player characteristics. intraleague trades should fall and their Daniel Marburger (2002) considers a dif- share of total trades increase. Marburger ferent implication of the invariance princi- found a statistically significant increase in ple. If trade is possible between two inde- the share of intraleague trades, from 60 dec03_Article 2 12/4/03 11:17 AM Page 1161

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percent to 73 percent, in MLB 1964 and forming teams to maintain competitive bal- 1992. This finding seems consistent with ance, and has since been adopted by all the the invariance principle. other major leagues (Fort and Quirk 1995, In European soccer, trading players for and Staudohar 1996 provide details). cash has always been an accepted part of the Daly and Moore (1981) first analyzed sport, and there have been no restrictions on whether the draft achieved its stated inten- trading such as those that emerged in North tion by examining competitive balance America in 1970s (see Daly 1992). In before and after the introduction of the England a system akin to the reserve clause MLB draft in 1965. They found a significant operated until 1963. Restrictions remained improvement in the balance of the National until 1978, when a form of free agency was League and a smaller improvement in the introduced that gave players the right to balance of the American League. The move club once their contract ended (typi- Japanese Professional Baseball League cally contracts lasted three years), but adopted a draft system at exactly the same allowed the selling team to demand substan- time as MLB, and a study by La Croix and tial compensation (i.e. well in excess of any Kawaura (1999) also found that competitive damages that would be paid for breach of balance improved over time (measured by contract). In 1995 the European Court of the Gini coefficient for pennants) in both the Justice, in what is known as the Bosman Central and Pacific Leagues.47 As they point judgment,46 outlawed all such compensation out, these results are “virtually identical” to payments for out-of-contract players and Fort and Quirk’s (1995) results for MLB. effectively established universal free agency. Kevin Grier and Robert Tollison (1994) In 2001 FIFA reached agreement with the examined the impact of the rookie draft in European Commission on a new set of trans- the NFL by running an autoregressive spec- fer rules. These laid down that compensa- ification for win percentage together with tion was only payable to clubs for players the average draft order over the previous under the age of twenty-three and only as a three to five seasons, and found that a low reflection of training costs. Beyond that age draft order significantly raises performance. no transfer fee is to be paid for players out of These results seem to provide consistent evi- contract and players can move clubs during dence against the invariance principle and in one of two prescribed “transfer windows.” support of the owners’ stated position. The Rookie Draft. The stated intention of Neither with free agency nor with the the rookie draft system is to provide weaker rookie draft is there much convincing evi- teams with opportunities to acquire talented dence on profits and consumer welfare. It is players by awarding them first pick. Of clear that free agency has increased the course, an additional consequence of this earning power of free agents, but it is not system is the creation of monopsony power. clear what the distributional effects have The draft system was instituted by the NFL been on the player market as a whole. For in 1936 as a way of strengthening weak per- example, it might be that increased expendi- ture on free agents caused by competition 46 Bosman was a Belgian playing for a Belgian team for their services has led to a reduction of who refused a new contract and decided he wanted to investment in the development of rookie tal- transfer to a French club, that was willing to hire him and ent or lower salaries on average for players pay a transfer fee. Under the rules of the Belgian Football Association, the Belgian club had the right to veto the with less than six years service. Zimbalist transaction without appeal (and so retain Bosman’s servic- es), which it did, on the grounds that it thought the buying club could not really afford the fee. This system was out- 47 However, the within-season measure (standard devi- lawed by the judgment (Court of Justice of the European ation of win percent) was significant only for the Pacific Communities, Case C-415/93). League. dec03_Article 2 12/4/03 11:17 AM Page 1162

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(1992) reports significant differences in the dictable level of playing success. Secondly, it rate of monopsonistic exploitation for play- is assumed that excessive dominance by one ers at different stages of their careers after team will lead to a fall in revenue generation the introduction of free agency. In Europe, by that team, although at low levels of suc- where there are no roster limits, it does cess revenues are increasing in team per- appear that the number of professional soc- formance. The main difference between the cer players has been falling over time, and team sports model and a conventional con- this could be associated with the trend test model is that instead of competing for a toward free agency that was visible in fixed prize with some probability deter- England even before the Bosman judgement mined by relative investment, each team (i.e., teams substituting quality for quantity). generates a revenue dependent on the share Eberhard Fees and Gerd Muehlheusser of matches won, where that revenue also (2002) compare the welfare implications of varies according to the revenue generating the pre- and post-Bosman transfer regimes capacities of the teams. Thus asymmetry in and argue that while the new regime may team sports is not typically modeled as a dif- increase player effort (since they can secure ference in the cost of effort (talent invest- a larger share of the returns) investment in ment), but as a difference in the value of the player development is likely to fall. These prize (revenue generating capacity). issues deserve empirical investigation. The nature of the prize in team sports is somewhat different than in an individualistic 6.2 The Invariance Principle and Gate- contest. Success is usually equated with win- Revenue Sharing ning percentage, which in turn depends on El-Hodiri and Quirk (1974) extended the the outcome of a sequence of bilateral con- invariance principle to gate revenue sharing, tests. However, what distinguishes league i.e. they claimed that a change in the per- competition from the kind of barnstorming centage of gate revenues allocated to the vis- match play observed prior to the creation of iting team (between 100 percent and 50 per- the National League is that fan interest is cent) would have no affect on competitive drawn to the progress of their team in the balance. Empirical testing of this proposition tournament as a whole, not just the individual is made difficult by the fact that revenue- matches. In other words, there is also a prize sharing rules change infrequently within a for success over the competition as a whole single league, while the comparison of rev- (the league championship) rather than simply enue sharing across different leagues is collecting income from a series of events. clouded by the interference of so many A further modeling issue concerns the way other league-specific factors. An alternative that decision makers interact. Fort and approach is to examine the theoretical basis Quirk, among others, support the cartel for this proposition. This section develops a interpretation, suggesting that clubs make simple contest model that illustrates the independent decisions subject to cartel rules basis of the invariance principle for gate- (i.e. a noncooperative game), and we follow revenue sharing. this approach below.48 The precise legal for- The conventional approach to the model- mat adopted, however, may vary. ing of league competition (as in e.g. Fort and Conventionally, teams are joint owners of Quirk 1995) is to some extent supported by the league and delegate an official to man- the empirical evidence in section 5. Firstly, it age collective negotiations. is normally assumed that teams choose 48 investment in playing talent that is homoge- Some maintain that leagues should be considered (at least for antitrust purposes) as single economic entities neous and perfectly divisible, so that a given (e.g. Gary Roberts 1984), which could imply centralized level of investment translates into a pre- decision making. dec03_Article 2 12/4/03 11:17 AM Page 1163

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Analysis of the invariance principle is only introducing the possibility of complementar- relevant when there are asymmetries among ities. Although this suggests a more complex the teams. If teams are symmetric, competi- set of interactions than is modeled here, the tive balance cannot be an issue if, as here, we existence of production externalities (the concentrate only on pure strategy equilibria. success of my team increases or decreases To concentrate on asymmetry we narrow our your team’s revenues) does not fundamen- focus to a two-team model, as has been usual tally change the decision problem, since in most of the literature. Assuming the CSF even in the two-team case each team’s takes the same logit form as in an individual- investment produces a negative externality istic contest (3) and that γ 1, we can write (my success reduces your income). The e important economic issue is that private p = 1 , pp=−1 1 + 21(3’) decision making will not necessarily be ee12 socially efficient when externalities, negative 50 where pi can be thought of as the expected or positive, exist. percentage of matches won by team i, which In general, demand for attendance at or is increasing in the relative share of invest- viewing of matches could be thought to ment in talent, which is how ei is now inter- depend on three main factors: 49 preted. In a standard contest model the * the suspense associated with a close “adding-up constraint” requires that the contest (uncertainty of outcome); probabilities sum to unity, while in a league * the likelihood of the home team’s suc- context the constraint is that the sum of win cess; percentages equals n/2. Obviously this con- * the quality of the match, including the dition is satisfied by (3’). Another way of aggregate of player talent on show.51 expressing the adding-up constraint is The interaction of these three factors will ∂ ∂ ∂ ∂ give rise to some general revenue-generating p1 =− p2 p2 =− p1 ∂ ∂ and ∂ ∂ . (11) function R(.). The requirement of tractabili- e1 e1 e2 e2 ty demands some simplification and so for Note that the CSF (3) is identical to win the moment we will ignore the impact of the percentage for a two-team model, but not with three or more teams, since expected win percentage then depends on the sum of bilateral investment shares (3’) rather than 50 For n 3 the CSF can be thought of as a champi- simply investment divided by the sum of onship success function (e.g. James Whitney 1988) In investments. Both functions will be increas- practice, the difference between the share of total match- es won in a season and win percentage is small and the two ing and concave in investment, and bounded measures are highly correlated. For example, in English by zero when investment is zero. soccer the correlation coefficient between league rank and It is sometimes argued that a two-team win percent is about 0.9. 51 Following most of the literature, we abstract from model fails to capture some central features price issues. In North America, monopoly pricing is plau- of a league championship. If n 2 it is pos- sible due to distance and territorial exclusivity (see e.g. sible to specify each team’s revenue function Donald Alexander 2001). Greater urban density and the promotion and relegation system in Europe make this less as a function of rival teams’ win percentage, likely. For example, New York has two major-league base- ball teams (population 20 million) while London (13 mil- lion) hosts six teams currently in the top division of English 49 Baik (1994) models asymmetry by assuming that the soccer, plus another six eligible to enter if promoted on sensitivity of CSF to effort differs among contestants, an merit. In Australian Rules Football and Australian Rugby assumption that implies that all teams do not have access League most of the teams are located around a single city to the same technology for transforming talent into suc- (Melbourne and Sydney respectively). The implications of cess. The assumption of symmetry effectively implies that population density for revenue generation remain to be all teams adopt best practice. The literature on team pro- explored (but see Forrest et al. 2002 on the spatial pattern duction functions sheds some light on this issue (see fn. 8). of demand for English soccer). dec03_Article 2 12/4/03 11:17 AM Page 1164

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demand for quality.52 We therefore focus on owners of each team are assumed to be prof- the impact of success and competitive bal- it maximizers. Under these assumptions the ance probabilities. In most of the literature first-order conditions are: these two aspects of demand are captured by dπ ∂R ∂p 1 = 11 1 −=c a revenue function that comprises a CSF de ∂p ∂e and the assumption that team revenues have 1 1 1 ∂p a unique maximum (e.g., at a winning record []11−−−−λµ()() 21 λp 1 −=c 0 1 ∂ that lies between 0 percent and 100 per- e1 cent). Here we assume that revenues are (13) simple linear functions of these variables: dπ ∂R ∂p R [1λ (1µ)] p (1λ)p 2 2 = 22 2 −=c 11 1 1 de ∂p ∂e λµ p (1λ)p (1 p ) 2 2 2 1 1 1 ∂p []121−−()λ p 2 −=c 0 (12) 2 ∂ pe12 λ 2 R22 p2 (1 )p2 These expressions state that owners invest in λ λ p2 (1 )p2 (1 p2) talent to the point where the marginal rev- enue from a unit of talent equals its margin- where R is either the revenue generated by ii al cost. For example, for team 1 the margin- team i from matches played at the ground of al revenue of a unit of talent equals the team i or the revenue generated by champi- marginal revenue of a win (1λ (1µ) onship success. µ 1 reflects the possibility 2(1λ) p )multiplied by the marginal that team 1 may be able to generate a high- 1 impact on win percentage of a unit of talent er revenue from a given level of success. (∂p /∂e ). Competitive balance can be measured by 1 1 The standard assumption in the North p (1p )p (1p ) and λ is a parameter 1 1 2 2 American team sports literature has been capturing the degree to which competitive that this latter quantity is equal to unity. balance matters in determining team rev- Thus Fort and Quirk (1995, p. 1271) assume enues; if λ1 only winning matters, while if “a one unit increase in t yields the same λ0 interest in a balanced contest domi- i increase in win-percent for any level of win- nates. Each firm’s profit function is simply percent” and Vrooman (1995, p. 973) uses a π R ce and π R ce , where c is 1 11 1 2 22 2 model where teams directly choose win per- the constant marginal cost of talent, which is cent, whose marginal cost is assumed to be treated parametrically by the teams, but a constant, so that a unit of talent in the adjusts to ensure that the supply of talent present model is equivalent to a unit of win equals demand. Note that if λµ 1 the percentage. Given identical marginal costs problem is isomorphic to the symmetric win- this implies that the marginal revenue of a ner-take-all contest of section 2.1.53 The win is equalized across teams. This seeming- 52 Intuitively, if this enters the revenue function of each ly innocuous assumption has important team symmetrically then it will shift out the demand for implications about the behavior of owners. talent. Some consequences of including the interaction of From (3’) quality in more complex cases are considered below.  de  53 +− +2 In the one-shot winner-take-all model, the payoff to ()ee12 e 11  ∂p  de  the contestant is an expectation of the prize dependent on 1 = 1 , relative effort but only one contestant receives the prize ex ∂ + 2 post, while in the one-shot team sports version each con- e1 ()ee12 testant generates an income based on the share of success   so that expected income equals ex post income (there is no +− +de1 ()ee12 e 21  stochastic element in the CSF). In an infinitely repeated ∂p  de  game with no discounting, the value of the expected and 2 = 2 . (14) ∂ + 2 actual payoffs are identical in both cases. e2 ()ee12 dec03_Article 2 12/4/03 11:17 AM Page 1165

Szymanski: Economic Design of Sporting Contests 1165 If we assume de1/de2 de2/de1 1 then, Note that the left-hand side of (15) is the normalizing the total supply of talent to ratio of the marginal impacts on win percent- unity, it will indeed be the case that age of a unit of talent and the right-hand side ∂ ∂ ∂ ∂ p1/ e1 p2/ e2 1. It should be obvious is the ratio of marginal revenues of a win. that this assumption is not the same as Under the “fixed supply conjectural varia- adding-up constraint (11). Since the tion” the LHS is unity and so the marginal expression (14) appears in the objective revenue of a win is equalized across teams. function of the teams de2/de1 is a conjec- This is not true using the Nash conjectural tural variation, i.e. the expectation of team variation, where it is only the marginal rev- 1 (resp. 2) of the response of team 2 (resp. enue from hiring a unit of talent that is always 1) to a unit increase in talent by team 1 equalized in equilibrium, while the marginal (resp. 2). If we assume that this conjecture revenue of a win will only be equalized at the equal 1, then each team is assumed to equilibrium of a symmetric contest (µ1).55 suppose that whenever they increase their At the asymmetric Nash equilibrium the investment in talent by one unit, their rival marginal revenue of a win will be greater for will decrease their investment in talent by the strong drawing team (µ 1) because this one unit. team hires a larger share of talent available The rationale for this assumption is that and therefore has a lower marginal impact on the total supply of talent is fixed, which is win percentage from an extra unit of talent. often thought a distinctive feature of the Nash conjectures and fixed-supply conjec- major leagues. It is probably true that all the tures produce very different results when it best baseball players, wherever they are in comes to the impact of gate-revenue shar- the world, would prefer to play in MLB, and ing. In the standard model it is assumed that that all the best basketball players in the each team retains a fraction α of revenues world would prefer to play in the NBA and generated by home matches and pays the so on. If the talent supply for each league is remainder 1α to the visiting team so that π α α fixed (at least in the short term) then if one profits are now 1 R11 (1 )R22 ce1 π α α team hires an additional unit of talent there and 2 R22 (1 )R11 ce2 and the is one less unit for all other teams to hire.54 first-order conditions are But modeling a fixed talent supply by assum- ing non-zero conjectural variations has sig- ∂π ∂R ∂p ∂R ∂p 1 = αα11 1 +−()1022 2 −=c nificant implications for the nature of the ∂ ∂ ∂ ∂ ∂ e1 p1 e1 p2 e1 , model’s equilibrium. The normal approach ∂π ∂R ∂p ∂R ∂p to identifying a Nash equilibrium is to 2 = αα22 2 +−()1011 1 −=c ∂e ∂p ∂e ∂p ∂e assume Nash conjectures, namely de1/de2 2 2 2 1 2 de2/de1 0. Without Nash conjectures pecu- (16) liar results may follow. which, using the adding-up constraint (11) To see the implications of this, combine can be rearranged to obtain the two expressions in (13) to obtain ∂p ∂R  ∂R ∂R  ∂p 2 11 αα11 −−()1 22  1 = ∂e ∂p 11−−−−λµ()() 21 λp  ∂p ∂p  ∂e 2 = 1 = 1 . 1 2 1 ∂p ∂R 121−−()()λ 1 −p 1 22 1  ∂R ∂R  ∂p ∂e ∂p αα22 −−()1 11  2 . (17) 1 2  ∂p ∂p  ∂e (15) 2 1 2

54 This assumes the supply is not so great that the If we now further assume fixed-supply con- demand curve intersects the horizontal axis at a point to jectures it should be clear that since the left of the fixed supply, implying that there is more 55 talent than MLB or the NBA require. With Nash conjectures the LHS of (16) equals e1/e2. dec03_Article 2 12/4/03 11:17 AM Page 1166

1166 Journal of Economic Literature, Vol. XLI (December 2003) ∂ ∂ ∂ ∂ p1/ e1 p2/ e2 (17) collapses to the drawing team’s revenues, the weak drawing equality team cuts investment by more.56 ∂ ∂ Because revenue sharing diminishes the R11 = R22 incentive of both teams to invest in talent, ∂ ∂ , (18) p1 p2 the demand for talent must fall. If the supply of talent is fixed then the wage rate per unit α which is clearly independent of , hence the of talent (i.e. the marginal cost c) will fall to conclusion that the distribution of talent restore labor-market equilibrium. However, and success is independent of the revenue- if competitive balance is to deteriorate then sharing formula. However, once we intro- it must be that the strong drawing team will duce Nash conjectures this result will no in fact increase its share of total talent while longer hold, and instead we obtain the weak drawing team reduces its share. If the supply of talent were elastic, however, ∂p  ∂R ∂R  2 αα11 −−()1 22  this result need not necessarily hold, even ∂e e  ∂p ∂p  2 ==1 1 2 . (15’) though competitive balance must still be ∂p e  ∂R ∂R  reduced. The assumption of elastic supply 1 2 αα22 +−()1 11  ∂ ∂ ∂ seems more reasonable in the case of e1  p2 p1  European soccer where no national league is It should be clear that the LHS of (15’) is dominant and players move freely between α identical to that of (15), but when 1 the leagues. Whether supply is fixed or not, total RHS of (15’) and the middle term of (15) are expenditure on talent will fall with gate-rev- not equal (unless revenue functions are sym- enue sharing and total profits will increase. metric), suggesting that the invariance prin- There is a fundamental problem with the ciple does not hold under Nash conjectures. assumption of fixed-supply conjectures. If Using the expressions for marginal revenue teams attempt to select win percentage, only in (15) after some manipulation it can be one team can be decisive, since the other shown that team’s choice is thereby fixed in a two-team model. It is like a model of market share e ()()12−−++−αλλαµα 1[] () 1 1 = where each firm tries to choose market −+ααλµ + . (19) e2 12() 1 share—at most one firm can succeed. More generally, in an n team model with fixed sup- Differentiating, we obtain ply conjectures only n1 teams can be deci- th  e  sive, and the n team must accept the alloca- ∂ 1  22 tion of talent implied by the profit maximizing  e  λµ()1 − 2 = < 0 . (20) choices of all the other teams. In the two- ∂α 2 []12−+ααλµ() 1 + team model with fixed-supply conjectures, every choice of winning percentage is a Nash Thus under Nash conjectures, revenue equilibrium, since there is only one feasible sharing will in fact make competitive balance response to this choice and so it is trivially the worse. Szymanski and Késenne (2004) show best response (see Szymanski 2004 for more that this is in fact true for any concave rev- detail). The way around this absurdity is to enue function. The intuition is that revenue sharing discourages both teams from invest- 56 Scott Atkinson, Linda Stanley, and John Tschirhart ing, but since the weak drawing team has (1988) also state that they do not obtain the invariance more to gain from a share of the strong result (p. 33, fn. 14) but attribute this to the assumption of a more general revenue function. The key differ- drawing team’s revenues than the strong ence, however, is that they do not assume fixed-supply drawing team does from a share of the weak conjectures. dec03_Article 2 12/4/03 11:17 AM Page 1167

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allow owners to select some variable that relatively short term it may be possible to affects the share of total talent, such as invest- draft in talent from outside the league, ment, without constraining the choice of effectively increasing total supply. The rivals by so doing. This approach will result in increasingly global search of the major the Nash equilibrium described above. leagues for talent suggests that in the longer It seems widely accepted in the broader term supply is elastic. It would be interest- economic literature that, in a static game of ing to see some empirical attempts to meas- this type, only Nash conjectures make sense ure the elasticity of supply. (see e.g. Xavier Vives 1999, pp 185–87) but Frederic Palomino and Joszef Sakovics alternative conjectural variations are some- (2000) develop a model based on competi- times defended as reduced forms of an under- tion for scarce talent to account for the com- lying dynamic model. The original model of mon observation that revenue sharing seems Quirk and El-Hodiri (1974) is indeed a more prevalent in North America than in dynamic model. The authors do not explain in Europe.60 In addition to the demand for detail the source of the invariance result but it success and competitive balance, they intro- appears to be a consequence of looking for an duce the demand for the quality of the con- equilibrium where not only the profit of each test (i.e. the talent of the players). team is maximized with respect to talent hired Regardless of the supply elasticity, revenue at that team, but also with respect to talent sharing reduces the demand for talent, since hired by every other team.57 This kind of joint own marginal revenue from success is profit-maximizing program is likely to pro- reduced and marginal revenue from rival duce an optimal allocation of talent regardless success (i.e. own failure at away matches) is of the distribution of revenues. It seems more increased. If the market for talent ensures natural, however, to examine revenue-sharing that marginal revenue equals marginal cost, rules in the context of a noncooperative game. then revenue sharing in the fixed-supply Fixed-supply conjectures reproduce the model simply drives down total cost and so results of a cooperative game between the raises profits (see Quirk and Fort 1995). teams,58 and therefore it is perhaps not sur- However, with elastic supply and competi- prising that a model based on these conjec- tion between rival leagues for players, any tures appears to support the Coase Theorem. reduction in the willingness to pay for play- The fact that almost all models of sports ers by the members of a league will reduce leagues in the literature have been based on the quality of that league (measured by total the assumption that the total supply of tal- units of talent employed) relative to its rivals, ent is fixed may be associated with the fact and therefore undermine its relative attrac- that most of the models have been written tiveness. in the context of the North American major Thomas Hoehn and Szymanski (1999) leagues, where arguably, at any point in develop an elastic model of European time supply is fixed.59 However, even in the league competition that presents a related reason why revenue sharing may adversely 57 See Noll (1974) p. 63, equation (ii) in particular. 58 Just as a conjectural variation of 1 produces affect competitive balance. In European the joint profit-maximizing solution in a quantity setting sports the leading teams typically compete oligopoly. in more than one championship in a 59 Scully (1989), referred to in Vrooman (2000), has dis- sented from the mainstream view on revenue sharing, and this could be interpreted as the holding of the contrary 60 Thomas Ericson (2000) also points out that in a view, that supply is elastic. Scully (1989, 1995) discusses European context the supply elasticity facing each league the elasticity of supply and cites as evidence the large is non-zero, and he applies this to analyzing the impact of salary gap between the stars and lesser players to support transfer rules on the distribution of talent across large and the proposition that supply is relatively inelastic. small market leagues. dec03_Article 2 12/4/03 11:17 AM Page 1168

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season—the domestic league and The first-order conditions are then European-wide league (e.g. The 61 ∂π ∂  ∂ ∂L  Champions’ League )—and typically these i = pi ααLi +− j = ∂ ∂  ∂ ()1 ∂  c , competitions run concurrently. Thus the top ei ei  ei ei  teams have a revenue function that depends = on success in both competitions, and the i,12. (22) weaker teams have a revenue function Taking the ratio of the two first-order condi- depending only on domestic competition. tions, we can obtain Under domestic league revenue sharing, the weaker team will be more willing to ∂p  ∂L ∂L  1 αα2 +−()1 1  reduce investment in talent to take advan- ∂e ∂e ∂e 1 =  2 2  . (23) tage of the strong team’s success than the ∂p  ∂L ∂L  strong team will be to reduce its own invest- 2 αα1 +−()1 2  ∂e  ∂e ∂e  ment, since by doing so the latter reduces its 2 1 1 expected revenue from the European-wide ∂L ∂L j =− j competition. If we suppose that ∂ ∂ then for ei ej fixed labor supply the LHS of (23) equals 7. Other Design Issues in Team Sports unity and hence local TV revenue sharing 7.1 Prizes and Lump-Sum Revenue Sharing has no impact on competitive balance. However, from the point of view of TV Fort and Quirk (1995) observe that shar- demand, there is no reason to suppose that ing of local TV revenues will tend to improve the marginal revenue from a unit increase in competitive balance, so that the invariance the quality of the opposition is the same as principle need not hold even with fixed sup- the marginal revenue from a unit decrease in ply conjectures. This finding arises out of the the quality of the home team (because in the independence of local TV revenue generat- former case the total quantity of talent on ing functions: no adding up constraints are show increases while in the latter case it involved and hence the problem resembles decreases). In general we suppose increasing more closely a standard Cournot-Nash the quality of the opposition will have a model where (a) noncooperative behavior higher value than reducing the quality of the does not yield joint profit maximization, and home team. In the absence of symmetry, (b) revenue sharing causes each firm to revenue sharing will reduce the marginal internalize the effects of its decisions on its revenue of the large market team more than rival and therefore leads to joint profit maxi- the marginal revenue of the small market mization. For example, suppose that in the team and therefore revenue sharing will two-team model each generated income improve competitive balance. Marburger only from local TV revenues, labeled L, and (1997) suggests that this kind of asymmetry that these revenues are increasing in the suc- might be true for gate revenues as well, cess of the home team. With revenue shar- where demand for absolute quality may be ing we can write the profit function for each important.62 team as 62 π p (e )[α L (1α)L]ce ,i1,2. He applies his model to the case of a luxury tax (see i i i i j i below). Stefan Késenne (2000a) shows that if team rev- (21) enues depend on the quality of visitors, proxied by their winning percentage, and that the marginal revenue from visitor quality differs across teams, then revenue sharing improves competitive balance. This is essentially the same 61 The “Champions” in this title being the domestic argument as that concerning local TV revenues. See also league champions of the previous season. Philip Cyrenne (2001). dec03_Article 2 12/4/03 11:17 AM Page 1169

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However, revenue sharing reduces the where V/2 is the lump tax on each team used marginal revenue to each team from hiring to create the prize fund V. Taking the ratio of an additional unit of talent, driving down the first order conditions we obtain wage rate per unit of talent and increasing ∂p profits in equilibrium. Revenue sharing 1 ∂ + works in the opposite way to a prize because e1 = 1 V ∂ µ + (25) it diminishes effort incentives. This naturally p2 V ∂ raises the question of how prizes would e2 affect competitive balance in a team sports context. While most individualistic sports from inspection the RHS of (25) converges offer substantial financial prizes to the win- to unity as V increases, implying that, for any elasticity of supply, a team funded prize will ners, this is usually not the case with team 64 sports. The team that wins a league champi- increase competitive balance. Since a prize onship may receive a cup, and team mem- also increases aggregate effort (as in an indi- bers may receive substantial bonuses, but vidualistic contest), a contest designer could the owners of the team in general stand to maximize both competitive balance and effort incentives through the use of such gain little or no direct monetary gain (i.e. 65 prize money) from winning a championship. prizes. The intuition seems quite straight- It is true that participation in the playoff or forward: when teams have differing revenue finals stage can be extremely valuable, and generating potential then the large (margin- also that sponsorship income and merchan- al) revenue generating team dominates. The dising are likely to be substantially increased creation of a prize fund equalizes incentives, by winning a championship,63 and that these so that small (marginal) revenue generating factors will impact on decision making in teams have as much to gain from winning as much the same way as an explicit prize. One their larger rivals. might hope to see future research attempt to While direct financial prizes are rare in quantify the value of prize like elements in team sports, European soccer leagues have the different team sports. adopted revenue sharing formulas for collec- Suppose that each team in the league tively negotiated TV income on a basis that were to contribute some fixed sum to a prize introduces the flavor of a prize, in contrast to fund awarded to the winning team. In the North America where all the major leagues two team case, where gate revenue depends distribute this income on the basis of strictly only on success, team 1 has a greater rev- equal shares. For example, in the English enue generating potential from success than Premier League 25 percent of annual TV team 2 (µ 1), and there is no local TV income is awarded on the basis of League income, we can write the objective functions rank, with the League champions receiving for each team as twenty times as much (of the 25 percent) as the team ranked last in the League.66 π µ 1 p1(e1)[ V] V/2 ce1, (24) 64 π It should be obvious that this argument will not be 2 p2(e2)[1 V] V/2 ce2, affected if we introduce demand for competitive balance or team quality into the revenue functions. 65 See Szymanski (2003) for a more detailed analysis of the implications of prizes in a model of team sport 63 The difference between first and second is likely to contests. nR+−1 be much greater than the difference between second and 66 The precise formula is V = where V third, a superstar effect of the kind identified by Rosen R n R (1981). Unlike a prize, the value of merchandising and ∑Ri related opportunities tends to differ between teams (e.g. i=1 because market sizes differ) and hence this kind of incen- is the prize awarded to the Rth ranked team and n is the tive promotes asymmetry. number of teams in the league. dec03_Article 2 12/4/03 11:17 AM Page 1170

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Palomino and Sakovics (2001) develop a did in aristocratic cricket.69 While in many model of TV revenue sharing to show that cases there may have existed a gap between for a joint profit maximizing league (a) full stated objectives and reality, real constraints revenue sharing is optimal when it has on behavior existed and continue to exist in monopsony power in the talent market, and many cases. Many clubs in Europe are also (b) performance based rewards (prizes) are “clubs” in the legal sense—operating under optimal when rival leagues compete for tal- a club committee who are volunteers and ent. With profit maximizing owners, equal have no powers of borrowing and no share- sharing of income from collectively sold holders to whom to distribute surplus. At the broadcasting rights will have no effect on very least, the taking of profits in these situ- competitive balance, and will just feed ations is likely to be discouraged. through directly to the profits of the owners. Furthermore, institutional rules often favor A sharing rule that equalizes ex ante incen- nonprofit objectives. In England the govern- tives (equality of opportunity) but leads to ing body still retains a maximum dividend inequality ex post (rewards winners) will, in rule, currently set at 15 percent of paid up the absence of capital market imperfections share capital.70 In France the government (e.g. credit constraints) generate a more bal- has legislated favorable tax treatment for anced contest. This proposition, though well clubs established as “companies with a sport- founded in economic theory, attracts consid- ing objective,” on condition that profit taking erable skepticism from noneconomists. This is restricted.71 may have something to do with beliefs about If teams have objectives other than profit the operation of capital markets or about the maximization then the outcome of competi- true objective function of team owners. tion and the implications of adopting 7.2 Win Maximization and Ownership specific incentive structures may be quite Rules different than under profit maximization. Vrooman (1997a) shows that, inter alia, So far we have assumed that all teams are player costs (effort) will be higher and profit maximizers, an assumption with which competitive balance greater in an asymmet- sports economists have been quite comfort- ric league of win maximizers compared to able in the United States,67 but which often profit maximizers. Késenne (2000a) seems less appropriate in the case of addressed the question of gate sharing in the 68 European soccer. . This has to do with both context of a league composed of win maxi- cultural and institutional factors. Culturally, mizers and shows that in general it will lead the men who set up soccer clubs were by and large amateurs who looked down on the pursuit of profit, just as their counterparts 69 In English cricket, amateurs and “players” (i.e. paid professionals) were segregated, changing in different rooms even when they were on the same team as recently as 1962. However, appearances can be deceptive: as far back as the 1880s the greed of many amateur cricketers in 67 Although Vrooman (1997a) considers seriously the demanding “expenses” led to the coining of the word “sha- implications of alternative objectives on the part of owners. mateurism”, to describe ostensibly amateur players who One aspect of the North American situation that has not demand kickbacks of one form or another. been considered in the economics literature is the pre- 70 Public corporations have managed to evade this rule dominance of ownership of sports teams as part of a larger by establishing the football club as a subsidiary of a hold- business empire, e.g. Ted Turner and the Atlanta Braves, ing company, which faces no such restrictions. Rupert Murdoch and the Dodgers. The idea that teams 71 Further discussion of this is to be found in Sloane might be operated as part of a wider business strategy (1971), Késenne (1996), and Jean-François Bourg and deserves some attention. Jean-Jacques Gouguet (2001). Discussion of changing 68 Dabscheck (1975) considered Australian sports behavior patterns in recent years can be found in Wladimir teams to be revenue maximizers. Andreff and Paul Staudohar (2000). dec03_Article 2 12/4/03 11:17 AM Page 1171

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to greater competitive balance. Intuitively, if been the introduction of veteran free teams spend all available income on hiring agency, minimum wages, and improved talent (i.e. they face a zero-profit budget pension provisions. The invariance proposi- constraint), then redistributing income from tion suggests that the unions would have wealthy teams to poor teams will tend to limited impact on competitive balance but equalize levels of talent and thus improve reduce the rents extracted by owners. competitive balance72. Support for the first of these propositions Given that different types of owners may was considered in section 6.1, while embrace different objective functions, and Zimbalist (1992) presents evidence on the that these objectives yield different out- second. comes, it is open to contest designers to The antitrust exemption for collective bar- favor particular types of owner whose equi- gaining agreements has bolstered the power librium behavior is expected to produce the of the unions by (a) enforcing exclusive bar- desired outcome. This idea is reminiscent gaining rights and (b) enabling owners to of the “strategic delegation” literature, enter into restrictive agreements that might where a profit maximizing owner might not be permitted in the absence of the choose to appoint a sales maximizing man- exemption. The value of the exemption to ager in an oligopoly (Chaim Fershtman and the owners has at times appeared so great Kenneth Judd 1987). Rules in North that some union members have attempted to America that prohibit stock flotation might decertify the union in order to bring an be deemed to encourage “sportsmen own- antitrust suit against the league, most ers” whose association with success might notably the NFL players’ union at the time lead them to behave more like win maxi- of the McNeil case (in 1989) and the NBA mizers than profit maximizers.73 Similarly, players’ union following the expiry of the restrictions in Europe that have until 1988 collective bargaining agreement (in recently limited the spread of ownership to 1994, for details see Staudohar 1996). In that the stock markets may have been intended case the union was aiming to get rid of the to create the same effect. Whether the ends salary cap (introduced in basketball in 1984) of league organizers can be achieved by which specified a maximum payroll equal to means of this kind of social engineering 53 percent of defined gross revenues, in must remain open to doubt. exchange for a complex set of arrangements specifying minimum player payments and 7.3 Salary Caps, Luxury Taxes, and the subsidies to weaker teams. Unions It is clear in theory that a salary cap should Since the 1970s, wage negotiations in the improve competitive balance,74 and equally North American major leagues have been clear that making a salary cap effective has characterized by collective bargaining. proved elusive. The NBA cap is perceived to Among the successes of the unions have have been ineffective because of the signifi- cant exemptions permitted (see Staudohar 72 As Quirk and Fort (2000) point out, this does not 1999) and Fort and Quirk (pp. 1277–82) find necessarily imply more competitive balance in a win-max- that the standard deviation of win percent imizing league for a given level of redistribution. Absent revenue sharing a win maximizing league could be less balanced than a profit-maximizing league and a given 74 Pace Vrooman (1995) makes the Coasian argument degree of revenue sharing might be inadequate to reverse that even if teams are constrained to pay identical the result. salaries, they still have incentives to ensure that talent 73 Brian Cheffins (1998) provides an interesting legal gravitates to its most profitable location. A team could perspective on the different approaches in North America evade the effect of the cap through the promise of and Europe. endorsements and non-pecuniary benefits. dec03_Article 2 12/4/03 11:17 AM Page 1172

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has increased since its introduction (see also agreed on a new luxury tax after narrowly Késenne 2000b). From the point of view of avoiding a strike.78 contest design, a salary-cap system should The roster limit, through which the num- have an effect similar to revenue sharing ber of players permitted on the payroll is when teams are win maximizers. Under win fixed, is a much more venerable institution in maximization an increase in revenue sharing North American sports, intended to prevent reduces the expenditure of the large rev- the stockpiling of top players, although there enue-generating teams, but also increases is surprisingly little academic research on its the spending of the small revenue-generat- impact. In baseball it is commonly argued ing teams, and both effects enhance compet- that the farm system has been the method by itive balance. To be fully effective a salary- which teams have evaded the roster-limit cap system also needs to ensure that the rules, but there is a complex interaction small revenue generating teams raise their between the rules and player contracts. The spending to the level of the cap.75 existence of roster limits is itself evidence A luxury tax works in a similar way to a that one of the most widely adopted assump- salary cap, but instead of imposing a fixed tions in modeling team sports contests (and limit (like a quota) it discourages acquisition one adopted in this paper), namely that tal- of playing talent by taxing expenditure over ent is perfectly divisible, does not hold. This a fixed limit (a tariff). The theoretical impli- is an issue clearly meriting further research. cations are discussed by Marburger Schemes such as salary caps, luxury taxes, (1997).76 The only instance of this system in and roster limits have not been introduced the major leagues has been the agreement into the European soccer system. One rea- between MLB and the MLBPA following son is that there is no collective bargaining the 232-day strike in 1994–95. When the two over salaries at the European Union level, parties agreed on a settlement, it included a another is that such bargaining would not, complex arrangement to tax expenditures of even if it existed, enjoy an equivalent the top five payrolls on expenditures over antitrust exemption. Nor is it likely that such fixed limits. The tax operated between 1997 agreements could be agreed among the and 1999 at a rate of 35 percent in the first clubs in a system of multiple leagues. A two years and 34 percent in the third year. salary cap tailored to the average team in the This system raised $30.6 million over the top division of a national league would seri- three years for redistribution to the weaker ously handicap a leading team in that league teams, compared to total MLB payroll which was also competing at the European spending of $3877 million over the same level. Moreover, a salary cap applied only in period. Not surprisingly the luxury tax was one national league would cause the most deemed to have little effect.77 In 2002, MLB talented players in that league to move to rival national leagues which did not operate a cap. Any European-wide system would 75 Arie Gavious, Benny Moldovanu, and Aner Sela face the obstacle of significant international (2002) show that imposing a bid cap in the context of an all pay auction reduces the bid of low cost (high revenue) differences in standards of living, tax rates types and increases the bids of high cost (low revenue) types, suggesting that even without imposing constraints 78 The tax regime was set for a four-year period, the tax there will be a tendency for competitive balance to thresholds being $117 million in 2003, $121 million in improve. 2004, $128 million in 2005, and $137 million in 2006. Tax 76 See also Gustafson and Hadley (1996). rates were 17.5 percent in 2003, rising to 22.5 percent for 77 Somewhat oddly, the Blue Ribbon Panel (Levin et al. first-time offenders and 30 percent for repeat offenders in 2000) attributed its failure to the fact that the tax threshold 2004 and 2005, with third-time offenders paying 40 per- was a floating one (p. 39), rather than the fact that the tax cent in the latter year, and then 40 percent in 2006 except threshold was simply set too high. for first-time offenders. dec03_Article 2 12/4/03 11:17 AM Page 1173

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and administrative systems. Only if a closed the league champion and that (1φ) is superleague system emerged in Europe, retained by the owner. Thus team profits are φ constructed on similar lines to the major equal to (1 ) UpiVei (the marginal leagues, is it likely that such arrangements cost of effort is normalized to unity). would become feasible (Hoehn and Maximizing with respect to ei yields (and Szymanski 1999 explore this possibility). assuming the supply of talent is elastic81) we can find the equilibrium profit of each team 7.4 Optimal Number of Teams in the to be: League  ()n − 1  An obvious puzzle for the design of a πγφ=−U1  . (26) sport’s league is its optimal size. This issue  n  has been a constant concern of league Since all consumer surplus is appropriated authorities in North America over time, and aggregate welfare is simply the sum of is also associated with the public policy con- profits: cern over the relocation of franchises (or the Wn πU[nγφ(n 1)]. (27) threat of relocation) to extract subsidies from local government (Noll and Zimbalist The derivatives of welfare and of profits with 1997). Vrooman (1997b) addresses the issue respect to the number of teams are: of optimal league size directly and draws the analogy with James Buchanan’s (1965) theo- ∂πγφ ∂W =−U <01and =−U()γφ . ry of clubs. If members have a joint interest ∂n n2 ∂n in total revenues generated by the club, then (29) the individual optimum is to agree to expan- sion to the point where average revenue per Since the derivative of profits with respect member is maximized, which in general to n is negative, teams will prefer smaller involves a smaller number of members than leagues, all else equal, while as long as either the social welfare optimum (that maximizes γ (the discriminatory power of the contest) total member revenues).79 or φ (the amount of locational utility allocat- The issue can be illustrated using a simple ed to the prize) are not too large, the deriva- version of the contest model. Suppose that tive of welfare is positive and so expansion teams in a league compete in a symmetric raises welfare. In the absence of side-pay- contest with a CSF as defined by (3) and a ments the members of a league will expand payoff function that depends on the expect- to the point where the marginal profit from ed value of the prize, the cost of effort/ expansion equals the average profit per talent, and some fixed “locational” rent or team, rather than where the marginal profit utility (U) of local citizens derived from the is zero. This problem is exacerbated further presence of a team.80 To avoid underinvest- if teams cannot fully appropriate locational ment issues we assume this rent can be fully rents. Teams oppose expansion to optimal appropriated by the local team. Further we levels in the contest model partly because assume that some fraction of this locational this reduces their own probability of winning rent is allocated to a prize fund V awarded to the prize, even though this matters little from the social planner’s perspective in the 79 This same argument has been applied to the ineffi- symmetric case. ciency of a labor-managed firm (e.g. Benjamin Ward 1958; James Meade 1974), which might be thought an appropri- 81 An assumption that can be justified here since the ate analogy for a sports league. optimal league size is a long-run decision, and in the long 80 See John Siegfried and T. Petersen (2000) for an run talent supply is elastic (e.g. talent can be attracted interesting analysis of locational rents. away from other sports). dec03_Article 2 12/4/03 11:17 AM Page 1174

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In a contest model where teams value gation system ensures that all locations have championship success, there will typically a right to enter the league structure at some be less expansion than in the “win percent” level, and after a period of years reach the model where teams generate revenue from highest level if the local willingness to pay is their success probability against each visit- adequate. ing team. In the contest model teams 7.5 Promotion, Relegation, and Exclusive oppose expansion since it reduces their own Territories probability of success in the contest. In the symmetric win percent model, absent The European Commission (1998) capacity constraints, the teams would favor described promotion and relegation as “one unlimited expansion since this would imply of the key features of the European model of unlimited additional revenues. With a fixed sport.” It is the rule whereby the worst-per- talent supply teams would only wish to forming teams at a given level of league expand to the point where all talent competition are demoted at the end of the resources are fully utilized. season to play in the immediately junior Fort and Quirk (1992, 1995) provide a league and are replaced by the best per- good deal of evidence to show that in fact forming teams from that league. For exam- expansion generally occurs to meet the ple, at the end of each season the three threat of entry of a new league. Since the teams in the English Premier League with expected profit required to facilitate entry the lowest number of points won are demot- by an entire league is much greater than that ed to the Football League Division One and required for a single team, underexpansion are replaced in the Premier League by the seems inevitable. In a contest, model, effi- three best performing teams from Division ciency requires side payments (as in the One. There is promotion and relegation at standard model of a cartel; see e.g. Kevin every level of English soccer, from the Roberts 1985) and in practice, new entrants Premier League right down to the lowest do make side payments in the form of expan- level of amateur competition, so that in the- sion fees. If all the locational rents are ory any English soccer team might one day appropriable (and municipal subsidies are reach the Premier League. This system is often substantial) then efficient expansion operated in all the major soccer nations and should occur. However, this is tantamount to applies to most other team sports played in assuming that leagues are capable of operat- Europe (e.g. rugby union, basketball, ice ing as efficient cartels. Efficient side-pay- hockey).83 In economic terms, promotion ments would in principle be tailored to the and relegation represents an opportunity for opportunity costs of each incumbent team teams to enter the market at every level of but the information requirements for this competition. Applied to baseball in the procedure would be both significant and United States, for example, it would mean subject to moral hazard and adverse selec- that AAA teams could one day play in the tion. With large numbers cartel agreements majors (and conversely, that the Yankees may become unenforceable (Peter Cramton might one day play AAA baseball). The eco- and Thomas Palfrey 1990).82 In Europe nomic consequences seem to be fairly simi- these issues have never arisen. The hierar- lar to the effects of open entry in any market. chy established by the promotion and rele- First, there is no credible threat of fran- chise relocation in Europe, since every city

82 Cyrenne (2001) considers a related issue, the optimal number of games in a season, and contrasts the choice of a 83 Noll (2002) and Ross and Szymanski (2002) analyze cartel to that of a social planner. the system in more detail. dec03_Article 2 12/4/03 11:17 AM Page 1175

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has at least one team with the potential to On the face of it this might suggest that enter the major league (as long as it is pre- promotion and relegation is a superior system pared to invest in player talent) without from the point of view of consumers, needing to attract someone else’s team. As a although clearly inferior for the profitability result teams are unable to extract large sub- of teams. However, the welfare questions are sidies from local government in the manner not so clear-cut. While promotion and relega- so familiar in the United States (see e.g. tion affords an opportunity for more cities to Siegfried and Zimbalist 2000).84 Second, participate in the major league, it might be teams are motivated not only to win, but also argued that the relegation of the Yankees to to avoid the punishment of relegation. It was be replaced by the home team of Boise, Idaho noted above that the variance of seasonal would not represent a net increase in welfare. win percentages is smaller in European soc- This is a fine judgement, even if in practice cer than the North American major leagues the major teams are almost never relegated. even though the variance of team expendi- A more subtle problem concerns the dis- ture is greater. That is because teams must tribution of talent. If this is fixed, and the fight to the end of the season even if they are promotion and relegation system leads to a out of contention for the championship.85 more even spread of talent across teams Promotion and relegation also undermines (because the incentive for the smaller teams the value of territorial exclusivity, and while to compete is greater) then the average qual- it is not theoretically inconsistent for the two ity of teams at the highest level (e.g. the thir- to co-exist, in practice open entry in Europe ty best teams) may fall, reducing the quality has meant freedom to establish a team wher- of individual matches.86 Finally, as ever one wishes. Szymanski and Valletti (2003) show, promo- Promotion and relegation also has some tion and relegation may undermine the advantages from the perspective of contest incentive to share revenues. The cost of rev- design. Authorities in a league system with enue sharing to large drawing teams is the promotion and relegation can optimize the foregone income from current success, number of teams eligible for the champi- while the benefit is their share in a more onship each season without simultaneously valuable (because more balanced) contest. having to determine the size of the league. In a closed league every team is guaranteed One consequence of this is that the top divi- to participate in that contest, while in an sions of European soccer leagues are in fact open league any team might be relegated in smaller (typically with fewer than twenty the future. This may be one factor con- teams) than the North American major tributing to the observation that leagues in leagues have become, and this can mean a Europe have adopted many fewer mecha- less extreme difference between the best nisms to promote competitive balance than and the worst. the North American majors. If an open system obliges teams to supply more effort and reduces profits, why would 84 Relocation is in general prohibited by the governing the leading teams simply not secede from bodies in Europe. Recently, Wimbledon, a team playing in the second tier of English soccer, was permitted to relo- cate, after lengthy debate, but only because the team’s sta- 86 It is a mistake to argue that there is not enough tal- dium had been closed and the local government did not ent to support a promotion and relegation system because allow them to build a new one (even at their own expense). talent will be spread too thinly. Rather, an efficient promo- 85 In the closed North American leagues low ranked tion and relegation system requires player mobility, since teams may prefer to lose toward the end of the season if the best talent will always migrate to the top division. In this gives them a better draft pick. Beck Taylor and Justin practice this often happens with extraordinary speed. Trogdon (2002) find empirical support for this proposition Promotion and relegation is a discipline on the owners in the NBA. rather than the players. dec03_Article 2 12/4/03 11:17 AM Page 1176

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the League and set up on their own? The letics and swimming) as well as the develop- answer to this in practice is the fear of expul- ment of new events (e.g. Taekwondo). In sion from the national Association and the team sports the soccer World Cup has been international network. Indeed, it is this fear a significant contributor to the development that inhibits the clubs from demanding com- of the sport in countries with limited profes- pensation for release of contracted players to sional leagues. The competition itself has represent their national team (for as many as helped to bring players from particular twenty matches in a season). FIFA pays no countries to international recognition while compensation to the clubs who continue to the profits generated by the competition pay the full salaries of their players during have been used in part to fund the develop- international tournaments, and while players ment of the sport (notably, on both counts, receive some appearance money, this is gen- in the case of the African countries). Most erally a tiny fraction of their total remunera- ostentatiously, the decision of FIFA to locate tion. This makes the World Cup Finals not the 1994 World Cup in the United States only the world’s most popular sporting event was seen by many as an blatant attempt to (33 billion viewers for a total of 64 match- promote the game in that country given its es87), but also, with turnover of $4 billion, revenue generating potential (see e.g. one of the world’s most profitable team Sugden and Tomlinson 1999). The North sports events. Clubs fear expulsion from the American major league sports have pursued Association since they know that most of the their own development activities abroad. In players are willing to play for their country Europe the NFL has established its own for almost nothing either because of patriot- league, with moderate success in Germany ism or because of the reputation effects and and Spain, MLB has made more than one its impacts on endorsement income.88 Thus attempt to enter the European market on a any breakaway league would find it hard to modest scale, and in China the NBA has retain players. established a subsidiary to develop the league in that market. However, they are all 7.6 Club versus Country to a degree hampered by their own com- National teams have been unimportant in mercial objectives, given that they are ulti- the development of the major team sports in mately responsible to profit-oriented team the United States, but in other sports nation- owners. al teams and international representative Soccer is simply one example of interna- sport has been the driving force in develop- tional representative competition dominat- ing the popularity of the game and providing ing domestic league competition. Other some of the most attractive events within the examples include cricket (the dominant sport. In individualistic sports it is clear that sport in India, as well as a major sport in the Olympics has provided a showcase for nations of the British Commonwealth development of traditional events (e.g. ath- including England, Australia, South Africa, Pakistan, New Zealand, Sri Lanka, and the Caribbean islands that play collectively as 87 This is FIFA’s claimed viewership for the “France ‘98” World Cup. This implies everyone on the planet could the “West Indies”), and Rugby Union, a have watched five games, around 50 billion viewing hours. sport similarly found in most The IOC claimed 36 billion viewing hours for Sydney Commonwealth countries and historically 2000. 88 In fact top players from weak countries with little dominated by New Zealand. What is striking chance of winning the World Cup are sometimes reluctant about these examples is that (a) competitive to appear. In the 2002 World Cup the captain of the balance plays no obvious role in the popular- Republic of Ireland walked out on his team claiming that the national Association was not prepared to spend enough ity of these sports; (b) the dominant teams money on training facilities for the players. are seldom drawn from the larger or richer dec03_Article 2 12/4/03 11:17 AM Page 1177

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nations; and (c) international representative open to the entire planet. Brazil has a 76 per- competition is used to subsidize domestic cent winning record in all World Cup match- league competition. es played. Yet this dominance does not seem On the first two points, consider the New to have undermined interest in these compe- Zealand rugby union team known as the “All titions. One reason may be that these inter- Blacks.” They have been playing in interna- national competitions bring together the best tional competition since 1903 and have an players in the world and when combined all-time winning record of 72 percent, with national fervor these factors outweigh a despite being dwarfed in terms of population rational concern with competitive balance. size by many of their larger rivals. For exam- The aspect of quality may also explain why ple, the All Blacks currently have a winning such competitions have, at least as yet, limit- record of 78 percent against England, with ed appeal for the North American major only 8 percent of the latter’s population. league sports- all of the best players are Similarly, the Australians in cricket have a already on show in the major leagues, so in winning record of 56 percent against that sense an international representative England in 209 matches over the period competition would not offer a higher level of 1877 to 2001 (ignoring ties), despite a much competition. If baseball, for example, were smaller population.89 The West Indies, draw- played to a higher level in other national ing on the smallest population90 of the ten leagues then international competition Test Match Cricket playing nations, have the would become attractive. In other words, the second highest all-time winning record (57 existence of a dominant national league in percent).91 While this phenomenon is not team sports seems to undermine the demand unknown in the individualistic sports, where for international representative competition. small and/or poor nations seem able to pro- By contrast, where there is no dominant duce a disproportionate number of winners, national league, international competition it is easily exaggerated. Andrew Bernard and becomes attractive. Meghan Busse (2000) show that population The dominance of international competi- and GDP are remarkably reliable predictors tion creates some interesting problems in of Olympic medal success. team sports. Most notably international In soccer, the dominant countries in the cricket has been seriously undermined by World Cup (played every four years) have the revelation that many of the top players been Brazil (five victories), Germany and have been accepting substantial bribes to fix Italy (three victories), Argentina and matches for gambling purposes (see Sir Paul Uruguay (two victories). These five teams Condon 2001). Ian Preston, Ross, and account for fifteen of the seventeen World Szymanski (2001) suggest that corruption Cup wins (88 percent), despite entry being stems not merely from moral frailty but also from the remarkably low salaries paid to the 89 Over the last twenty years Australia’s dominance has players who were induced to accept as become embarrassing, with a 66 percent winning record in bribes what were, for world class athletes, decisive matches. remarkably small sums of money (e.g. as lit- 90 The other ten are Australia, Pakistan, England, South Africa, India, Sri Lanka, New Zealand, Zimbabwe, and tle as $10,000). Low salaries in cricket are Bangladesh, with a combined population of 1.4 billion, due not to the lack of popularity of the game compared to the Island population of around 4 million. (an international series of five matches can Even excluding India, this would amount to no more than 1 percent of the population of the cricketing nations. generate an income of $30 million) but to 91 If baseball were regularly played at the international the use of these funds to subsidize domestic representative level, such phenomena might also emerge. leagues which attract no interest from pay- For example, it is well recognized that the tiny Dominican Republic would be a competitive nation, not to mention ing fans due the focus on international Cuba. matches. Without the subsidy there would dec03_Article 2 12/4/03 11:17 AM Page 1178

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be no competitive environment in which to term popularity may be worthy of further raise players to the necessary international research. standard. The case of cricket contrasts with soccer where there is a balance of interest in 8. Antitrust and Public Policy club competition (with healthy finances) and international representative competition, In the words of Michael Flynn and which means that the former can afford to Richard Gilbert (2001), “One is struck by the supply talent at no cost to the latter. In theo- frequency with which the structure and rules ry this can be seen as a kind of league tax to of professional sports leagues have been the fund the development of the sport. subject of antitrust challenges in recent In the case of rugby union the interna- decades.” It is not intended to provide an tional representative game traditionally exhaustive review of these issues, which can 93 dominated, but in recent years a successful be found elsewhere. However, given the international club competition has emerged abiding interest of the courts and legislators in the southern hemisphere (played between in the fortunes of sports leagues, the impli- teams from New Zealand, Australia, and cations of both the theory and the empirical South Africa) and may be emerging in research reviewed here are worthy of brief Europe (where the dominant teams are discussion. Broadly speaking, the legal issues located in England and France).92. This sug- associated with individualistic sports have gests three models of sporting development: been far less numerous and weighty than a dominant national league (North America) those of team sports. For example, in Weiler with limited international competition, a and Roberts’ exhaustive textbook, out of dominant international competition and 1007 pages only 69 are devoted to individual weak national leagues (cricket, Rugby sports, while most of the remainder is Union) and a combination of powerful focused on team sports. This is perhaps national leagues with strong international because the object of competition—to find representative competition (soccer). Given the best players/athletes—is clear-cut, and that talent is to a degree substitutable the appropriate mechanism to achieve this— between sports in its developmental years contests with very large prizes and spreads— (i.e. early to late teens) and sports increas- is not in question. Any restriction intended ingly compete to find the best talents world- to prevent these mechanisms from working wide, it is tempting to suggest that only while raising profitability (e.g. excluding ath- sports with a strong financial structure based letes from competition without due cause) 94 on a viable model of league competition will would be unlikely to stand up in court. survive as major sports. (see Ross and The focus of dispute, and in some cases Szymanski 2003 for an analysis of optimal legislative intervention, in team sports has league design.) Already cricket is suffering been the contention of team owners and from a loss of interest in some of its tradi- league authorities that economic restraints tional centers (e.g. the West Indies). Culture of one form or another are required to main- may defend other sports more robustly, but tain a competitive balance which is in the the notion that structure may influence long 93 The U.S. literature is particularly rich—e.g. Flynn and Gilbert (2001), Thomas Piraino (1999), Roberts 92 John McMillan (1997) provides an interesting discus- (1984), Ross (1989, 1997, 1998, 2001), Ross and Lucke sion on the balance between centralized coordination and (1997), Paul Weiler and Gary Roberts (1998). There are decentralized decision making in the case of New Zealand also a number of European texts, e.g. Simon Gardiner et rugby union. But see Dorian Owen and Clayton al.(1998), Alexandre Husting (1998). For an Australian per- Weatherston (2002) for analysis of how provincial compe- spective see Dabscheck (2000). tition in that country has been subordinated to the needs 94 Some issues remain, such as rules relating to eligibil- of the national team. ity, and in particular eligibility and disabilities. dec03_Article 2 12/4/03 11:17 AM Page 1179

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interest of consumers. A natural starting whether such restraints are proportional to point therefore is the nature of the relation- their intended benefit (see also Herbert ship between the teams and the league. As Hovenkamp 1995 and Piraino 1999 for the Gilbert and Flynn observe, the antitrust legal perspective on these issues). analysis of agreements among business units The types of restraints that might fall depends to a significant degree on their under this analysis include both labor mar- ownership—subsidiaries of a holding com- ket restraints (e.g. reserve clause, draft, pany cannot collude among themselves, salary cap, roster limits, restrictions on play- while independent entities may. In the four er trading), product market restraints (e.g. major leagues (MLB, NFL, NBA, and revenue sharing, collective selling, exclusive NHL) the teams are independent business territories) and capital market restraints (e.g. entities which associate as a league to agree restrictions on ownership). Most of these the rules of competition and so on. In Major issues have been the subject of litigation. League Soccer, however, the team owners The most famous litigation in sport is have a stake in the MLS entity itself, which Federal Baseball v. National League, (259, in turn owns all the player contracts. U.S. 200 (1922)) that reached the now wide- Moreover, it seems clear that this business ly condemned conclusion that baseball was structure was selected specifically to avoid exempt from the federal antitrust laws since the attention of the antitrust authorities.95 it did not involve interstate commerce. See Gilbert and Flynn suggest that a natural Zimbalist (2003) for an interesting analysis interpretation of the economic structure of of the exemption. Since then the courts have the major leagues is as a joint venture. set out to interpret this exemption for sport- Recognizing the “peculiar economics” of ing leagues as narrowly as possible, and team sports—Neale’s (1964) famous where possible to conduct a rule of reason phrase—that production requires the coop- analysis of challenged restraints. eration of rivals, so that each team has a vest- In the labor market, Flood v. Kuhn (107, ed interest in the existence, and even the U.S. 258 (1972)), examined the reserve success, of its competitors, it is reasonable to clause in baseball but refused to prohibit it suppose that some kinds of agreements can on the grounds that it is for Congress to be legally entered into. Most obviously these overturn the now venerable antitrust exemp- include agreements on the rules of the tion of baseball. Smith v. Pro Football, Inc. game. This is no different from the antitrust (593 U.S. F.2d 1173 (1978)) considered the treatment that would be accorded an agree- NFL draft and declared it an unreasonable ment between two competitors entering into restraint of trade. Writing contracts intended an agreement to bring a product to market to evade salary cap restrictions was consid- that would not exist in the absence of the ered (Bridgeman v. NBA (re: Chris Dudley), joint-venture agreement. Facilitating the 838 F. Supp. 172 (D.N.J. 1993)) and upheld joint venture may in all likelihood require in this limited context. Mackey v. NFL, 543 the agreement of restraints among the part- F.2d 606 (8th Cir.1976) rejected the ners. The essential legal issue is whether “Rozelle Rule” that required teams signing a such ancillary restraints have the effect of free agent in the NFL to compensate the significantly limiting competition, and player’s previous team with a draft pick, and McNeil et al. v. NFL (70, F. Supp. 871 8th 95 In Fraser v. MLS the Appeal Court cast doubt on the Circ. 1992) rejected the NFL’s subsequent credibility of the single entity claim of MLS (LLC 284 F plan (Plan B) to allow teams to protect up to 3d.47 (1st Circ. 2002)), describing it as “somewhere 37 players on their roster. Finley v. Kuhn between a single company (with or without wholly owned subsidiaries) and a cooperative arrangement between (569, F. 2d 1193, 6th Circuit 1978) upheld existing competitors.” the right of the commissioner of baseball to dec03_Article 2 12/4/03 11:17 AM Page 1180

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penalize teams selling players for cash on the nance of labor market restraints. Moreover, grounds that it might weaken the selling Congress has intervened through the 1961 team and reduce competitive balance. Sports Broadcasting Act to exempt collec- The relationship between collective selling tively negotiated national sponsored broad- of TV rights, competitive balance and rev- casting agreements from antitrust scrutiny. enue sharing was considered in United States As a result, in practice the major leagues v. NFL, 116 F. Supp. 319 (E.D. Pa. 1953) operate a wide range of restraints, adum- and NCAA v. Board of Regents, 468 U.S. 85, brated in much of the foregoing discussion. 107 (1984) and in both cases competitive bal- In European sports the power of the ance justifications were considered poten- courts is supplemented less by the role of tially valid reasons for the maintenance of the legislature, which has not interfered sig- the challenged restraints (on individual sell- nificantly in the operation of team sports, ing) and so were not per se illegal, but in than by the European Commission, which both cases on a rule of reason the restraints acts as an executive body representing the were deemed either excessive or not tailored member states (who hold a power of veto to achieve the stated aim.96 In the Raiders’ over many of its activities). The competition case (Los Angeles Memorial Coliseum directorate (DG IV) of the Commission Commission v. NFL, 726 F.2d 1381 (ninth wields considerable power and has inter- Cir. 1984) the court upheld a jury verdict vened to challenge various restraints in that the league’s application of the NFL rule recent years, and has in most cases reached requiring a majority of three-quarters of agreement with the leagues prior to going to member teams to permit a relocation (thus court. In European competition law the protecting exclusive territories) restrained Commission in general only acts on the com- competition. It rejected the claim that the plaint of parties deeming themselves to be rule was justified by any legitimate interest harmed by a challenged restraint, but in of the NFL, including maintaining competi- recent years, as the value of TV contracts has tive balance. In Sullivan v. NFL (U.S. Court escalated so has the number of complaints of Appeals, First Circuit, 34 F.3d 1994) the received. court allowed that motives such as competi- In the Bosman case (see above) the com- tive balance might on a rule of reason justify plaint was taken to the European Court of prohibiting public ownership of a franchise. Justice. The court held that competitive bal- On balance it might be argued that the ance was not a valid defence of the old trans- courts have demonstrated some skepticism fer system, even though in other cases it about competitive balance as a justification could justify a restraint (such as revenue for restraints, although they have accepted it sharing). Moreover, the free movement of as a possible justification under a rule of rea- labor, a principle enshrined in the Treaty of son. However, this state of affairs has been Rome, overrode any specific consideration complicated by the nonstatutory exemption of the interests of the league. In 2000 the for collective bargaining agreements, which Commission went further and challenged has rendered the unions in North American the economic basis of the transfer fees being sports so much more powerful than their paid for players within contract on the European counterparts. As discussed in the grounds that they restricted the free move- case of salary caps, above, the exemption has ment of labor within the European Union. In enabled unions to bargain away rights won 2001 it was announced that the Commission in the courts and to facilitate the mainte- had reached agreement with the football governing bodies (FIFA and UEFA, the 96 The NCAA case also considered in detail the effect European governing body to which all the of broadcasting on live gate. national governing bodies belong) on a com- dec03_Article 2 12/4/03 11:17 AM Page 1181

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pensation system that would allow clubs to are already organized in an exclusive bar- claim significant fees for players under age gaining group called G14) break away to 23 on the grounds of investment in training form their own closed superleague along costs. Players over 23 would have the right to North American lines. If competitive bal- move clubs annually, even if employed under ance really matters then we should expect a long-term contract, subject to an economi- the European system to collapse. cally justifiable (presumably moderate) compensation payment.97 9. Conclusions Later in 2001 the Commission issued a statement of objections98 to the collective sale It is a commonplace among economists to of broadcasting rights to the lucrative hold up sports as an example of contest/tour- Champions’ League competition for the top nament theory in action, but in practice a lot European clubs, run by UEFA. Agreement remains to be done both to understand the was later reached over UEFA’s right to market relationship between tournament structures the Championship as a whole subject to some and incentives in theory, and to test theories significant restrictions. Collective selling of against the data. One objective of this review broadcasting rights has been challenged at has been to discuss the contest theory litera- the national level in a number of European ture in the context of sports. While there countries, notably Germany (ruled illegal and been a good deal of research that has direct then given an antitrust exemption by parlia- implications for the design of individualistic ment), the United Kingdom (upheld), contests, empirical testing remains limited Denmark (upheld), the Netherlands (no deci- despite widespread agreement that this sion), Italy (ruled illegal), and Spain (prohib- would be a very fruitful area in which to con- ited); see Szymanski (2002) for details. duct testing. Moreover, there are many It seems that the soccer leagues of Europe aspects of the organization of individualistic have received much less favorable antitrust sports that could be modeled more fully with treatment than the North American leagues. a view to establishing an optimal design: e.g. Given that the European leagues have main- optimal prize spreads in asymmetric contests, tained a high degree of public interest and competition between rival contest organiz- structural stability over the last half century ers, the entry rules for contestants and opti- despite having fewer restraints and less com- mal handicapping, to select just a few. petitive balance than the North American The relationship between team sports and leagues, would it be correct, as the contest theory seems even less well devel- European Commission (1998) has done, to oped. The role of prizes in providing incen- speak of a European model of sport?99 tives has been largely ignored in the team Currently the main issue is whether the sports literature, where much of the policy existing structures are stable or whether the oriented research has focused on redistribu- growing commercialization of the sport will tion mechanisms such as revenue sharing, lead to restructuring. Hoehn and Szymanski and has been preoccupied with the proposi- (1999) suggest one kind of restructuring in tion that such sharing is likely to have a neu- which the dominant clubs of Europe (who tral impact. In this paper that claim is shown to depend on the assumption that an inelas- tic supply of talent is incorporated into the 97 See FIFA Regulations for the Status and Transfer of Players, July 2001 (see also the comments in section 6.1 conjectural variations of the owners generat- above). ing an equilibrium that is not Nash. This 98 European Union Official Journal, C 169, 13.06.2001, seems a relatively unfruitful avenue for p. 5. 99 See Didier Primault and Arnaud Rouger (1999) for a research. An alternative way forward is the trenchant assertion of difference. analysis of incentive structures. That prizes dec03_Article 2 12/4/03 11:17 AM Page 1182

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enhance incentives is surely a fundamental punishment for low quality—severe enough that proposition of economic theory, but one that salary treaties, league sharing arrangements, and unified player drafts are so far thought to be has been little studied in the team sports lit- unnecessary, even though star salaries are enor- erature. The analysis of revenue sharing has mous. It is an interesting economic question as to paid little attention to the different ways that which system achieves better results. revenues for sharing can be collected or the basis of their allocation. For example, even if Careful consideration of the impact of TV rights are sold collectively, different rules institutional differences may eventually lead for distributing that income have quite dif- to a better understanding of the incentive ferent implications for incentives (and prof- effects of contest design. its). The impact of prize funds also depends Empirically, some fundamental issues on the organizational structure of a sport remain unresolved. For example, the central (e.g. with or without inter-league economic claims of sports economists, that uncertainty rivalry). of outcome boosts demand for sporting con- One weakness of much of the existing lit- tests and that inequality of economic erature is that the appropriate definition of a resources leads to more certainty of outcome welfare function against which the optimali- obtain only weak support in the literature. ty of contest can be measured is not careful- Given that many successful team sports are ly specified. This paper has not touched in characterized by highly unbalanced compe- detail on this issue, but it is clearly critical. A tition (e.g. soccer) and that proposed balance conventional IO approach would be to focus enhancing measures are almost always prof- on consumer surplus, but the complex spec- it enhancing, there are grounds for caution. ification of consumer demand, given the role From a policy point of view it may be that of team loyalty, competitive balance and the invariance principle has been unhelpful team quality, as well as the more mundane in encouraging the view that restrictive issue of price, makes this approach problem- measures would at least do no harm, even if atic. In the contest literature the convention they do no good. Given the role that econo- has been to focus on the issue of rent dissi- mists frequently play in antitrust analysis, pation—but is this an appropriate yardstick these theoretical and empirical perspectives for sporting contests? More work remains to have important policy implications. be done to settle this crucial issue. We are still some way from being able to Comparative institutional analysis has fully model and test an optimal design of a much to offer for our understanding of orga- sporting contest. Such a project, however, is nizational issues in team sports, not just not beyond the capabilities of the economics between North America and Europe, but profession. with other countries such as Australia with REFERENCES developed national sports and with other Alexander, Donald. 2001. “Major League Baseball: multinational sports such as cricket. Rosen Monopoly Pricing and Profit-Maximizing Behavior,” and Sanderson (2001) reflected on the dif- J. Sports Econ. 2:4, pp. 341–55. ference between North American and Andreff, Wladimir and Paul Staudohar. 2000. “The Evolving Model of European Sports Finance,” J. European leagues thus: Sports Econ. 1:3, pp. 257–76. All schemes used in the United States punish excel- Atkinson, Scott; Linda Stanley and John Tschirhart. lence in one way or another. The European football 1988. “Revenue Sharing as an Incentive in an Agency Problem: An Example from the National Football approach punishes failure by promoting excellent League,” Rand J. Econ. 19:1, pp. 27–43 minor league teams to the majors and demoting Baik, Kyung. 1994. “Effort Levels in Contests with Two (relegating) poor performing major league teams Asymmetric Players,” South. Econ. J. 61, pp. 367–78. back down to the minors. The revenue loss from a Baimbridge, Mark; Samuel Cameron and Peter potential demotion to a lower class of play is severe Dawson. 1996. “Satellite Television and the Demand dec03_Article 2 12/4/03 11:17 AM Page 1183

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