Efficiency measurement of professional football clubs: a non-parametric approach. Lidiya Ivanovna Kulikova, Anna Valeryevna Goshunova

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1 Effcenc meaement of pofeonal football clb: a non-paametc appoach Lda Ivanovna Klkova, Anna Valeevna Gohnova Inttte of Fnance and Economc, Kazan (Volga Regon) Fedeal Unvet. Btleov t., 4, Kazan, 4212, Ran Fedeaton Abtact. In th atcle the effcenc of pofeonal football clb fom Atala, Bazl, England, Fance, Geman, Ital, Netheland, Potgal, Ra, Scotland and Span wa nvetgated ng data envelopment anal (DEA). In ode to ae mpact of accontng polce on plae egtaton on football clb effcenc, football clb not ecognzng pofeonal plae egtaton a aet wee added n data. The elt of anal how that captalzaton of pchaed plae egtaton nflence effcenc of football clb, bt t n't a ccal facto. Anothe mpotant facto affectng on effcenc of football clb ae ze of clb and t captal tcte. [Klkova L.I., Gohnova A.V. Effcenc meaement of pofeonal football clb: a non-paametc appoach. Lfe Sc J 214;11(11): ] (ISSN: ).. 27 Kewod. Effcenc; Football clb; Fnancal effcenc; Spot effcenc; Data Envelopment Anal (DEA); Regeon anal. Intodcton A lot of tde ae devoted to the anal of pofeonal football clb effcenc [1]. Vao eeache dffeentl evalate effcenc of clb fom economc [2-13] and pot [6-15] pont of vew. In o eeach we contne tadton of evalatng football clb effcenc b ng non-paametc method of anal, bt at the ft tme we take nto accont football clb whch don t ecognze pofeonal plae egtaton a aet. Thee clb ae fom Ra and Atala. It done n ode to ae whethe captalzaton of pchaed plae egtaton can affect on effcenc of football clb. Stcte of wok nclde ntodcton, methodolog, data, elt and conclon. Methodolog. Geneall all vaet of method ed to analze effcenc of football clb can be dvded nto two lage gop: - Paametc method; - Non-paametc method. Paametc method ae a gop of method, whch e tool of detemntc coelaton and egeon anal. Thee method nclde lnea and non-lnea egeon model, mple and mltple egeon, the Cobb-Dogla fncton etc. Th appoach can dentf and defne tpe of elatonhp between the tded vaable; t alo allow dentfng the fnctonal dependence. Non-paametc method ae foced pmal on the oveall aement of the effcenc. Th aement baed on the anal of a et of npt and otpt whch chaacteze the actvt of the object nde evew. In th cae, the etablhment of a fnctonal connecton not ctcal, becae pefomance evalaton made ng weghted ndce and weght fo all vaable. Fo example, tpcal non-paametc method ae tochatc fonte model and DEA. It hold be noted that the mot popla method of anal of clb effcenc DEA. The dea of DEA belong to Faell [16]. He ha ted to meae the effectvene of one nt of fnal podct n example of one npt facto and one otpt paamete. Faell appled th model to meae the pefomance of agclte n the USA compaed to othe conte. Bt he cold not fnd a wa to combne all vao npt and otpt nto a ngle vtal npt and otpt epectvel [16]. Ft DEA-model developed b Chane, Coope and Rhode wa baed on the method of Faell fo meang the effectvene of each decon makng nt (DMU) wth the fncton of podcton capact, o podcton fncton. Accodng to Chane, Coope and Rhode 1% effcenc detemned a follow: - None of otpt can be enhanced wthot nceang of one o moe npt o edcng othe otpt; - None of npt can be edced wthot edcng one o moe otpt o nceang othe npt. Pefomance meaement n the model of Chane, Coope and Rhode ealzed on the bae of optmal weghted ato between patcpatng otpt and npt. Th method detemne etmaton of paamete n ch a wa that the obeved DMU le on cale fom (lowet effcenc) to 1 (maxmm effcenc) and take effcenc vale e o, a hgh a poble n gven 117

2 ato of npt and otpt of all obeved nt. Fomall, th tak cont of olvng the followng maxmzaton poblem [16]: e j j j1 1 bject to: j1 1 j m jm 1 max! ; m = 1,2,, n, j v ; j = 1,2,..., ; = 1,2,..., whee, ae amont of npt and otpt of the DMUj; and ae the weght gven to otpt and npt. Th, DEA gve an anwe to the qeton whethe analzed bne nt effectve o not and how mch t cent effcenc dffe fom the deal. At the ame tme DEA pont ot oce of neffcenc, whch lead to the two geneal wa of mpovement of cent effcenc level - b mpovng neffcent wok of bne nt (pe techncal effcenc) o b elmnatng nfavoable condton (cale effect). Howeve, DEA method cannot dentf and qantf the mpact of facto nvolved n calclaton of effcenc mak. Accodng to contant etn to cale otpt changng n the ame popoton a npt. Changng npt on condton of vaable etn to cale can elt n dpopotonate vaaton of otpt. Th defnton ha an mpact on the effcenc vale - moe bnee ma be ecognzed a effectve on condton of vaable etn of cale. Mathematcal epeentaton of vaable cale effect can be made b addton of new vaable o to the ntal fncton of effcenc model (the eqaton 2) [16]: e j j j1 bject to: 1 max! cale; j1 j 1 jm m 1 ; m = 1,2,, n j, v ; j = 1,2,..., ; = 1,2,..., Whle: If If If deceang etn to nceang etn to cale; contant etn to cale. Cetanl, etablhment of fom whch bette decbe ealt ha an mpact on the aement of effcenc. In contat to model wth contant etn to cale, acceptance of vaable cale allow to etmate both geneal effcenc of DMU and effcenc of t decon, whle dffeence n eoce bae ae netalzed. Data. Data wa collected fom fnancal epot of football clb fo 28 ea and football tattc evew. The ample fo the nvetgaton compe 51 pofeonal football clb fom Atala, Bazl, England, Fance, Geman, Ital, Netheland, Potgal, Ra, Scotland and Span. Geneall, eeache conde effcenc of football clb fom dffeent pont of vew. In centfc lteate two appoache ae alead developed to td effcenc of pofeonal football clb [1]: - Evalaton of economc effcenc; - Aement of pot effcenc. The ablt to geneate ncome a a feate of clb effectve wok wa analzed n wok of Agletta et al., 21 [2]; Bao et al., 211 [3]; Bao and Gaca-del-Bao, 28 [4]; Camchael et al., 211 [8]; Foke, 25 [5]; Gzman and Moow, 27 [9]; Haa, 23 [1]; Jadn, 29 [11]; Ken and Smth, 23 [12]; McNamaa et al., 211 [13]. In tem of pot pefomance the bject of td, a a le, condeed a the ndcato of pla pefomance - the nmbe of pont fo the eaon, goal dffeence, goal coed, the nmbe of tophe won n the ntenatonal tonament, etc. The mot emakable centfc wok belong to Ba and McKeatng, 29 [6]; Bao and Dov, 29 [7]; Fck and Smmon, 27 [14]; Gaca- Sanchez, 27 [15]; Gzman and Moow,

3 [9]; Haa, 23[1]; Jadn, 29 [11]; Ken and Smth, 23[12]; McNamaa et al., 211 [13]. In o eeach we conde both tpe of effcenc. We ppoe jont aement of football clb effcenc fom fnancal and pot pont of vew wll allow to etmate geneal effcenc of clb and alo t ablt to each optmm elt both n bne and on feld. Two otpt wee ed to bld effcenc coe: - Tnove whch eflect fnancal effcenc of football clb; - Rank of clb n the natonal champonhp whch chaacteze qalt of clb team, effcenc of t pot actvt. Seveal npt wee ed: Total cot; Intangble aet (plae egtaton); Boowed captal; Pchae of plae egtaton; Peonnel cot; Aveage nmbe of plang taff; Nmbe of pont coed n natonal champonhp fo the eaon 27/28. We ppoe that ndcato of total expene and boowed captal have mpact on effcenc of football clb a bne nt whle ntangble aet (plae egtaton), pchae of plae egtaton and peonnel cot pomote achevement of hgh pot elt. Nmbe of pont coed n natonal champonhp fo a pot eaon dectl eflect pot effcenc becae t a tandad wa of clb cce meaement n natonal champonhp whch nflence on dtbton of pze-wnnng ncome. Aveage nmbe of plang taff ed n ode to take n accont clb' wellbeng on whch depend the oppotnt to contan a long bench. Decptve tattc of all vaable ae gven n table 1. Fg. 1. Dependence of Tnove and Rank on Intangble aet (plae egtaton) Fg. 2. Dependence of Tnove and Rank on Pont Table 1. Data decptve tattc (nmbe of obevaton 51) Fg. 3. Dependence of Tnove and Rank on Boowed captal Fo the ppoe of DEA-model detemnaton we ed gaphcal anal whch howed that otpt Tnove and Rank have dpopotonate dependence on npt Intangble aet (plae egtaton), Boowed captal, Pont etc. (Fg. 1, 2 and 3). Fom fge 1, 2 and 3 we can ee that n all cae vaaton of npt change vale of otpt n dpopotonate ato. Th, fo the ppoe of DEA we wll el on the otptoented DEA-model wth vaable etn to cale. Relt. A a elt of calclaton we have got effcenc etmate fo 51 football clb of Aa, Ameca and Eope. Relt of calclaton ae povded n Table

4 Table 2. DEA effcenc elt Table 3. Football clb effcenc coe In otpt-oented model ppoe of optmzaton maxmzaton of otpt wthot changng et of npt. Decompoton of geneal effcenc on pe techncal effcenc and effcenc dependng on the ze of cale allow to fnd ot neffcenc oce: whethe the neffcenc wa caed b neffcent wok of DMU (PTE) o nfavoable condton (SE), o both eaon togethe [17]. Table 3 how football clb whch have maxmm coe both n geneal effcenc and t component pe techncal effcenc and cale effcenc. On the bae of elt hown n table 2 we can make a conclon that DEA-effectve clb e both accontng polce a captalzaton of pchaed plae egtaton a ntangble aet and wtng off to the cent expene. Howeve mot of effectve clb pefe accontng polc on captalzaton. Theefoe, ecognton of plae egtaton a epaate aet nflence effcenc of football clb, bt t n't a ccal facto. Abolte effcenc of football clb Manchete Unted (England), Poto (Potgal) and Celtc (Scotland) caed b the hgh pot pefomance dng the eaon 27/28 at the end of whch the became champon of the conte. Fthemoe, addtonal calclaton how that thee clb have the maxmm hae n total tnove wthn cont ample. Th, FC Manchete Unted ha 16,42% of total tnove of all 2 Englh clb nclded n ample. The Scotth FC Celtc epeent moe than 37% of total tnove of tded Scotth clb. Th, thee clb ae effectve both fom pot and fnancal pont of vew. The Scotth FC Abedeen wa not fa fom FC Celtc, champon of the Scotth Peme leage of 28, occpng the foth place n natonal champonhp. The clb demontated hgh fnancal elt, havng cloed ea wth net poft. Moeove, etn on ale (ROS) n FC Abedeen wa 8,6% that wa almot 3% hghe, than n FC Celtc at the ame peod. Abolte DEA-effcenc of othe clb ma be alo logcall explaned. Depte the low ncome and low poton n the natonal champonhp, thee clb demontate good elt on condton of lmted eoce bae. Th, the Ran FC Chenomoet ha the mallet amont of total aet among eeached clb bt t acheved a hgh etn on aet (ROA) at the end of 28 (table 3). In patcla, n tem of etn on eqt (ROE) Chenomoet occpe econd place among football clb nde evew. Smlal, football clb fom Atala Pot Adelade, Eendon and Hawthon wee able to geneate poft n 28 wthot bg aet. In 12

5 patcla, FC Pot Adelade anked thd accodng to etn on aet (ROA) and the twelfth accodng to etn to ale (ROS) among tded clb. Moeove, FC Hawthon made geat cce n tem of pot effcenc b takng econd place n the natonal champonhp (table 4). Table 4. Fnancal coeffcent of football clb Effcenc of Scotth clb Falkk and Invene CT can be explaned b the fact that depte the abence of net poft n 28 the ae the onl clb n Scotland, whch wee able to povde 1% of eqt wthot boowed captal. Th, poeng mall aet fll eced b owne eqt, thee clb howed hgh effcenc. Scotth FC St Men alo ha hgh concentaton of eqt (98,56%). Depte the low pot coe clb cloed 28 ea wth hgh ate of poftablt (ROE, ROA, and ROS). Unfotnatel, abolte effcenc of the Atalan FC Melbone doen t have logcal explanaton. Th clb took lat place n the tandng of Atalan champonhp of 28, wa npoftable, wth hgh concentaton of boowed captal. Th, DEA-effcenc of th clb can be condeed a a calclaton eo. Conclon. Smmng p the elt of o eeach we wold lke to pont ot eveal moment. Abolte effcenc fo football clb athe ae phenomenon. Among 51 tded clb onl 12 clb ae effectve both n tem of pe techncal effcenc and cale effcenc. Among them thee ae wold known football clb lke Manchete Unted (England), Poto (Potgal) and Celtc (Scotland), whch ae the mot ccefl clb n fnancal and potng tem. Howeve, o eeach how that abolte effcenc not pvlege of the football gant. The elt of anal how that DEAeffectve clb e both accontng polce a captalzaton of pchaed plae egtaton a ntangble aet and wtng off to the cent expene. Howeve mot of effectve clb pefe accontng polc on captalzaton. Theefoe, ecognton of plae egtaton a epaate aet nflence effcenc of football clb, bt t n't a ccal facto. Effcenc of clb, eekng to maxmze evene and ank n the natonal champonhp, to a lage extent dven b the ze of clb. Man bg football clb whch take leadng poton n the natonal champonhp ae economcall neffcent becae of too low etn on lage nvetment. Fom th pont of vew mall clb have gnfcant advantage. Fo example, Ran and Atalan clb. Anothe mpotant facto of effcenc captal tcte of football clb. In patcla, the hgh concentaton of eqt, ndependence fom extenal fndng contbted to the effcenc of Scotth clb, depte of the low poton n the natonal tandng and lack of ncome. Coepondng Atho: D. Klkova, Inttte of Fnance and Economc. Kazan (Volga Regon) Fedeal Unvet. Btleov t., 4, Kazan, 4212, Ran Fedeaton. Refeence 1. Klkova, L.I. and A.V. Gohnova, 213. Meang effcenc of pofeonal football clb n contempoa eeache. Wold Appled Scence Jonal, 25(2). Date Vew Agletta, M., W. Andeff and B. Dt, 21. Floatng Eopean football clb n the tock maket. EconomX Wokng Pape, 24. Date Vew economx.f/pdf/dt/21/wp_ecox_21-24.pdf. 3. Bao, C. P., A.G. Aaf and A.F. de Aajo J., 211. Cot pefomance of Bazlan occe clb: A Baean vang effcenc dtbton model. Economc Modellng, 28(6): Bao, C.P. and P. Gaca-del-Bao, 28. Effcenc Meaement of the Englh Football Peme Leage wth a Random Fonte Model. Economc Modellng, 25(5): Foke, J., 25. Dcon of Accontng, Valaton and Daton of Football Plae Contact. Jonal of Bne Fnance and Accontng, 32(3-4): Ba, D.G. and C. McKeatng, 29. The Beneft of Fnancal Maket: A Cae Std of Eopean Football Clb. The Inttte fo Intenatonal Integaton Stde Dcon Pape See. Date Vew dp283.pdf. 121

6 7. Bao, C.P. and J. Dov, 29. Compaatve anal of football effcenc among two mall Eopean conte: Potgal and Geece. Intenatonal Jonal of Spot Management and Maketng, 6(2): Camchael, F., I. McHale and T. Denn, 211. Mantanng maket poton: team pefomance, evene and wage expendte n the Englh peme leage. Blletn of Economc Reeach, 63 (4): Gzmán, I. and S. Moow, 27. Meang effcenc and podctvt n pofeonal football team: evdence fom the Englh Peme Leage. Cental Eopean Jonal of Opeaton Reeach, 15 (4): Haa, D.J., 23. Podctve effcenc of Englh football team-a data envelopment anal appoach. Manageal and Decon Economc, 24(5): Jadn, M., 29. Effcenc of Fench football clb and t dnamc. Mnch Peonal RePEc Achve. Date Vew mpa.b.n-menchen.de/ Ken, M. and B. Sümth, 23. Manageal Effenc n Geman Top Leage Socce. Mnch Dcon Pape, 3. Date Vew epb.b.n-menchen.de/5/. 13. McNamaa, P., S. Peck and A. Saon, 211. Competng Bne Model, Vale Ceaton and Appopaton n Englh Football. Long Range Plannng. Date Vew dx.do.og/1.116/j.lp Fck, B. and R. Smmon, 27. The Impact of Manageal Qalt on Oganzatonal Pefomance: Evdence fom Geman Socce. Wokng Pape See, 7-8: Gacía-Sánchez, I.M., 27. Effcenc and effectvene of Spanh football team: a thee-tage-dea appoach. Cental Eopean Jonal of Opeaton Reeach, 15(1): Lta, A. and T. Babéceva, 23. Data envelopment anal (DEA) Shell data anal (DEA) - a moden technqe fo detemnng the effcenc of podcton. Inttte of Agcltal Development n Cental and Eaten Eope, 5. Date Vew hdl.handle.net/1419/ Coell, T., A Gde to Deap Veon 2.1: a Data Envelopment Anal. CEPA Wokng Pape 8/96: /27/