WORKING PAPER SERIES Long-term Competitive Balance under UEFA Financial Fair Play Regulations Markus Sass Working Paper No. 5/2012

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1 WORKING PAPER SERIES

2 Impressum ( 5 TMG) Herausgeber: Otto-von-Guercke-Unverstät Magdeburg Fakultät für Wrtschaftswssenschaft Der Dekan Verantwortlch für dese Ausgabe: Otto-von-Guercke-Unverstät Magdeburg Fakultät für Wrtschaftswssenschaft Postfach Magdeburg Germany Bezug über den Herausgeber ISSN

3 Long-term Compettve Balance under UEFA Fnancal Far Play Regulatons Markus Sass Unversty of Magdeburg, Faculty of Economcs and Management, Char of Economc Polcy (VWL3), Postbox 4120, Magdeburg, Germany, Tel.: , Fax: , Abstract Ths paper analyzes the long-term development of compettve balance n a professonal team sports league wth wn-maxmzng clubs facng a strct break-even constrant as mposed by UEFA s new Fnancal Far Play Regulatons. A classcal model of professonal team sports leagues s employed to calculate seasonal compettve balance, whch solely depends on the market sze of clubs. In the mult-perod verson of the model, a market sze functon, whch captures the emprcal fact that a club s revenue potental s postvely affected by ts hstorc success, s ntroduced. The model shows that there s only one long-term steady-state equlbrum, n whch bg clubs totally domnate small clubs and compettve balance s maxmally uneven. The ntuton s that a club, whch becomes more successful, s able to attract more and more spectators yeldng hgher revenue and leadng to the club beng able to afford more playng talent. Ths n turn leads to greater success, whch n turn attracts even more spectators and so forth. Snce small clubs are no longer allowed to overspend and thereby nvest ther way to a greater market sze n the future, the model predcts a negatve trend n compettve balance to be the result of the new UEFA Fnancal Far Play Regulatons. Keywords: Sports Economcs, Professonal Team Sports, Compettve Balance, UEFA Fnancal Far Play JEL: L83 Preprnt submtted to European Journal of Poltcal Economy March 8, 2012

4 1. Introducton In recent years, many teams from professonal European football leagues have suffered severe fnancal losses. Some teams, most notably perhaps Chelsea FC and Manchester Cty n England, have been taken over by very wealthy new owners, who spent huge amounts of prvate money to strengthen ther teams. Ths subsequently led other teams to overspend on ther budgets n order to compete for the best players n the market. To stop ths rat race and to guarantee the long-term fnancal survval of the clubs, Europe s football governng body UEFA decded to ntroduce the so called Fnancal Far Play Regulatons, whch forces clubs to lve wthn ther means. As of 2015, clubs have to break-even over a three years perod or face excluson from UEFA s prestgous nternatonal compettons, the UEFA Champons League and UEFA Europa League. The am of ths paper s to analyze the long-term consequences on compettve balance caused by the ntroducton of a strct break-even constrant. In secton 2, a classcal model of professonal team sports leagues s employed to calculate seasonal wnnng percentages of clubs. Compettve balance n such a model s typcally solely dependent on the market sze of clubs, a varable summarzng a club s revenue potental. In secton 3, the sngle-perod model s adapted to a mult-perod framework that ntroduces a market sze functon, whch accounts for the emprcal fact that a club s revenue potental s postvely dependent on ts hstorcal success (the glory hunter phenomenon). 1 If a club becomes more successful, t s able to attract more and more spectators, whch ncreases market sze and guarantees even greater success n the future. The model predcts that there s only one long-term steady-state equlbrum of compettve balance, n whch bg clubs totally domnate small clubs and compettve balance s maxmally uneven. Secton 4 concludes. 1 For example, German clubs 1.FC Kaserslautern and Borussa Mönchengladbach orgnate from rather small towns/metropoltan areas, but today have many supporters and thus a hgh market sze, presumably because of the clubs hstorcal success n the 1950s and 1970s respectvely. 2

5 2. The sngle-perod model Ths chapter replcates the basc framework of common sngle-perod team sports models, whch wll later be adapted to the mult-perod model. Typcally a league wth only two clubs ( =1, 2) s consdered (see, e.g., Qurk and Fort 1992, Vrooman 1995, Szymansk 2004, Kesenne 2006). The clubs dffer wth respect to ther potental revenue from sellng match tckets, merchandse, and broadcastng rghts as well as sponsorshps, whch are ndcated by a club s market sze m. In the sngle-perod model the market sze s assumed to be exogenous and cannot be nfluenced by the club. Revenue s also affected by a club s wnnng percentage w, whch has a postve but decreasng margnal effect up untl a certan level of success at whch the club becomes too domnant to keep spectators nterested n the competton and revenue begns to declne (uncertanty of outcome hypothess, (Rottenberg 1956)). In the followng concave revenue functon R, the preference for the uncertanty of outcome s reflected by β, wth1 β 2: such that R (w,m,β)=m w m β w2 (1) R w > 0forw < β 2 R w =0forw = β 2 R w < 0forw > β 2 (2) Perfectly dvsble unts of playng talent are avalable to the clubs on the professonal players labor market at constant margnal costs of c>0(flexble talent supply, see, e.g., Szymansk 2004). A team s wnnng percentage depends both on the number of own playng talents T andalsoonthenumber of playng talents T j of the competng club. The followng smple Tullock contest success functon s assumed: w = T T + T j (3) 3

6 Clubs choose ther number of playng talents under the assumpton of wnmaxmzng behavor and subject to a seasonal budget constrant that does not allow for losses: max w s.t. R ct =0 (4) T Snce the acquston of an addtonal unt of playng talent causes an external effect on the competng club s wnnng percentage, the two clubs fnd themselves n a strategc rent seekng game. Rewrtng (4) yelds the clubs reacton functons: T = m β + m 2cT j + ( ) 2 m m 4cm β + T j β 2c (5) Fgure 1: Reacton functons and compettve balance n Nash equlbrum The Nash equlbrum s found graphcally at the ntersecton of the two reacton functons (see Fgure 1). The rato of the amount of talent unts 4

7 hred by the clubs n equlbrum measures compettve balance, whch s solely dependent on market sze. Snce n equlbrum both clubs spend as much money as possble on playng talent wthout generatng losses, the budget constrants n (4) strctly hold for both clubs and thus club s wnnng percentage can easly be calculated: m m β w = m j m j β (1 w ) w = β (m m j )+m j (6) m + m j Wthout loss of generalty, t s assumed that m + m j = 1. In order to have wnnng percentages rangng between 0 and 1, the followng condtons must hold: β 1 2β 1 m β 2β 1 Snce 1 β 2andm + m j =1,1/3 m 2/3 s suffcent to guarantee a vald soluton wth respect to the wnnng percentages regardless of β. Therefore, let m max =2/3 andm mn =1/3denote the maxmal and mnmal market szes requred for the model to work. If the two clubs are assumed to orgnate from equally bg ctes and market sze s nterpreted as the share of nhabtants nterested n ther local club, m mn represents the amount of uncondtonally loyal supporters, who never lose nterest n ther team, whle m max represents the greatest amount of people that could become nterested n the club. It follows that w max =(β +1)/3 andw mn =(2 β)/3. The model s set up such that the club operatng n the bgger market can generate a hgher revenue than the smaller club at any gven level of wnnng percentage and can subsequently afford more talent unts and thus outperforms the small market team on the playng feld. In ths sense, the model s well-behaved and does not allow for the rather mplausble outcome of the smaller club domnatng the bgger club, whch cannot be ruled out f no addtonal assumptons are made on the clubs revenue functon beyond concavty and club owners objectves (see Fort and Qurk 2004, Kesenne 2006). (7) 5

8 3. The mult-perod model The theoretcal framework from the prevous secton s now adapted to model the long-term development of compettve balance n professonal team sports leagues. An nfnte tme horzon and a dscrete tme scale s assumed, wth each perod representng a sngle league season. Clubs agan only dffer wth respect to market sze, but market sze s no longer exogenous but nstead assumed to be postvely dependent on a club s hstorcal success. Ths dea s motvated by what s known as the nfamous glory hunter phenomenon amongst sports fans: clubs enjoyng a spell of ncreasng success attract spectators who prevously had no strong connecton to the club but are now keen to assocate themselves wth a wnnng team. Obvously ths effect also works n the opposte drecton, so f a club s success declnes, the glory hunters jump shp and market sze decreases. To model the endogenety of market sze, a recursve symmetrc market sze functon s consdered, whch smply assumes market sze of club n season t to be dependent on wnnng percentage n season t 1: m t = m t (w t 1 )wthm + m j =1 (8) Club s revenue R n season t s then gven by: R t [w t,m t (w t 1 ),β]=m t (w t 1 ) )w t mt (w t 1 β w t2 (9) The characterstcs of the revenue functon (9) wth respect to the crtcal level of success that trggers decreasng seasonal revenue are the same as those of the sngle-perod model s revenue functon. In each season perfectly dvsble unts of playng talent are avalable on the players labor market at constant margnal costs c>0. Unts of talent hred n a prevous perod do not persst nto the next perod, thus a club s not constraned n ts decson on the amount of talent unts n season t other than through ts budget. In each perod, clubs are assumed to maxmze wnnng percentage under a seasonal break-even constrant as mposed by new UEFA Fnancal Far Play Regulatons. Note that under these regulatons, clubs cannot use savngs from prevous seasons to balance out an operatng loss n a later season wthout nfrngng the break-even constrant. Thus for clubs maxmzng wnnng percentage t s a strctly domnant strategy to break even by spendng ther entre seasonal revenue on player salares. It follows that wnnng percentages n equlbrum n season t are calculated n the same 6

9 way that wnnng percentages were calculated n the sngle-perod model (6) and compettve balance s solely dependent on market szes n t: w t = β ( ) m t m t j + m t j m t + mt j Assume now a market sze functon wth the followng propertes: (10) dm t dw t 1 d 2 m t dw t 1 d 2 m t dw t 1 m t = m mn m t = m max > 0forw mn 2 > 0forwmn 2 for w t 1 for w t 1 <w t 1 w mn w max <w max <w t 1 < 1/2 d 2 m t 2 =0forwt 1 =1/2 dw t 1 < 0for1/2 <wt 1 <w max (11) In order to get vald equlbrum solutons, market sze at any pont n tme should nether exceed m max nor fall below m mn. For convenence t s assumed that m t = m mn for w t 1 w mn and m t = m max for w t 1 w max. Between w mn and w max market sze monotoncally ncreases. For 1/2 < w t 1 <w max the market sze functon s concave, so the margnal effect on market sze decreases as t becomes ncreasngly dffcult for the club to attract new spectators. From symmetry t follows that m t ( 1)= 1. Fgure llustrates the aforementoned propertes of the market sze functon. 7

10 Fgure 2: Propertes of the market sze functon There are two possble long-term equlbra: and w 1 = w 2 = m 1 = m 2 =1/2 (12) w1 = w max ; m 1 = m max w 2 = w mn,m 2 = m mn (13) From m t ( 1) = 1 t follows that (12) represents a long-term equlbrum. 2 2 Wthout any external shock to ether wnnng percentage or market szes, both clubs wll forever be locked n a perfectly balanced competton. Ths equlbrum s not stable though. Any shock to ether market sze or wnnng percentage wll start a convergence that leads to the steady-state equlbrum represented by (13). The ntuton behnd ths s rather smple. A club becomng more successful n t wll attract more spectators n t +1and therefore enjoy a greater market sze n t + 1. Ths yelds an ncrease n club revenue, allowng the club to afford more talent unts, whch n turn wll lead to a hgher wnnng percentage n t + 1 than prevously n t, ncreasng 8

11 market sze even further n t + 2 and so forth. The growth of the market sze slows down over tme untl the steady-state equlbrum n (13) s reached. The model predcts that bg clubs wll become bgger and bgger over tme, totally domnatng smaller clubs n the long-term equlbrum, n whch compettve balance s maxmally uneven. Fgure 3 llustrates the development of market szes and wnnng percentages over tme. Fgure 4 llustrates the mpact on wnnng percentages and market szes through a sudden break-n of the bgger club s wnnng percentages durng the convergence to the long-term steady-state equlbrum. In the short-term, ths shock leads to a perod of lesser success on the playng feld, but n the long-term the club wll exceeds ts prevous market sze and enjoy greater success. Fgure 3: Market szes and wnnng percentages n the long run 9

12 Fgure 4: External shock to club 1 s wnnng percentage 4. Concluson The object of ths paper was to analyze the long-term consequences on compettve balance n a professonal team sports league wth wn-maxmzng clubs, that follow from the ntroducton of a strct break-even constrant as ntended by UEFA s new Fnancal Far Play Regulatons. The model presented accounts for the emprcal fact, that a club s revenue potental or market sze s postvely dependent on ts hstorcal success, caused by the glory hunter phenomenon: If a club becomes more successful, t s able to attract more and more spectators, whch ncreases the club s market sze and future success, whch n turn ncreases market sze even further. Snce under the break-even constrant small clubs cannot overspend or nvest n a greater market sze for the future, they are unable to stop ths process and a maxmally uneven compettve balance n the long run, where bg clubs totally domnate small clubs, s the resultng outcome. 10

13 References [1] Fort, R., Qurk, J., Owner objectves and compettve balance. Journal of Sports Economcs 5 (1), [2] Kesenne, S., The wn maxmzaton model reconsdered: Flexble talent supply and effcency wages. Journal of Sports Economcs 7 (4), [3] Qurk, J., Fort, R., Pay Drt: The Busness of Professonal Team Sports. Prnceton Unv. Press, Prnceton NJ. [4] Rottenberg, S., The baseball players labor market. Journal of Poltcal Economy 64 (3), [5] Szymansk, S., Professonal team sports are only a game: The walrasan fxed-supply conjecture model, contest-nash equlbrum, and the nvarance prncple. Journal of Sports Economcs 5 (2), [6] Vrooman, J., A general theory of professonal sports leagues. Southern Economc Journal 61 (4),

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