Productivity and Competitiveness: The Case of Football Teams Playing in the UEFA Champions League

Transcription

1 Ahens Journal of Spors March 2016 Producvy and Compeveness: The Case of Fooball Teams Playng n he UEFA Champons League By Manuel Espa-Escuer Luca Isabel Garca-Cebran The purpose of hs sudy s o evaluae he compeve suaon of he UEFA Champons League n relaon o oher eneranmen alernaves. As ools of analyss, Malmqus ndces for he fooball eams ha have parcpaed n he UEFA Champons League among he years wll be calculaed. The Malmqus ndex measures he change n producvy whereas he effcency raos used for he calculaon of he former were found by applyng a Daa Envelopmen Analyss (DEA). The relaonshp beween producvy and compeveness n an economc secor s as follows: an ncrease n producvy allows he remuneraon of he facors o be ncreased whou havng o rase he prce of he produc offered. The UEFA Champons League may see s compeveness hreaened n relaon o oher eneranmen alernaves, because parcpang eams do no show a clear ncrease n producvy. Keywords: Daa envelopmen analyss, Fooball, Malmqus, Producvy. Inroducon In hs sudy we calculae and analyze he changes n producvy experenced by fooball eams parcpang n he UEFA Champons League from The heorecal framework ha has been adoped and whch jusfes hs sudy s he managemen heory. Accordng o hs heory, he sgnfcance of an organzaon s producvy rao ranscends he mere producve funcon and has sraegc mplcaons. I ndcaes he percenage by whch he remuneraon of he facors of producon can be ncreased, whou he need of ncreasng he prce of he goods or servces o he consumers and herefore, whou alerng he profably of he organzaon or s compeveness whn s secor. In prevous sudes, Blass (1992) and Mazur (1994) have suded he producvy of he eam members of spors clubs o relae o her salares; however, he approach of hs sudy dffers n wo aspecs. Frs, he producvy rao used s he Malmqus ndex, whch ncorporaes nformaon on all of he frm s producve resources n s calculaon and herefore, may be consdered an ndex of oal facor Professor, Unversy of Zaragoza, Span. Lecurer, Unversy of Zaragoza, Span. 57

2 Vol. 3, No. 1 Espa-Escuer e al.: Producvy and Compeveness... producvy whch overcomes he dffcules of he nerpreaon of paral ndexes. Second, hs sudy evaluaes he producvy of he fooball eams ha have parcpaed n he UEFA Champons League durng he perod defned by he sudy for he purpose of evaluang how compeve hey are n relaon o her compeors, whch n broad erms would be oher eneranmen opons. Ths las saemen requres furher developmen, snce fooball clubs have o deal wh spors rvalry and spor compeon whch should no be confused wh compeon n he economc sense. Boh he compeors and he objecves of he fooball clubs are dfferen dependng on wheher he eams are consdered ndvdually or n he conex of he ournamen n whch hey are nvolved. From an ndvdual pon of vew, a eam faces a rval n each game plays wh he objecve of defeang he opponen and by accumulang vcores, wnnng he ournamen n queson. On he oher hand, each compeon (such as he UEFA Champons League, World Cup and he Naonal Leagues) has a governng board whose nvolvemen goes beyond merely esablshng he rules of he game, snce can nervene n negoaons regardng, for nsance, he schedulng of he maches or gamblng. Therefore, srcly from a spors perspecve, each ndvdual eam employs s resources and uses he accs has developed o compee agans s rvals n he leagues and ournamens n whch he eam parcpaes. A he same me, each spor champonshp can be consdered an organzaon whose governng boards ac and represen all parcpang eams as a whole, as hey are n charge of negoang aspecs ha are of common neres o all of he clubs. These negoaons wll have repercussons on he revenues ha each club receves, gven ha hey nclude aspecs such as elevson broadcas rghs. However, hese revenues wll also depend on he produc/servce ha he eams offer, whch n hs case s he spors even self. Demand wll be generaed f he poenal consumers receve suffcen uly o mer he prce hey mus pay o aend he game. Fooball, as a specacle for specaors, mus compee wh all hose secors relaed wh eneranmen, whch may nclude oher sporng evens or alernaves furher removed from a produc/servce pon of vew, such as he cnema or he heaer. Ths s where he consderaon of producvy can conrbue o mprovng he compeveness, n he economc sense, of he fooball eams. Only ncreases n he producvy of he facors employed by he eams can jusfy an ncrease n he rerbuon of hose facors; oherwse, an ncrease n he remuneraon of he facors of producon would ranslae o an ncrease n he prce of he spors even and s compeveness would suffer. The dea of he relaonshp beween he use of producve resources and compeveness n fooball eams s also presen n Pesana Barros e al. (2014). In shor, each eam has a spors objecve, whch s o defea s rvals. However, all of hose rvals hen group ogeher n a governng body for each 58

3 Ahens Journal of Spors March 2016 one of he ournamens and from an economc pon of vew, he profably of he ndvdual eams s boh nfluenced and proeced by he negoaons underaken by he governng body of he ournamen or league n whch parcpaes. Ths sudy akes as a premse ha he UEFA, as he organzer of he Champons League, should ensure ha he produc/servce beng offered s compeve, n oher words ha s suffcenly aracve o generae demand. Therefore, should be concerned wh ncreasng he producvy of he parcpang eams by, for example, esablshng rules ha reward he mos producve eams. The Malmqus ndex s he measure of he change n producvy used n hs sudy. The bass for s calculaon s he effcency ndces resulng from he applcaon of Daa Envelopmen Analyss (DEA) for he eams ha make up he sample. The Malmqus ndex akes no accoun all of he producon facors used by he organzaon, herefore he conclusons ha can be drawn overcome he lmaons of sngle facor producvy ndces. On he oher hand, calculang he Malmqus ndex usng he DEA mehod allows consderng he change n producvy as he resul of wo dfferen effecs: effcency change and echncal change (Grosskopf 1993). The effcency raos mus refer o he producve process beng evaluaed. In a smplfed form and followng he posulaes of Schofeld (1988), Carmchael and Thomas (1995) and Carmchael e al. (2000) for spors eams, he producve process o creae he produc/servce offered by he fooball clubs s composed by wo phases. The frs s he ranng responsble for he physcal condonng of he players, where he accs ha he eam wll use durng he games s decded. The second phase nvolves he games hemselves, where he eams face her rvals and where he fnal produc of hese ypes of organzaons, relaed o spors eneranmen, s produced. A he same me hese wo phases are lnked, snce he produc of he frs phase (he plays made durng he game), would be he npu o he second. The presen sudy s srucured n he followng manner. Nex, he paper revews he heorecal relaonshp among producvy, compeveness and s applcaon o he case of fooball eams. Subsequenly, shows he mehodology used o calculae he changes n producvy usng he Malmqus ndex and he represenave varables used for he fooball eam s producve process. In he las wo secons he auhors presen he resuls and he conclusons. Applcaon of he Theory of he Frm o Fooball Clubs Classcal economc heory uses soquan o represen organzaons producon sysems. Assumng perfec nformaon, freedom o ener/ex he ndusry and he absence of nfluence n seng marke prces, organzaons ha consue a secor wll launch he amoun of produc demanded by consumers on he marke a a prce se hrough he neracon of supply and 59

4 Vol. 3, No. 1 Espa-Escuer e al.: Producvy and Compeveness... demand. On an ndvdual level, each frm, n s ques o maxmze prof, launches he amoun of produc ha equals prce and margnal cos, uses a combnaon of facors suaed on he soquan and earns no exraordnary profs. However, emprcal evdence shows ha he model used n he classcal economc heory depcng frms as prof maxmzng agens wh he resrcon of he nal endowmen of resources s oo smplsc. Besdes, he non-complance wh he underlyng hypohess of he classcal economc heory s model has opened up new lnes of research. Imperfec nformaon and he bounded raonaly may resul n he choce of a combnaon of facors ha produce he oupu ha s above he soquan. The frm s echncal sysem s represened by s possbles of producon, whch show all he amouns of fnal producs ha could be produced by a gven combnaon of he facors; he soquan only represens he maxmum amoun of hese possbles of producon. In realy all of hem could acually occur alhough, from a concepual pon of vew, hey mply a deparure from he soquan, whch Farrell (1957) defnes as neffcency and supposes a ulzaon of resources n greaer quanes han wha s srcly necessary. Lebensen (1962) arbues he same meanng o he erm when rasng he mporance of he loss of effcency due no o mperfecons of he marke, bu raher o a wrong allocaon of resources whn he frm. The vew of boh auhors vares grealy from he consderaon of frms as "black boxes" ha s characersc of he economc heory and gves more relevance o he role of managers n he nernal admnsraon of he frms. Frms are consdered complex organzaons where members are specalzed n her asks. Managers, hrough her knowledge, he nsrucons hey gve and he ncenves hey esablsh are he ones ha have he responsbly of suang he frm on he soquan as far as producon s concerned. A ool avalable o help managers acheve hs are he classcal managemen approaches snce, as Chavenao (1999) emphaszes, boh Taylor and Fayol were concerned wh ncreasng he effcency of he frms hrough he raonalzaon of he workers asks and he organzaon and applcaon of scenfc managemen prncples, respecvely. However, he effcen use of resources n producon, ha s, he absence of wase, whch concepually would be represened by he choce of a combnaon of npus on he soquan, s no an end n self. Gven ha organzaons develop producs and servces wh he dea of launchng hem n he marke and compeng wh he oher organzaons of he secor, producng a produc effcenly resuls n cos savngs ha conrbue o he frm s compeveness and long-erm survval. If emprcal evdence shows ha organzaons choose combnaons of facors ha are above he soquan hen he producvy rao, whch s he rao of he amoun of produc obaned o he amoun of resources employed, wll no be he same for all frms. The producvy rao s, once agan, anoher concep ha relaes producon wh compeveness and herefore could serve as gudance for manageral decsonmakng. 60

5 Ahens Journal of Spors March 2016 Producvy s a measure for he evaluaon of he producve acvy of he organzaons ha relaes he amoun of produc obaned o he resources employed; s a concep ha s lmed o he producve area of he organzaon and herefore based on he deas of npus, oupus and he producon funcon. Besdes, only ncreases n producvy can jusfy an ncrease n he rerbuon of he facors of producon, whou a correspondng ncrease n he prce of he produc. In oher words, an ncrease n he rerbuon of he facors ha s no accompaned by an ncrease n producvy would mean an ncrease n he prce of he produc ha would negavely affec he compeveness of he frm. I s of neres o analyze he producvy changes of fooball eams due o he relaonshp beween hs concep and he compeveness of he organzaons. Compeveness s relevan o fooball clubs, because hey operae n a compeve envronmen composed by, no only he eams ha dspue he ournamen, bu also oher eneranmen opons ha he fans could choose o aend f he compeon does no mee her expecaons or f hey consder he prce o be excessve. There s no consensus n he leraure as o wheher he objecve pursued by spors eams s he maxmzaon of economc performance or he maxmzaon of spors resuls, as can be seen n he sudes of For and Qurk (1995), Szymansk (2003), Sandy e al. (2004), For (2006), Késenne (2007), Garca del Barro and Szymansk (2009). The perspecve adoped n hs paper s he followng: regardless of he lack of consensus n he leraure regardng he fooball clubs objecves, economc prof mus ceranly be aken no accoun and can provde nformaon abou he managemen of he clubs 1. Therefore, even n he even ha fooball clubs are no consdered for-prof organzaons whose objecve s prof maxmzaon, hey should be aware of he opporunes hey have o ncrease, he repercussons ha her decsons have on and he rsks hey are exposed o ha could decrease. In shor, all of he saed above regardng effcency, producvy and compeveness apples o hem. Therefore, s necessary o reflec abou he naure of he produc of a fooball eam and wha acves are needed o produce. Tha would allow he represenave varables of he producon funcon o be esablshed, he soquan o be used as a heorecal reference ool and he producvy o be calculaed as an approxmaon o he compeve suaon whn he secor. The fooball eam s produc s he show hey offer durng each game or hroughou a ournamen and he spors resuls hey acheve. For hs, hey need an opponen wh whch o dspue he vcory n accordance wh he rules and scorng sysem esablshed for each compeon. Therefore, he eams do no compee among hemselves for wha would be he equvalen of a marke, bu raher for he spors resul; he vcory n he game or he overall ournamen (composed of he sum of he vcores n he ndvdual games ha make up ha ournamen). Consequenly, he rue compeor for he marke s no he spors 1 For example, Szymansk (1998) evaluaes, among oher varables, he economc prof of he European fooball club Mancheser Uned, lnkng revenues and coss o spors resuls. 61

6 Vol. 3, No. 1 Espa-Escuer e al.: Producvy and Compeveness... opponen. Therefore, f he games are he producve acvy of he fooball eams and he spors resuls are he produc, hen he analyss of her producvy mus focus exclusvely on he plays made. As n all organzaons, he prof of fooball eams s he dfference beween revenues and expenses. The frs depend on he demand for he "produc" of he eams, whch are he games and ournamens played and come from he sales of ckes and passes, broadcasng rghs, adversng, sponsorshp, he sale of merchandse such as -shrs, ec. Revenues are nfluenced by he spors resuls of he eam, he exsence of oher eneranmen alernaves and he prce a whch he produc s offered. Expenses are made up of hngs such as personnel, facles, ravel, ransporaon, ec. A reducon n he expenses ncreases he profs. Gven ha a poron of he coss are generaed n he producon funcon, effcency, undersood as he choce of a combnaon of resources suaed on he soquan and herefore as he absence of wase, conrbues o reducng hem. Furhermore, heorecally, he change n producvy s a reference for deermnng he ncrease n he remuneraon of he facors of producon ha he club can absorb whou alerng s sellng prce hereby mananng s compeveness 2. Mehodology and Varables Ths sudy follows he proposals of Grosskopf (1993) o calculae he changes n producvy of he fooball eams ha parcpaed n he UEFA Champons League. Ths auhor argues ha her approach dffers from ha of oher auhors, snce allows for neffcency n he organzaons, meanng ha he combnaon of he facors used o produce he produc may no be on he soquan. In consequence, he ncrease n producvy s no he equvalen of echncal progress. The approach of Grosskopf (1993) belongs o he froner models of effcency calculaon naed by Farrell (1957) who consders devaons from he soquan o be neffcency. Farrell (1957) also proposes o measure effcency as he dsance exsng beween he combnaons of facors acually used by he organzaon under sudy and ha are suaed on he soquan 3. Furhermore, he proposal of Farrell (1957) o calculae he effcency of an organzaon consss of sarng from he observaons of he npus acually consumed and he oupus obaned from a homogeneous sample and 2 Ths dea should be compleed wh he prce elascy of he demand funcon for he eneranmen ha he fooball eams offer n comparson o oher eneranmen opons. Tha s, only n he case ha he demand for fooball was nelasc he ncrease n prce, due eher o an ncrease n he prce of he npus or for any oher reason, would have lle effec on he quany demanded by consumers. 3 The normal wo-dmensonal represenaon of he soquan corresponds o producon processes ha use wo npus and oban he same oupu. However, he concep can be generalzed for mul-oupu and mul-npu producon processes and he Formulae presened and used n hs paper also allow for. 62

7 Ahens Journal of Spors March 2016 ake he envelopmen of acual daa as he soquan - hus he denomnaon "froner" by whch he mehodology proposed by hs auhor s known. In hs conex, Grosskopf (1993) defnes he ncrease n producvy as he ne change n he amoun of oupu produced due o changes n he effcency and o echncal change. She also saes ha changes n effcency are modfcaons over me n he dsance beween he observaons of an organzaon s npus/oupus and he represenave soquan of s producon echnology. On he oher hand, echncal change could be nerpreed as changes over me n he poson of he soquan wh respec o he orgn of he coordnae sysem. The defnon of hese wo conceps can also be found n Thry and Tulkens (1989). In order o measure he changes n he producvy of an organzaon, Grosskopf (1993) proposes he Malmqus producvy ndex as a sarng pon, as Caves e al. (1982). Under he assumpon ha he organzaons can be neffcen and hs neffcency wll be calculaed by froner mehods, observaons of he amouns of npus consumed and he producs produced are needed for each of he organzaons n he sample for wo consecuve perods. Ths nformaon wll be used n he followng Formula (1) o calculae he Malmqus producvy ndex for each organzaon: m λ (x, y ) λ (x, y ) (1) where, he subscrp refers o he organzaon beng suded and he superscrp or +1 refers o he perod from whch he nformaon was aken. In greaer deal: m x : y : : λ (x, y ) : λ (x, y ) : s he Malmqus producvy ndex of organzaon based on he soquan correspondng o perod. s he vecor of he quanes of npus consumed by organzaon I n perod. s he vecor of he oupus obaned by organzaon n perod. s he effcency value of organzaon n perod akng he echnology of perod as a reference, ha s he dsance ha separaes he combnaon of facors ha organzaon used n perod from he soquan or froner, calculaed usng he nformaon of he enre sample for perod. s he effcency ha organzaon would have acheved f s consumpon of facors and s producon for perod +1 were valued wh respec o he soquan correspondng o perod. 63

8 Vol. 3, No. 1 Espa-Escuer e al.: Producvy and Compeveness... Measurng he ncrease n he producvy of an organzaon Grosskopf (1993) proposes usng he geomerc average of he wo Malmqus ndexes for he consecuve perod s and +1 by calculang he followng expresson: M (x, y λ (x, y, x, y ) λ (x, y ) ) λ * (x λ (x,, y y ) ) 1/2 (2). Ths can be re-wren n he followng manner: M (x, y λ, x, y ) λ (x (x,, y y ) ) λ * λ (x (x, y, y ) λ * ) λ (x, y ) (x, y ) 1/2 (3). Accordng o Grosskopf (1993), he Malmqus ndex s made up of wo componens. Breakng down as shown n (3) allows hem boh o be calculaed: he erm ousde of he brackes measures he effcency change, whle he brackeed erm measures he echncal change. The way o calculae he effcency values ha form par of he Malmqus ndex proposed by Grosskopf (1993) reman o be deermned. Among he possble froner approaches, hs sudy has oped for DEA. I s no necessary o specfy he form of he producon funcon o apply DEA; however, s based on he concep of process as he ransformaon of producve resources no fnal producs for he deermnaon of he varables ha nervene n he calculaon. The effcency value of he uns ha compose he sudy sample s he rao found by solvng he followng lnear programmng problem 4 : where, Mnmze I (4) s.. * x u* X y u * Y u R + : s he effcency rao found by solvng he problem. x : s he vecor of he amouns of npu used by un. y : s he vecor of he amouns of oupu obaned by un. X: s he marx of he amouns of npu used by he uns of he sample. Y: s he marx of he amouns of oupu obaned by he uns of he sample. u: s he vecor of he coeffcens from solvng he problem. 4 In he noaon of hs problem superscrps denong he perod of reference are no used, because n s orgnal Formulaon DEA uses he sample daa referrng o only one perod. Therefore, he effcency rao for each organzaon s calculaed by akng he daa of he consumpon of he facors, he producon and he soquan wh respec o whch s calculaed for he same perod. 64

9 Ahens Journal of Spors March 2016 The formulaon of he problem ha has been presened assumes consan reurns o scale 5. An npu orenaon has been adoped whereby s nerpreed as he proporon by whch he amouns of all producve resources employed by he un under analyss mus be reduced o suae on he soquan or froner. Therefore, hose uns n he sample whose s equal o uny wll be classfed as effcen, whle hose whch have a rao value below one wll be classfed as neffcen. Gong back o he Malmqus ndex, hs can show values lower han, hgher han or equal o one. If an organzaon s Malmqus ndex s below one, he nerpreaon s ha he organzaon has lowered s producvy beween he wo perods aken n consderaon. If he producvy has ncreased he ndex wll be hgher han one and f he producvy has no changed he ndex wll be equal o one. Each of hese hree possbles can be he resul of he combnaon of dfferen values of he change n effcency and echncal change, whch can ake on values lower han, hgher han or equal o one. A value for he change n effcency less han one means ha he effcency of he organzaon under sudy has dmnshed over me because shows a lower value n perod +1 wh respec o perod ; he nerpreaon s he oppose where he value s greaer han one and a rao equal o one means ha here has been no change n effcency. If a echncal change shows a value lower han one means ha he soquan ha represens echnology for perod +1 s farher from he orgn of he coordnae sysem han n he precedng perod, hus ndcang ha here has been a echncal regresson. I s also possble o show a value greaer han uny, whch would have he oppose nerpreaon and a value equal o one would ndcae ha here has been no echncal change. Ths paper focuses on he calculaon and mplcaons of he changes n he producvy of he fooball eams ha have parcpaed n he UEFA 5 DEA also allows he calculaon of he organzaon s effcency rao under he assumpon of varable reurns o scale. Gven ha, one of he advanages of DEA s ha does no requre he specfcaon of he producon funcon, seems coheren no o make assumpons concernng he reurns o scale ha he producon process of he sample under sudy could show. Ths affrmaon s no n conradcon wh he possbles of calculaon ha DEA offers: f he effcency rao s calculaed under he assumpon of consan reurns o scale, wha s known as a global echncal effcency s obaned, whch measures neffcency caused by boh he wase of resources n producon and he wrong choce of he sze of he organzaon. The calculaon of he effcency rao under he hypohess of varable reurns o scale elmnaes he nfluence of hs second facor and reveals he value of he so-called pure echncal effcency, whch evaluaes exclusvely he wase of resources; he rao of global echncal effcency o pure echncal effcency s he effcency of scale, whch measures he loss of effcency due o he wrong choce of he sze of he organzaon. Consequenly, n hs paper, calculang DEA under he assumpon of consan reurns o scale does no mean ha he echnology used by fooball clubs does no show varable reurns, raher ha he effcency raos ha wll be calculaed o be used n he calculaon of he Malmqus ndex nclude boh he effecs of he proper use of producve resources and he choce of he sze of he organzaon. 65

10 Vol. 3, No. 1 Espa-Escuer e al.: Producvy and Compeveness... Champons League from 2003 o Ths s no he only compeon n whch hey parcpae, so her enre "producon" whch would nclude consumed resources and obaned spor resuls n naonal champonshps, s no aken no accoun n he npu and oupu vecors. Ths could be seen as a lmaon of he sudy however also has he advanage ha all of he eams ha play n he UEFA Champons League have had o be placed among he op posons of her domesc compeon n he prevous season. Ths makes he sample more homogenous and he homogeney of he sample uns s one of he requremens for he correc applcaon of DEA n he calculaon of he effcency raos. As for he oupu varable, ha s, he varable ha represens he success of he eams n he ournamen n whch hey parcpae, s mporan o emphasze ha he UEFA Champons League s a knockou ournamen; herefore, wha s mporan s qualfyng for he successve phases and n case of qualfyng for he fnal, wnnng. I s common for sudes of he effcency of fooball eams o use he pons earned durng he ournamen 7 or he number of goals scored 8 as varables. However, neher of hese wo varables guaranees ha he eams ha oban he hghes values acheve a beer classfcaon n he UEFA Champons League. The UEFA Champons League s group sysem makes possble for eams o advance o he followng sage havng earned fewer pons han ohers ha fal o advance only, because hese played n a group where he combnaon of vcores was less favorable o hem. On he oher hand, a hgher number of goals scored does no mean beer spors resuls, as he number of goals does no guaranee vcory. Scorng more goals han he opponen does provde he vcory n one game. Bu a bg dfference beween goals scored and goals conceded for he whole ournamen can be he resul of only one or a few won games wh a bg dfference beween hese wo varables, showng loses n he remander games. So a bg dfference beween scored and conceded goals hrough he whole ournamen no always correspond wh good spors resuls. Takng no accoun he prevous consderaons, hs sudy proposes he number of games played as he varable ha bes represens he success of he eams n UEFA Champons League. Ths oupu varable has he nconvenence ha akes he same value for he wnner as for he runner-up, even hough he wnner s obvously more successful. Concernng npus o be consdered n he producon funcon for fooball eams, leraure shows no agreemen. One group of auhors akes expenses as a 6 Producvy of fooball eams has been calculaed for naonal champonshps by Guzman and Morrow (2007), Espa-Escuer and Garca-Cebran (2008), Douvs and Pesana-Barros (2008), Jardn (2010) for nsance. 7 Dawson e al. (2000), Haas (2003a, 2003b), Gonzalez-Gomez and Pcazo-Tadeo (2010) use hs oupu varable, alhough ransformed or n combnaon wh oher complemenary varables. 8 Carmchael e al. (2000) use he dfference beween goals scored and goals conceded as oupu when specfyng her producon funcon and Bosca e al. (2009) sae ha he number of goals s a smple varable o measure he producon of he fooball eams. 66

11 Ahens Journal of Spors March 2016 varable represenave of he consumed resources. Examples of hs lne are Haas (2003a, 2003b), Haas e al. (2004) and Guzman (2006). Neverheless, Sexon e al. (1986) warn abou he rsk of confusng echncal and prce effcency and recommend usng varables measured n physcal uns. Also from a more general pon of vew, Border (2004) analyzes he Cobb-Douglas funcon and shows ha prces should no be ncluded n a producon funcon. Auhors ha follow hs suggeson n he case of fooball eams are Espa- Escuer and Garca-Cebran (2008) and Bosca e al. (2009). In boh papers npu varables are plays made durng games n lne wh he work of Carmchael e al. (2000). The presen arcle can be framed n hs second group as he players ha parcpae, as represenaves of labor force and he plays made durng he games are aken as he facors of producon. The number of players ha each eam uses durng he ournamen s aken as he represenave varable of he frs. I can be argued ha no all of he players are of he same qualy and hs wll have an nfluence on he effcency. However, qualy s a concep ha refers o he produc offered on he marke by an organzaon and no o he facors used n s producon. The characerscs of he resources used n a producon process wll have an nfluence on he qualy of he produc, bu hose dfferences are precsely he ones ha could explan he dfferences n he levels of effcency acheved by he organzaons ncluded n he sudy 9. Wh regards o he plays made, he players make boh offensve and defensve plays durng he game, however only he offensve plays conrbue o he vcory. There are several jusfcaons for makng hs affrmaon. Frs, n he exreme case n whch a eam only defends, would no score any goals and herefore he bes resul could acheve would be a scoreless e, never a vcory. On he oher hand, he eam execues defensve plays o offse he acons of he opposng eam and n he represenaon of producve processes by soquans, whch s wha DEA esmaes, acons aken o adap o he envronmen are never o be consdered npus 10. Fnally, he defensve plays made by he opposng eam could be consdered, as hey mpede an offensve play from becomng a posve spors resul. However, defensve plays from he rval canno be consdered facors of producon for he eam whose effcency s beng calculaed. To do so would volae a condon consdered as such: he quany and use of he producve resources mus be under he conrol of he frm. The eam under sudy has no conrol over he defensve plays made by s opponen. Furhermore, connung wh he applcaon of he characerscs of manufacurng o fooball eams, 9 Golany and Roll (1989) recommend dsngushng beween he facors of producon and he varables ha explan he dfferences deeced n he effcency values acheved by he organzaons n he sudy. 10 For example, he chemcal ndusry obans producs followng he chemcal Formulae, whch would be he equvalen of he soquan. However, he companes mus also make effors o comply wh envronmenal laws or face resrcons o explong deposs whch means addonal effor, bu s no refleced n her producon funcon. Smlarly, n manufacurng and n servces, adversng could also be consdered an acvy o couner or ancpae, he acons of compeors and agan s no consdered a producve resource. 67

12 Vol. 3, No. 1 Espa-Escuer e al.: Producvy and Compeveness... he manufacurer should ake he amoun of produc acually sold by he frm as he oupu value, snce sales are wha generae profs and sales may dffer from producon due o poor forecasng by he company or he acvy of compeors and hese crcumsances are no refleced n he soquan. In he case of a fooball eam, he dfference beween he spors resuls ha could acheve hrough s offensve plays and he resuls acually acheved, are due o he defensve plays of he opponen and herefore should no appear as npus n he represenaon of he soquan. In concluson, for hs sudy, n addon o he eam s offensve plays, he mnues of possesson and shos aken have been chosen as represenave varables of he resources employed n he game. The defensve plays made, eher by he eam or by s opponen, would be aken as explcave varables of effcency, as proposed by Golany and Roll (1989) 11. Gven ha for hs sudy he producon funcon only conemplaes one oupu and ha oupu s he number of games played durng he UEFA Champons League compeon, an npu orenaon was seen o be more approprae for he calculaon of he effcency raos. I makes more sense o recommend reducons n he consumpon of npus han o ncrease he oupu, snce he laer would mply ha neffcen eams should ncrease he number of games hey play, when n fac he values ha hs varable can ake on are se by he compeon rules hemselves. All he varables represenng he fooball eam s producon process used n hs sudy have been obaned from he OpaSpors daabase 12. The calculaons have been made usng he oal of each eam s values for each of he seasons analyzed. The descrpve sascs of he varables used are shown n Table 1. Resuls The samples for whch he changes n producvy have been calculaed n hs sudy are he fooball eams ha played he UEFA Champons League for he seasons among As shown n Formula (3), o calculae he Malmqus ndex, he effcency raos of each eam are needed for wo consecuve seasons. They are calculaed from he npu and oupu daa, boh for he eam and for he oal sample. Snce he eams ha compee n he UEFA Champons League change from year o year, he calculaons were done as follows: he sample used for he year n queson s composed by all he eams ha parcpaed n he compeon, regardless of wheher or no hey 11 Guzman (2006) also calculaes and analyzes he producvy of fooball eams usng he Malmqus ndex, however he npus used are personnel coss and general expenses and he oupu, revenues. Sexon e al. (1986) recommend he use of varables measured n physcal uns, herefore excludng he remuneraon of he facors, so as no o confuse he values of echncal effcency wh prce effcency. 12 OpaSpors s a prvae nernaonal company who provdes nformaon abou eams parcpang n naonal and nernaonal fooball champonshps. Is web se s 68

13 Ahens Journal of Spors March 2016 connued n he followng season. However, he Malmqus ndex was only calculaed for hose eams ha played a leas wo consecuve seasons and herefore was possble o oban all of he erms ha are used n he Formula (3). Table 2 shows he resuls obaned. Table 1. Descrpve Sascs of he Varables Used Analyzed seasons Inpu varables Oupu varable Offensve Number of Mnues of Number of Games played plays players possesson shos 2003/2004 Maxmum 1, Mnmum Average Sd. Dev /2005 Maxmum 1, Mnmum Average Sd. Dev /2006 Maxmum 1, Mnmum Average Sd. Dev /2007 Maxmum 1, Mnmum Average Sd. Dev /2008 Maxmum 1, Mnmum Average Sd. Dev /2009 Maxmum 1, Mnmum Average Sd. Dev /2010 Maxmum 1, Mnmum Average Sd. Dev /2011 Maxmum 1, Mnmum Average Sd. Dev Source: Auhors esmaons. I should be sressed ha for each one of he seasons n he sudy, Table 2 shows he value of he change n he producvy of he fooball eams, wh respec o he prevous season, as measured by he Malmqus ndex. Furhermore, for each one of he values of he Malmqus ndex he values of s wo componens, effcency change and echncal change, are also shown. On he oher hand, he blank cells n Table 2 represen suaons n whch s mpossble o calculae he Malmqus ndex correspondng o a gven eam; eher because ha eam dd no parcpae n he UEFA Champons League n 69

14 Vol. 3, No. 1 Espa-Escuer e al.: Producvy and Compeveness... ha or he prevous season. Fnally, he las row of Table 2 shows he average values for each column, ha s, he average of he Malmqus ndex and s wo componens for each season. Focusng on he average producvy change n each of he seasons analyzed, should be emphaszed ha here are ncreases n only hree of hem and by very small amouns (2004/2005, 2008/2009 and 2009/2010). Season 2006/2007 showed no change over he prevous year and n he res decreased, wh he declne n season 2010/2011 beng especally noeworhy. In he hree seasons n whch here was an ncrease n producvy on average, all of he eams experenced echncal progress. Wh regards o he average changes n effcency, n he seasons 2004/2005 and 2009/2010 here was a decrease n effcency ha was offse by echnologcal progress and n 2008/2009 here was no change. Also, n hese hree seasons dfferen cases regardng he evoluon of effcency can be observed f he eams are aken ndvdually: here are some ha ncreased, whle ohers decreased and among he laer, some compensaed he decrease wh echncal progress o he exen ha hey showed an overall ncrease n producvy. In season 2006/2007 he average producvy dd no change wh regard o he prevous season and also, on average, can be seen ha he decrease n effcency s compensaed by echnologcal progress. Wh regard o he suaon of he ndvdual eams parcpang n he UEFA Champons League durng ha season, he majory experenced echncal progress; however, hs was no accompaned by an ncrease n effcency n all cases. Among hose ha decreased effcency predomnaed hose ha dd no offse her decrease n effcency wh echncal progress and herefore showed an overall declne n producvy. On he conrary, for he eams ha suffered a echncal regresson n season 2006/2007, he evoluon of her producvy concdes wh ha of her effcency,.e. hose ha ncreased her effcency, also ncreased her producvy and vce versa. In he res of he seasons analyzed, on average he eams parcpang n he UEFA Champons League decreased her producvy and alhough hey ncreased her average effcency, was no enough o compensae her echncal regresson. In season 2010/2011, all of he parcpang eams experenced a echncal regresson and of hose ha ncreased her effcency, only wo ncreased her producvy (Mlan AC and Real Madrd). In he 2005/2006 season only one eam (PSV Endhoven) showed neher echncal progress nor regresson nor dd s effcency change, consequenly s producvy remaned unchanged. The res experenced echncal regresson, however he majory of hem showed an ncrease n effcency, hs compensaed he echncal regresson and her producvy ncreased. Fnally, n he season 2007/2008, only fve eams dd no experence echncal regresson. Two of hem (Celc and Lverpool) showed no change, nor dd hey vary her effcency, herefore her producvy remaned unchanged. 70

15 Ahens Journal of Spors March 2016 Table 2. Malmqus Index Values by Season for he Teams Parcpang n he UEFA Champons League 2004/2005 over 2003/ /2006 over 2004/ /2007 over 2005/ /2008 over 2006/ /2009 over 2007/ /2010 over 2008/ /2011 over 2009/ AC Roma Ajax Arsenal Al. de Madrd Bayern München Benfca Celc Chelsea CSKA Moscu Dep. A Coruña F.C. Barcelona FC Dynamo Kyv FC Poro FC Shakhar Fenerbache Forenna Grondns Iner Juvenus FC Llle Lverpool Lyon Mancheser U Mlan AC Monaco

16 Vol. 3, No. 1 Espa-Escuer e al.: Producvy and Compeveness... O. Marselle Olympakos P Panahnakos PSV Endhoven Rangers FC Real Madrd Rosenborg RSC Anderlech Rubn Kazan Spara Praha Sporng de Lsboa Seaua Bucares Valenca Werder Bremen Average Noe: 1: Effcency change, 2: Techncal change, 3: Malmqus. Source: Auhors esmaons. 72

17 Ahens Journal of Spors March 2016 The oher hree ha showed echncal progress (CSKA Moscu, Seaua Bucares and Valenca) could no, however, offse her decrease n effcency, herefore her producvy dropped. Of hose showng echncal regresson and ncreased effcency, four of hem ncreased her producvy (FC Barcelona, FC Dynamo Kyv, Lyon and Olympakos P), whle he producvy decreased for sx (AC Roma, Arsenal, FC Poro, FC Shakhar, Iner and Real Madrd). In summary, n vew of he resuls, could be sad ha on average, for he seasons ha show ncreases n producvy, hose ncreases are due o echncal progress. When he performance of he eams s analyzed ndvdually, he evoluon of effcency only appears o have a greaer nfluence on he change n producvy durng he seasons 2005/2006 and 2006/2007, snce n he majory of he cases n whch he change n effcency shows he oppose sgn of ha for echncal progress, effcency prevals. In he res of he seasons, wh he excepon of 2007/2008 for whch he nfluence s nconclusve, s he echncal progress or regresson ha domnaes he sgn of he change n producvy when does no concde wh he sgn of he change n effcency. If he resuls are analyzed eam by eam, should be noed ha he eams ha play he UEFA Champons League n all of he seasons analyzed n hs sudy show errac changes n producvy, alernang ncreases wh decreases and showng a drop a he end of he perod. The only excepon s Real Madrd, whch has a Malmqus ndex below uny for every season analyzed excep for he las wo, when s producvy ncreases. Among he eams ha do no play he UEFA Champons League n all of he seasons analyzed, bu for whch here are values of her changes n producvy for a leas wo of he seasons, can be seen ha AC Roma, FC Dynamo Kyv and Juvenus FC always ncrease her producvy, Celc ncreases or manans and decreases for Fenerbache n all of he cases. The evoluon of he producvy of he res does no follow any defned paern. Fnally, among he eams for whch a Malmqus ndex value could only be calculaed once durng he span of hs sudy, he producvy of some eams decreased, whle for ohers ncreased. The change n producvy and s wo componens were also calculaed for he eams ha parcpaed n he UEFA Champons League n he seasons 2003/2004 and 2010/2011, as f hey had been consecuve years, wh he objecve of approxmang he evoluon of her producvy over he enre perod analyzed n hs paper. The resuls are shown n Table 3. On average he resuls show a decrease n producvy, a decrease n effcency and echncal regresson. If he resuls are nerpreed ndvdually for each eam, only AC Mlan ncreases s producvy, due o an ncrease n effcency ha compensaes for s echncal regresson. On he oher hand, Panahnakos and Rangers FC experence no change n producvy or effcency and show neher echncal progress nor regresson. 73

18 Vol. 3, No. 1 Espa-Escuer e al.: Producvy and Compeveness... Table 3. Malmqus Index Values for he Teams Parcpang n he UEFA Champons League n he Frs and Las Seasons of he Perod Analyzed 2010/2011 over 2003/2004 Effcency change Techncal change Malmqus Ajax Arsenal Bayern Munchen Chelsea FK Parzan Iner Lyon Mancheser Uned Mlan AC Panahnakos Rangers FC Real Madrd Average Source: Auhors esmaons. The res of he eams show a declne n producvy, mos of hem due o a drop n boh effcency and echncal progress, however, boh Iner and Real Madrd ncrease her effcency, for Mancheser Uned remans unchanged, and FK Parzan shows echncal progress. Analyzng he nformaon n Table 3, one could conclude ha over he perod suded here s a wdespread declne n producvy, whch s also evden n s wo componens, bu prmarly n a echncal regresson. Conclusons The produc of he fooball eams s he eneranmen hey offer, whle her producve acvy s he games played; he resources consumed are he plays made durng he games. Snce s a process ha could be consdered labor nensve, sudes such as he presen, whch evaluae he ulzaon of he resources consumed, can be nerpreed from he pon of vew close o ha of he coach who s n charge of desgnng he accs mplemened on he feld and he ulzaon of he resources avalable. However, he fundamenals of he sudy are underpnned by ools suppled by he economc scence and especally, adopng an organzaonal managemen perspecve. Wh regards o hs should be sressed ha he plays execued by each ndvdual player durng he game and her conrbuon o he fnal resul, could be consdered an applcaon o fooball eams of he deas se forh by he admnsraon heory. Recenly, here have been repors n he spors press abou fooball coaches makng use of very dealed sascs of he plays made on he feld 13. The use of hs nformaon can serve o mprove he performance of he players, boh n ranng and durng he games. Ths ype of nformaon and he purpose, for whch s used, could be lnked o he poneerng sudes of he classcal approach o managemen, whch focused on work mehods, he 13 An example would be found n he web page: hp://goo.gl/7y3wx5. 74

19 Ahens Journal of Spors March 2016 movemens necessary o execue a ask and he me requred for s execuon (Chavenao 1999). Teams ha parcpae n a fooball champonshp compee among hemselves for he spors resul, bu are no consdered compeors n he marke from whch hey oban he revenues ha are a componen of her economc prof. Consequenly, he ndex of producvy can be relaed o he economc compeveness of he organzaons whn her economc secor. In hs arcle, changes n producvy n fooball eams playng n UEFA Champons League from have been calculaed by means of he Malmqus ndex. Also, effcency raos needed o calculae he Malmqus ndex have been obaned usng DEA. As a non-paramerc and deermnsc ool, DEA does no need he specfcaon of a funconal form for a producve process. Bu hs lack of consrans makes resuls sensve o he sample analyzed. In he presen arcle hs dffculy have be overcome: he sample under analyss s well defned, as every sngle eam parcpang n he UEFA Champons League durng me horzon has been ncluded n he sample, even f s parcpaon has been reduced o a unque season and has no been possble o calculae s Malmqus ndex. Of course, he choce of varables represenng npus and oupus have a bg nfluence n numercal resuls. In order o presen more robus ndexes, we have focused on games as he producve area n fooball eams and only varables measured n physcal uns have been consdered here. The resuls obaned n hs arcle show no clear ncrease n producvy durng he perod suded, boh on he average and ndvdually. In concluson, does no appear ha he organzer of hs ournamen has been able o ncrease he producvy of he eams ha has parcpaed n durng he perod analyzed. In hs respec could be sad ha he UEFA Champons League s an eneranmen alernave whose compeveness relave o oher opons could be hreaened. If he fooball eams ha parcpae n he ournamen showed a conssen and prolonged ncrease n producvy, hey would be able o afford an ncrease n he cos of her facors of producon n he same proporon whou havng o ransfer hese ncreases o he prces. Consequenly, he overall recommendaon for he fooball clubs analyzed n hs sudy would be o mprove her producvy. Breakng down he Malmqus ndex no effcency change and echncal change and seeng ha neher of he wo show a clear ncrease, he general recommendaon can be made more specfc: f he UEFA Champons League preends o say compeve wh oher compeors n he eneranmen secor (ha means, o afford ncreases n he rerbuon of s facors of producon whou ncreasng he prce a whch offers s eneranmen or o make he parcpang eams more profable), frs he eams should elmnae all use of facors of producon ha could be consdered excessve and choose a combnaon of hem ha s on he soquan and second hey should nroduce mprovemens n he use of her resources ha would suppose echncal progress, n oher words ha would make he soquan approach he orgn of he coordnae sysem. 75

20 Vol. 3, No. 1 Espa-Escuer e al.: Producvy and Compeveness... Therefore, he recommendaon would be o desgn rules for he ournamen ha would mprove he producvy of he parcpang eams by lnkng spors success o he ncrease n producvy. The lack of a relaonshp beween he spors resuls and he evoluon of he producvy of he eams ha parcpae n he UEFA Champons League s also revealed by he fac ha obanng a Malmqus ndex above one does no guaranee her connuy n he compeon snce for AC Roma, Celc, FC Dynamo Kyv, FC Shakhar, Juvenus FC, Olympakos P, Panahnakos, Spara Praha and Seaua Bucares her seres end n seasons n whch hey ncreased her producvy and he cases n whch only one Malmqus ndex could be calculaed durng he perod suded corroborae hese fndngs, snce ncreased producvy dd no guaranee permanence n he compeon. Therefore, he value of he Malmqus ndex for he eams ha parcpae n he ournamen s no relaed o her permanency n he compeon. Fuure lnes of research could nvolve relang he producvy values o he evoluon of he economc profs or oher varables ha are represenave of he eam s economc survval and he search for rules ha reward and value he spors resuls acheved as a resul of ncreases n producvy. Acknowledgemens We would lke o hank GECA Spor for s cooperaon n provdng he daa for hs sudy. Ths work was done whn compee research group and was funded by projec ECO C03-01 from Mcnn and Feder. Appendx Table A1. Descrpve Sascs of he Varables Used for Teams n he Sample Inpu varables Oupu varable Obs Offensve Number of Mnues of Number of Games plays players possesson shos played Aalborg BK 1 Maxmum Mnmum Average AC Roma 2 Maxmum 1, Mnmum Average Sd. Dev AEK Ahens FC 2 Maxmum Mnmum Average Sd. Dev Ajax 4 Maxmum Mnmum