MPRA Munch Personal RePEc Archve A non-parametrc analyss of the effcency of the top European football clubs George Halkos and Nckolaos Tzeremes Unversty of Thessaly, Department of Economcs May 2011 Onlne at https://mpra.ub.un-muenchen.de/31173/ MPRA Paper No. 31173, posted 29. May 2011 14:45 UTC
A non-parametrc analyss of the effcency of the top European football clubs By George E. Halkos and Nckolaos G. Tzeremes Unversty of Thessaly, Department of Economcs, Kora 43, 38333, Volos, Greece Abstract Ths paper analyses how European football clubs current value and debt levels nfluence ther performance. The Smar and Wlson (J Econometrcs, 136: 31 64, 2007) procedure s used to bootstrap the data envelopment analyss DEA scores n order to establsh the nfluence of football clubs current value and debt levels on ther obtaned effcency performances. The results reveal that football clubs current value levels have a negatve nfluence on ther performances, ndcatng that football clubs hgh value doesn t ensure hgher performance. At the same tme, the emprcal evdence suggests that there s no nfluence assocated of football clubs debt to ther effcency levels. Keywords: European football clubs; Data Envelopment Analyss; Truncated regresson; Bootstrappng. JEL classfcaton: C14, C69, L83 Address for Correspondence: Professor George Halkos, Department of Economcs, Unversty of Thessaly, Kora 43, 38333, Volos, Greece. Emal: halkos@econ.uth.gr, http://www.halkos.gr/ Tel.: 0030 24210 74920 FAX : 0030 24210 74701 1
I. INTRODUCTION Several studes have appled effcency analyss on sport teams performances 1. However the economc framework of professonal sportng actvty t s based on the works of Rottenberg (1956), Neale (1964), Jones (1969) and Sloane (1969, 1971, 1976). In addton the frst emprcal evdence n a average producton functon framework was found n the work of Scully (1974) who nvestgated the performance of baseball players. By usng the percentage of matches won n order to model teams output and management, captal and team sprt as nputs Scully s emprcal work was the frst to apply a producton functon n order to provde emprcal evdence. However, the sportng producton process has been modeled by several others n a smlar way (among others Zech, 1981; Atknson et al., 1988; Schofeld, 1988). The applcaton of fronter producton functon n order to measure teams performance has been dated back on the works of Zak et al. (1979), Porter and Scully (1982) and Fzel and D Itr (1996, 1997). In addton over the last two decades several scholars have been applyng parametrc and nonparametrc fronter analyss n order to establsh football teams performance and ther determnants. Dawson et al. (2000), applyng stochastc fronter approach (SFA), measure managers effcency for a panel of managers n Englsh soccer s Premer league usng as output the percentage of matches won and as nputs several player qualty varables, for the tme perod of 1992 to 1998. Haas (2003a) appled a data envelopment analyss (DEA) measurng team effcency of the USA Major League Soccer (MLS). In a DEA settng and for the year 2000, Haas used head coaches and players wages as nputs; and revenues, ponts 1 For a lterature revew on the subject matter see Barros and Garca-del-Barro (2008). 2
awarded and number of spectators as outputs. In addton Haas (2003b) n a smlar DEA settng has performed an effcency analyss for twenty Englsh Premer League clubs for the year 2000-2001. Barros and Leach (2006a, 2006b, 2007) applyng a stochastc Cobb-Douglas producton fronter and DEA measured the performance of football clubs n the Englsh F.A. Premer League for the tme perods 1989-1990 to 2002-2003. They appled a combnaton of sport and fnancal data n order to measure football clubs effcency levels. Frck and Smmons (2008) by applyng SFA on data for German premer soccer league (Bundeslga) showed that manageral compensaton mpact postvely on team success. Smlar to our study, Barros et al. (2010) by applyng Smar and Wlson s (2007) DEA bootstrap procedure analyzed the performance of the Brazlan frst league football clubs. More recently Barros and Garca-del-Barro (2011) measured the effcency of the Spansh football clubs for the seasons 1996 1997 and 2003 2004 by applyng the two-stage procedure (Smar and Wlson 2007). In ther DEA settng they have used operatng cost, total assets and team payroll as nputs, whereas, attendance and other recepts as outputs. In the second stage of ther analyss they regressed the obtaned team effcency levels on several factors usng truncated regresson and tobt model (for comparson reasons) n order to explan Spansh clubs effcency varatons. Our study, smlarly to the ones already presented, by applyng a two-stage DEA bootstrap procedure nvestgates how clubs value and debt levels nfluence ther performances. In contrast to the man research stream, nstead of usng data of a specfc natonal football league, our study uses a sample of the top 25 rchest European football clubs and proposes for the frst tme a composte ndex for measurng output. 3
II. DATA AND METHODOLOGY II.1 Descrpton of varables In our analyss we use a sample of the top European football clubs 2 based on ther current values. All the data are extracted from Forbes database (2011) and concern data recorded for the year 2009. In our DEA formulaton we use one nput and one composte output. The nput used s football clubs revenues (measured n mllons $) and one composte output whch measures football clubs European and domestc trophes. The composte output contans the sum of the number of European champons cups (weghted by 5), UEFA cups/ Euroleague cups (weghted by 4), European cup wnners cups (weghted by 3), Intercontnental cups (weghted by 3) and FIFA Club World cups (weghted by 3). In addton the composte output contans also the sum of the number of domestc champonshps (weghted by 2) and domestc cups (weghted by 1). Both the number of the weghted domestc champons and domestc cups (ncludes all domestc cups,.e. supercups, league cups, natonal cups... etc) are agan weghted by FIFA world rankng score (FIFA, 2010). Ths extra weght has been added n order to reflect the dfferent dffculty levels of obtanng a domestc cup and/ or champonshp among the dfferent European leagues 3. We also assume that club revenues are used from the clubs n order to buy the best (n term of football qualty) possble managers 2 Nne football clubs are from the Englsh Premer League, sx from German league, four from Italan league, two from Spansh league, two from French league and two from Scottsh league.the 25 European football club n a descendng order based on ther current value are: Manchester Unted FC, Real Madrd FC, Arsenal FC, Bayern Munch FC, Lverpool FC, AC Mlan FC, Barcelona FC, Chelsea FC, Juventus FC, Schalke 04 FC, Tottenham Hotspur FC, Olympque Lyonnas FC, AS Roma FC, Internazonale Mlan FC, Hamburg SV FC, Borussa Dortmund FC, Manchester Cty FC, Werder Bremen FC, Newcastle Unted FC, VfB Stuttgart FC, Aston Vlla FC, Olympque Marselle FC Celtc FC, Everton FC and Glasgow Rangers FC. 3 We assume that t s not of the same dffculty to obtan a domestc champonshp or cup between the Englsh, the Scottsh, the Spansh, the German and the Italan football league. All the weghts used n order to for the composte output to be constructed are subjectve and can be subject to crtcsm. 4
and players whch can lead to team success (based on world, European and domestc champonshps and cups). Smlarly, a recent study for the Englsh Premer League suggests that revenues are related to clubs success (Carmchael et al., 2010). Then by applyng a second-stage analyss we examne n what way European football clubs current value and debt levels (measured n mllons of $) affect ther obtaned effcency levels. Table 1 presents the descrptve statstcs of the varables used n our study. As can be realzed table 1 reports several varatons of the varables used ndcated by the hgh standard devaton values. Fnally, n our DEA settng we assume an output orentaton suggestng by how much football clubs can ncrease ther outputs whle keepng the level of nputs fxed. Table 1: Descrptve statstcs of the varables used External Varables Input Current Value($ml) Debt($ml) Revenue ($ml) Mean 597.080 218.238 274.720 Std 443.374 338.197 128.008 Mn 194.000 0.002 128.000 Max 1870.000 1284.000 576.000 Output components Intercontnental Cup FIFA Club World Cup Domestc Champonshps Mean 0.56 0.08 13.80 Std 1.00 0.28 12.70 Mn 0.00 0.00 2.00 Max 3.00 1.00 51.00 Output components European Champons Cups Uefa Cups/Euroleague Cups European Cup Wnners Cup Mean 1.600 0.840 0.800 Std 2.432 1.143 0.913 Mn 0.000 0.000 0.000 Max 9.000 3.000 4.000 Output components Domestc Cups FFA country Rankng Composte Output Mean 13.48 7.04 27.29 Std 13.04 8.88 33.82 Mn 2.00 1.00 1.46 Max 57.00 35.00 142.00 5
II.2 Effcency measurement Based on the work by Koopmans (1951) and Debreu (1951) the producton set Ψ constrants the producton process and s the set of physcally attanable ponts ( x, y) : Ψ = N + M, R+ x can produce y (1), ( x y) where N x R+ s the nput vector and M y R+ s the output vector. Then the output orented effcency boundary Y( x) s defned for a gven as: { } ( ) ( ) ( ) N x R + Y x = y y Y x, λy Y x, λ>1, (2) and the Debreu-Farrell output measure of effcency for a producton unt can be defned as: { } ( xy, ) sup ( x, y) λ = λ λ Ψ (3). In equaton (3) by constructon ( ) acheved when λ ( ) λ xy, 1 and techncal effcency s xy, = 1. As suggested by several authors (Førsund and Sarafoglou, 2002; Førsund et al., 2009), Hoffman s (1957) dscusson regardng Farrell s (1957) paper was the frst to ndcate that lnear programmng can be used n order to fnd the fronter and estmate effcency scores, but only for the sngle output case. Later, Boles (1967, 1971) developed the formal lnear programmng problem wth multple 6
outputs dentcal to the constant returns to scale (CRS) model n Charnes et al. (1978) who named the technque as data envelopment analyss (DEA) 4. Followng Zelenyuk and Zheka (2006, p.149) we apply the assumpton of CRS due to the fact that t enables to obtan greater dscrmnatve power, whch n turn would result n larger varaton of the regressand. In addton, snce we examne the 25 European football clubs wth the hghest values, we are not expectng great dfferences among ther szes. Ths formulaton can be expressed as: CRS N+ M {( xy, ) y γ y; x γx for ( γ1,..., γn) Ψ = R = 1 = 1 such that γ 0, = 1,..., n n } n (4). whch then can be computed by solvng the followng lnear program: λ CRS n { λ λy γ y x γ x ( γ γ ) = sup ; for,..., 1 n = 1 = 1 such that γ 0, = 1,..., n n } (5). II.3 A bootstrap approach for bas correcton of the effcency estmator Smar and Wlson (1998, 2000, 2008) suggest that DEA estmators were shown to be based by constructon. They ntroduced an approach based on bootstrap technques (Efron, 1979) to correct and estmate the bas of the DEA effcency ndcators 5. The bootstrap bas estmate for the orgnal DEA estmator λcrs ( x, y) can be calculated as: 4 Later Banker et al. (1984) used convex hull of Ψ FDH (Derpns et al., 1984) to estmate Ψ and thus n to allow for varable returns to scale (VRS) addng the constrant γ = 1 n equatons (4) and (5). 5 The essence of bootstrappng effcency scores has been hghlghted by several authors. For further applcatons of the bootstrap technque on DEA effcency scores see also Smar and Wlson (2002), Zelenyuk and Zheka (2006), Smar and Zelenyuk (2007) and Halkos and Tzeremes (2010). = 1 7
B 1 * B CRS (, ) CRS, b (, ) CRS (, ) BIAS λ x y = B λ x y λ x y (6). b= 1 Furthermore, * CRS b λ, ( x, y) are the bootstrap values and B s the number of bootstrap replcatons. Then a based corrected estmator of λ ( x, y) can be calculated as: λcrs ( xy, ) = λcrs ( xy, ) BIASB λcrs ( xy, ) B 1 * 2 λcrs ( x, y) B λ CRS, b ( x, y) = b= 1 (7). II.4 A two-stage analyss usng a double bootstrap procedure Followng Smar and Wlson (2007) n order to account for envronmental varables ( z ) on effcency scores ( λ ) a double bootstrap procedure must be used n a second stage regresson analyss n order to produce vald estmates. Let us consder the followng model: λ = z β + ε (8), where β s a vector of parameters an ε s the statstcal nose. Accordng to Smar and Wlson (2007) when usng a conventonal method of analyss lke the Ordnarly Least Squares (OLS) method two are the man problems that lead to nvald estmates. Frstly, when usng small samples the basc assumpton that z s ndependent fromε s volated due to the hgh correlaton of nputs/outputs used and the explanatory varables. Secondly, the DEA effcency scores are expected to be correlated due to the fact that the effcency levels of one football club s a product of the data of the other clubs of the same data set. Therefore Smar and Wlson (2007, p.42-43) proposed a double bootstrap procedure (Algorthm #2) n order to avod the 8
dependency problems and produce vald estmates of the second-stage regresson analyss. Synoptcally the algorthm contans the followng seven steps: 1. Usng the orgnal data, we compute ( ) equaton (5). λ = λ x, y, = 1,..., n, by applyng 2. Then the maxmum lkelhood estmates β and σ ε from the left normal > truncated regresson of λ on z (by usng only λ 1 ) are appled. 3. For each football club = 1,... n, we repeat the next four steps (a-d) L1 tmes n order to obtan λ * b L1 b= 1, = 1,..., n: a. For = 1,... n, we draw * ε from N 0, 1 β ' z. σ ε wth left truncaton at b. Then we compute λ * * β ε = ' z +, = 1,..., n. c. We set * * * λ λ x = x, y = y / for all = 1,..., n. d. Then we compute * * * λ = λ x, y Ψ, = 1,..., n, where Ψ s obtaned by replacng (, ) * * x y by (, ) x y. 4. We compute the bas corrected estmator λ usng the bootstrap estmates n step 3 and the orgnal estmate λ. 9
5. Then we estmate by maxmum lkelhood the truncated regresson of λ on z n order to get the β, σ. 6. For each football club = 1,... n, we repeat the next three steps (a-c) L2 tmes n order to obtan L2 * * β, σ ε : b b= 1 a. For = 1,... n, we draw ** ε from N 0, σ wth left truncaton at 1 β ' z. b. Then we compute λ ** ** β ε = ' z +, = 1,..., n. c. Then we estmate by maxmum lkelhood the truncated regresson of ** λ on z n order to get the β *, σ*. 7. Fnally usng the bootstrap values from step 6 and the orgnal estmates of β, σ we construct confdence ntervals for β. III. EMPIRICAL RESULTS AND CONCLUSIONS Table 2 presents the results obtaned from the effcency analyss assumng the CRS assumpton. Lookng at the descrptve statstcs we realze that there s a consstency wth prevous research on European football leagues (Barros and Leach 2006a, 2006b, 2007; Barros et al. 2010; Barros and Garca-del-Barro 2011) ndcated wth sgnfcant dfferences of the orgnal (DEA) and the based corrected (BC) effcency scores obtaned. The standard devaton values are 0.34 for the orgnal 10
estmates (DEA) and 0.35 for the based corrected (BC). The results ndcate two football clubs (Glasgow Rangers FC and Real Madrd FC) that are reported to be effcent (.e. wth effcency score equal to 1) under the orgnal effcency estmates. In addton when lookng at the based corrected results the fve European clubs wth the hghest effcency scores are reported to be: Glasgow Rangers FC, Juventus FC, AC Mlan FC, Celtc FC and Aston Vlla FC. Whereas the fve European clubs wth the lowest effcency levels are reported to be Manchester Unted FC, Arsenal FC, AS Roma FC, Olympque Lyonnas FC and Chelsea FC. In addton the largest bound dfferences of the based corrected effcency scores are reported for Real Madrd FC, Barcelona FC, Olympque Lyonnas FC, Bayern Munch FC and for Manchester Unted FC. Table 2: Effcency scores under the CRS assumpton a/a Football Clubs DEA BC BIAS STD LB UB Bound dfference 1 Manchester Unted FC 1.681 1.773-0.091 0.005 1.950 1.688 0.262 2 Real Madrd FC 1.000 1.209-0.209 0.016 1.466 1.013 0.454 3 Arsenal FC 1.752 1.814-0.062 0.002 1.923 1.760 0.163 4 Bayern Munch FC 1.350 1.449-0.099 0.005 1.621 1.358 0.263 5 Lverpool FC 1.141 1.198-0.057 0.002 1.315 1.145 0.171 6 AC Mlan FC 1.051 1.112-0.061 0.002 1.227 1.055 0.171 7 Barcelona FC 1.051 1.186-0.135 0.010 1.415 1.056 0.359 8 Chelsea FC 2.380 2.457-0.077 0.003 2.586 2.388 0.198 9 Juventus FC 1.053 1.096-0.044 0.001 1.185 1.057 0.129 10 Schalke 04 FC 1.511 1.560-0.049 0.001 1.644 1.516 0.128 11 Tottenham Hotspur FC 1.342 1.384-0.042 0.001 1.455 1.347 0.108 12 Olympque Lyonnas FC 1.914 2.040-0.126 0.007 2.212 1.919 0.293 13 AS Roma FC 1.902 1.971-0.069 0.002 2.093 1.909 0.184 14 Internazonale Mlan FC 1.097 1.142-0.045 0.001 1.234 1.101 0.133 15 Hamburg SV FC 1.269 1.309-0.040 0.001 1.379 1.273 0.106 16 Borussa Dortmund FC 1.130 1.166-0.036 0.001 1.226 1.134 0.092 17 Manchester Cty FC 1.281 1.374-0.092 0.003 1.483 1.289 0.195 18 Werder Bremen FC 1.279 1.331-0.052 0.002 1.422 1.282 0.140 19 Newcastle Unted FC 1.429 1.486-0.058 0.002 1.588 1.432 0.156 20 VfB Stuttgart FC 1.375 1.471-0.096 0.003 1.591 1.381 0.210 21 Aston Vlla FC 1.092 1.137-0.046 0.001 1.216 1.095 0.121 22 Olympque Marselle FC 1.461 1.523-0.063 0.002 1.629 1.465 0.164 23 Celtc FC 1.079 1.133-0.054 0.001 1.214 1.085 0.130 24 Everton FC 1.115 1.168-0.052 0.001 1.251 1.120 0.131 25 Glasgow Rangers FC 1.000 1.075-0.075 0.002 1.158 1.011 0.147 11
Mean 1.349 1.423-0.073 0.003 1.539 1.355 0.184 Std 0.346 0.350 0.039 0.003 0.364 0.347 0.085 Mn 1.000 1.075-0.209 0.001 1.158 1.011 0.092 Max 2.380 2.457-0.036 0.016 2.586 2.388 0.454 Furthermore, as explaned earler we apply the approach of Smar and Wlson (2007) n an estmated specfcaton for the regresson taken the form of: λ = β + β Current Value + β Debt + ε (9) 0 1 2 where λ represents the DEA model effcency scores presented n table 2. In addton Current Value refers to the football clubs current value levels measured n mllons of dollars, whereas Dept refers to football clubs debt levels measured also n mllons of dollars. Followng Smar and Wlson (2007) we employed a bootstrap algorthm of 2000 replcatons n order to construct 95% confdence ntervals. The results of the truncated bootstrapped second-stage regresson are presented n table 3. It can been seen that the constant term and the football clubs Current Value levels are statstcally sgnfcant, whle football clubs Debt levels does not seem to explan ther effcency varatons. In addton we can observe a negatve sgn on the Current Value coeffcent ndcatng that the hgher football clubs value doesn t necessary results on hgher effcency levels. Table 3: Truncated bootstrapped second-stage regresson results Bas-adjusted coeffcents (2000 bootstrap replcatons) Varables Coeffcent Std. Err. 95% Bootstrap confdence nterval Lower Upper Constant 1.62892* 0.08723 1.45795 1.79989 Current Value -0.00052** 0.00020-0.00091-0.00012 Debt -0.00031 0.00029-0.00088 0.00026 Varance 0.19362* 0.03670 1.45795 1.79989 Statstcally sgnfcant at *: 1%, **: 5% Fnally, n terms of polcy mplcatons t appears that when comparng the top European football clubs, ther determnants of hgher effcency (n terms of the 12
number of domestc and European club trophes) are not based on ther hgher revenue and value levels. The determnstc nature of DEA methodology proved to be a vtal tool for showng that money alone does not ensure football clubs success. Other factors lke manageral effcency (Fzel and D Itr 1996, 1997; Dawson et al. 2000) and team sprt (Scully 1974) may be more mportant when comparng the top European football clubs wth the hghest value. In addton referrng back to our prmary DEA formulaton t appears that the characterstcs of the football clubs presdents are also crucal determnants of the clubs success. Most of the tmes the presdent of a club s the prmary decson maker who s responsble for the allocaton of resources (.e. revenues) and responsble for the rght nvestments (.e. on the rght players and managers) whch n turn can result on football clubs success. 13
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