Reinventing the Economics of Sport

73 Pages·1983·1.639 MB·English

by  Simon Chadwick & Angel Barajas

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Reinventing the economics of sport atio
Guest Editor: Associate Professor Angel Barajas n
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193 Editorial advisory board l J An International Journal
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194 Guest editorial rn
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196 Productivity in professional Spanish basketball l
Marta Brosed Lázaro, Manuel Espitia-Escuer and Lucía I. García-Cebrián
Reinventing the economics of
212 Using a brief questionnaire to assess the overall perceptions of basketball spectators
Ferran Calabuig Moreno, Josep Crespo Hervás, Vicente J. Prado-Gascó and Juan M. Núñez-Pomar
sport
223 Is human capital protection effective? The case of the Basque Country in Spanish football
Jonatan Calero and Julio del Corral
Guest Editor:
237 Economic crisis, sport success and willingness to pay: the case of a football club
Pablo Castellanos Garcia, Jaume García Villar and José Manuel Sánchez Santos Associate Professor Angel Barajas
250 Top European football clubs and social networks: a true 2.0 relationship?
Noelia Araújo, Pablo de Carlos and Jose Antonio Fraiz
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EDITORIALADVISORYBOARD Editorial
DrAndyAdcroft DrDuncanMurray advisory board
UniversityofSurrey,UK UniversityofSouthAustralia,Australia
DrAngelBarajas ProfessorNikolayPeshin
UniversidadedeVigo,Spain RussianInternationalOlympicUniversity,Russia
ProfessorZivCarmon DrScottRosner
INSEAD,Singapore WhartonSchooloftheUniversityofPennsylvania, 193
USA
ProfessorDavidCarter
UniversityofSouthernCalifornia,USA ProfessorKenShropshire
WhartonSchooloftheUniversityofPennsylvania,
ProfessorDaeRyunChang
YonseiUniversity,SouthKorea USA
ProfessorLucioColantuoni DiederikSlob
UniversityofMilan,Italy NyenrodeBusinessSchool,TheNetherlands
ProfessorCaryL.CooperCBE ProfessorStenSoderman
LancasterUniversityManagementSchool,UK StockholmUniversity,Sweden
ProfessorAntonioDavila ProfessorLeighSparks
IESEBusinessSchool,Spain UniversityofStirling,UK
DrMarkDibben ProfessorStefanSzymanski
MonashUniversity,Australia CassBusinessSchool,UK
ProfessorMikkelDraebye DrTroelsTroelsen
SDABocconiSchoolofManagement,Italy CopenhagenBusinessSchool,Denmark
ProfessorEduardoFernandez-Cantelli ProfessorDarinW.White
IEBusinessSchool,Spain SamfordUniversity,USA
ProfessorMarkJenkins DrMathieuWinand
CranfieldUniversity,UK UniversityofStirling,UK
DrRogerLevermore ProfessorMohammedYamin
UniversityofLiverpool,UK ManchesterBusinessSchool,UK
DrClaireMoxham
UniversityofLiverpoolManagementSchool,UK
Sport,BusinessandManagement:
AnInternationalJournal
Vol.4No.3,2014
p.193
rEmeraldGroupPublishingLimited
2042-678X
SBM Guest editorial
4,3
Reinventing the economics of sport
194 Itisapleasuretointroducethisspecialissue,collectingaselectionofpaperspresented
at the IV Congreso Iberoamericano de Econom´ıa del Deporte (IV Iberoamerican
Conference on Sport Economics) in Madrid in 2013 under the title “Reinventing the
economics of sport”. During the conference, researchers from Spain, Portugal and
severalLatinAmericancountriespresented54scientificpapersinfieldsrelatedtothe
economy of sports and its management. The conference included the following
research areas: economic impact of sports; financial balance in sports organizations;
economic planning in sports; financial health of public and private sports entities;
competitivebalanceinsportsleagues;efficiencyandsportbetting;andmarketingand
newsportingmodels.AllthesetopicsareincludedinthescopeofSport,Businessand
Management: An International Journal.
The papers selected for this special issue, even though they analyze football and
basketball,coverawiderangeoftopicssuchasproductivity,efficiency,perceivedquality,
perceivedvalue,satisfaction,humancapital,contingentvaluationandsocialnetworks.
The first paper, by Brosed-La`zaro, Espitia-Escuer and Garc´ıa-Cebria`n, aims to
determine whether basketball teams perform at their potential limit or whether they
shouldwinmorematchesandthenwhicharetheaspectsofthegamethatdeservethe
attentionofthemanagerstoorganizethestaffinanefficientway.Thestudymeasures
the efficiency of the Spanish basketball teams (ACB League) and develops their
productiveactivityfortheachievementofwinsaswellastheevolutionoftotalfactor
productivity between the seasons 2008/2009 and 2011/2012. This issue is relevant
giventhatperformingonthefield efficiently isthebestwayto generatesavings and
thisminimizescosts.MostofthepapersonbasketballfocusonNBAsothepaperby
Brosed-L(cid:2)azaroetal.contributebyapplyingDEAtoEuropeanbasket.Moreover,they
haveincludedtheplayoffsintheiranalysis.Thisfactisrelevantbecausethechampion
is the winner in that stage.
The second paper, by Calabuig, Crespo, Prado-Gasc(cid:2)o and Nu´n˜ez-Pomar, provides
evidenceofthevalidityandreliabilityofabriefandholisticquestionnairethatallows
managersofsportingeventstoobtainglobalinformationabouttheperformanceofthe
servicedelivered.Furthermore,themodelconfirmsperceivedvalueandsatisfactionas
predictors of future intentions of basketball spectators. The authors highlight the
existing relation between service quality, perceived value, satisfaction and future
intentions.Hispapercomestocorroboratethattheperceivedvalueisaprecedentfor
futureintentions.
The third paper, by Corral and Calero, focusses on the human capital policy and
analyseswhetherthe protectionofferedbysomefootballteamstolocalplayershasa
positive effect on the quality of the players from these regions. They conclude that
the effect of protection on the productive factors in a competitive environment, like
football,createsapositiveinfluenceonthedevelopmentandgrowthofthisproductive
Sport,BusinessandManagement:
AnInternationalJournal factor. This is consequent to the fact that protection offers more chances to promote
Vol.4No.3,2014 and improve productivecapacity.
pp.194-195
rEmeraldGroupPublishingLimited The work by Corral and Calero address a topic that is going to require more
2042-678X
DOI10.1108/SBM-05-2014-0027 attentioninthecomingyears.Thehumancapitalpolicyiscloselylinkedtothe“quota
systems” where the governing bodies of different sports try to limit the number of Guest editorial
foreign players or to impose a number of national players. For example, the Spanish
basketballauthoritieshaveimposedthesystemknownas“quotaofSpanishformation
players”thatforceseveryclubtohireeveryseasonfiveorsixplayersformedinSpain.
Thiskindofquotascouldmaybe,asCorralandCaleroassert,improvethecapacitybut
thenext question to ask willbe: whichis the cost of that kind of measures?
ThepaperbyCastellanos,GarciaandSanchezquantifiesthevalueoftheintangible 195
benefits associated with the existence of a professional football club in A Corun˜a
(Spain).Itisinterestingtopointoutthattwocontingentvaluationsurveyswereusedto
estimateandcomparethewillingnesstopayinordertoavoidaloss(teamrelegation)
in two different contexts: economic prosperity (2003) and crisis (2012). The
comparisons between the results from both surveys give rise to the conclusion that
factors such as general economic conditions and the plausibility of the hypothetical
disappearance of a football team influence the consumption of the public goods
generated by the team and the value that city residents assign to them.
Finally,thepaperbyArau´jo,deCarlosandFraizstudiestheusemadeofthesocial
network,Facebook,bythemainEuropeanfootballclubs,theresponseoftheusersand
theinteraction betweenclubs and fans. Theyassert that the European football clubs
are using their official sites in Facebook as a bidirectional communication tool
thatmakestheinteractionwiththefanseasier.Previousstudieshavefocussedonthe
presence of football in the web 2.0 in general but they do not pay much attention
to the kind of contents offered in a particular social network and how users have
respondedto them.
Summarizing, this special issue reflects the varietyof possible researchesin sport
management. Here there are five different topics analyzed from five different
perspectives.Moreover,somequestionshavebeenansweredbutalsosomeothershave
arisen and open new lines of research as: how to measure productivity in sports in
ordertoimprovetheefficiencyanalysis?Howtoincreasetheperceivedqualityinorder
to increase the future consumption? Do the protective measures for talent have also
positive effects or will they increase the salaries? Which would be the real financial
supportthatclubscouldexpectfromtheirfans?Or,howcantheclubsmanagebetter
their socialnetworkto increase their value?Herethere aresomequestions but,ifthe
special is attractive, sure that each paper will stimulate the readers to try to answer
them or find otherlines of research.
AngelBarajas
Departmentof AccountancyandFinance,University of Vigo,Ourense,Spain
AbouttheGuestEditor
Angel Barajas is an Associate Professor at the Department of Accountancy and Finance,
UniversityofVigo,Spain.HeisaVisitingLecturerattheUniversitiesinGermany,Russiaand
UK. He is currently the Director of the MBA in Sport at the University of Vigo and is a
Researcher for the Spanish Economic Observatory of Sport. His research interests include
investmentvaluation,intellectualcapitalandfinanceofsports.
Thecurrentissueandfulltextarchiveofthisjournalisavailableat
www.emeraldinsight.com/2042-678X.htm
SBM Productivity in professional
4,3
Spanish basketball
Marta Brosed L(cid:2)azaro
Department of Applied Economics, Universidad Aut(cid:2)onoma de Barcelona,
196
Barcelona, Spain, and
Manuel Espitia-Escuer and Luc´ıa I. Garc´ıa-Cebri(cid:2)an
Department of Economics and Business Administration,
University of Zaragoza, Zaragoza, Spain
Abstract
Purpose – The purpose of this paper is twofold: first, to evaluate the performance of Spanish
first-division basketball teams, in terms of efficiency, by defining previously a productive function
andobtainingalsotheirpotentialoutput.Second,toexaminethetotalfactorproductivityevolution
havinginformationfromseveralyears,whichallowsustodrawconclusionsaboutthechangesinthe
efficientfrontier.
Design/methodology/approach–Inordertoassesstheefficiencylevelandthepotentialoutputof
eachteamintheACBcompetition,betweentheseason2008/2009and2011/2012,aninput-oriented
version with constant returns of data envelopment analysis is used. The total factor productivity
evolutionisstudiedbyemployingthevaluesoftheMalmquistindex.
Findings–ThemainconclusionisthatthefinalpositionoftheSpanishbasketballteamsdependson
theefficiencyandanytechnologicalprogressisneededtomaintainthemselvesontopofrank.
Practicalimplications–Performingonthefieldefficientlyisthebestwaytoincreasetheprofitsby
generatingsavings,whichminimizecosts.Thisanalysisallowsustomakeaseriesofobservations,
comments and conclusions with regard to the management of the budgets and the relationship
betweenefficiencyandsportsperformance.
Originality/value–Theinnovationsprovidedbythispaperaretheuseofadifferentmethodology
andadifferentanalysisunitfromthepreviousstudies.Moreover,itfocusesonEuropeanbasketball,
specifically the Spanish league, which is considered the most powerful league after NBA and
whose connection with academic studies is quite limited to date. Finally it tries to incorporate
theplay-offstage,whichiscomplicatedbutreallyinterestingbecauseofthecontestdesignofthese
competitions.
Keywords Dataenvelopmentanalysis,Efficiency,Malmquistindex,Basketball,Potencialoutput,
Spanishbasketballteams
Papertype Researchpaper
Introduction
Mostfrequentlysportsfirmsmisleadthetwomajorobjectivesthattheyhavetofulfil,
since they need financial health and at the same time sporting success, maximizing
the utilityof the firm (Neale, 1964). In manyoccasions this duality incites a decision
makingwithoutaclearaimandmotivation,nottomentionthespecialwayoflooking
attheprofessionalsportsfirmsinacompetitivemarket.Theseinefficienciescouldbe
solvedby using thetoolsthateconomic theoryputsat businessworld disposal.
Consideringtheframeworkofthesportsfirms,itwouldbejustifiedtoprovidethem
Sport,BusinessandManagement: withaneconomicanalysistodeterminetheirproductiveaspects.However,termssuch
AnInternationalJournal
Vol.4No.3,2014
pp.196-211
rEmeraldGroupPublishingLimited JELClassifications—L83,L20
2042-678X
DOI10.1108/SBM-07-2013-0024 ThisresearchhasbeenfinancedbyResearchProjectECO2009-09623.
asproduction,productionfrontierorefficiencyhaveanambiguousmeaningrelativeto Professional
sports management, since there is no agreement about the final objectives and the Spanish
available means of production.
basketball
Inordertoclarifytheoperatingsystemofthesportsbodies,thispaperfollowsthe
portrayalmodelofthefirmsuggestedbyFandel(1991)andadaptedbyEspitia-Escuer
and Garc´ıa-Cebri(cid:2)an (2004) for the case offootball, inwhich the market supplies with
severalinputsandresourcestothefirm,inshapeofphysicalandhumancapital.The 197
physicalcapitalisfoundinfacilitiesandtechnicalprogress,throughthedevelopment
of training techniques and the improvement of the physical qualities. However,
thebiggestexpendituresareassignedtohiringplayersandcoaches.Theseresources
are converted into sports results thanks to the productive process carried out during
weeklyworkoutsandgames.Themoreefficientateamis,thelessresourcesareused
to obtain satisfactory results. Sportive results coming from the productive activity
are useful to obtain revenues shaped in sales of sports entertainment. According to
Guzm(cid:2)an(2006),bycorrectlyorganizingresourcesandadaptingthefinancialstructure,
sports clubs achievegoodlevelsof efficiencyandasustainablegrowth.
This study tries to give an answer to questions such as teams perform in their
potential limit or otherwise they should obtain a bigger number of wins; there is
technologicalprogressinbasketball;whataspectsofthegamedeservetheattentionof
themangers to organizethe staff in an efficientmanner.
Themotivationbehindthissportingdisciplineisfirst,theavailabilityofdata,since
statistics playanimportantroleinsportingandmanagementdecisions.Andsecond,
thetroublingfinancialsituationintheSpanishindustry.Theexistingempiricalstudies
make reference to NBA basketball mainly, so there is a gap in the application to
European basketball, whichworks in averydifferentmanner in manyaspects.
Thispaperisorganizedasfollow.Thenextsectioncoversareviewofthereference
literature about efficiency in sports and the theoretical framework in which is
developedthiswork.Thethirdsectionisrelatedtomethodologicalaspects,thatis,the
specification of a production function, measurements of efficiency and a brief
presentation of the Malmquist index. The fourth and fifth sections describe the
database and obtained results, respectively. Finally, the last section emphasizes
themost important conclusions.
Theoretical framework
Sports economy is a relatively recent yet growing discipline and during the last 60
yearshasgeneratedanimportantflowofarticles,sparkinginterestamongacademics.
Theprofessionalteams,evensatisfyingtherequiredfeaturestobetriedasanyother
entity, present a number of peculiarities, which motivate an especial literature. This
isconsideredinseveralarticlessuchasNeale(1964),ElHodiriandQuirk(1971),Cairns
etal. (1986).
AfterRottemberg,severalstudieshave estimatedtheimpactofthe playfactorsin
thefinaloutcomeofthegameandtheefficiencyforawiderangeofsports;Carmichael
et al. (2001) and Carmichael and Thomas (1995) formulate a production function and
obtain the production frontier of soccer and rugby, respectively; Mazur (1994) and
Ruggieroet al. (1996) evaluate technical efficiency in baseball; Hadley et al. (2000)
analyse the performance of American football teams with regard to their potential.;
Schofield (1988) estimates a production function of cricket; Dawson et al. (2000a,b),
Espitia-EscuerandGarc´ıa-Cebri(cid:2)an(2004),Bosc(cid:2)aetal.(2006)andHaas(2003)inrelation
to soccer.
SBM There are also many works that deal with the efficiency of basketball teams,
4,3 normallyfocusedonNBAteam’sperformancesandtheimpactsofthegamefeaturesin
American league. It presents a wide disparity of approaches depending on the time
interval (during either one season or several of them), the technical unit analysed
(teams or players) or the selected output (wins, per cent of wins, probability of
winning). The pioneering article in the NBA production frontier was written by Zak
198 etal.(1979),whereinputsareratiosmeasuringperformanceofoneteam,dependenton
theirrival’s,overfinaloutcome.Teamsareefficientwhentheyachievetheirmaximum
potentialtakingintoaccounttherival’spotential.ThedocumentsofHoflerandPayne
(1997)takeastepbyincreasingthesampleuntil29teams,generatingapaneldatafor
sevenseasons,thereforeinputsandoutputsareabsolutevalue,withnoratios,thisway
avoiding multi-colineality problems. This work not only manages to estimate the
impactofthefeaturesofthegameinthefinalresult,butalsoadjuststotheimpactof
the coaches and player quality, which supposed an innovation to that moment. Berri
(1999)introducesfixedeffectsinatwostepsmodel,whichlinksplayer’sstatisticstototal
wins,andsubsequentlymeasurethemarginalproductoftheplayersinsteadofmarginal
productoftheinputsasZaketal.(1979)andHoflerandPayne(1997)hadalreadymade.
Theinnovationsprovidedbythispaperaretheuseofadifferentmethodologyand
adifferentanalysisunit.ItusesEuropeanbasketball,specificallytheSpanishleague,
which is considered the most powerful league after NBA and whose connectionwith
academicstudiesisquitelimitedtodate.Ithastobenotedthat,despitebeingthesame
sport,thereareconsiderabledifferencesbetweenAmericanandEuropeanbasketball,
asmuchinrulesasinthewaythespectacleisconceived.Finallyittriestoincorporate
the play-off stage, which is complicated but really interesting because of the contest
design of these competitions.
Spanish professional basketball is going through a worrisome situation from a
financialpointofview.Manyteamsareinvolvedinfinancialproblems,withanadded
danger of insolvency. During past economic growth, the development of the market
and the power of the teams with bigger economic capacity, pushed modest teams to
assumeinvestmentswhose incomeswerenot ableto bear.Hence,during the seasons
2008/2009,2009/2010and2010/2011 FC.BarcelonaandReal Madrid concentrated33,
35 and 37 per cent of the expenses in sports staff, respectively. If the sample is
expanded with Baskonia and Unicaja, the four teams accumulate 52, 54 and 55
percent.Consideringtheassumptionthattheincomeofabasketballclubdependson
obtained results, the best way to improve the financial situation is through a better
utilization of resources detected by the calculation of efficiency.
Specifying the production function
The featuresand statistic richness of basketball allow it to be analysed as anyother
productiveactivity,forwhichaproductionfunctionisrequired.Rottenberg(1956)was
pioneer on shaping the production function of a sports activity. After that, the first
empiricalestimationscamefromthehandofScully(1974),Medoff(1976),Zech(1981)
and specifically with Zak et al. (1979) what was the first attempt to consider the
production function in professional basketball.
A basketball team is a technical unit that produces output from a combination of
inputs.Let the productive processin basketballbe specified as:
Y ¼fðXÞ; i¼1;2;...;n ð1Þ
i i
Where Y is the team i output (generally per cent of wins, probability of win or, Professional
i
asinthiscase,numberoftotalwins)andXiisourvectorofinputs.Theseinputsare Spanish
responsible for measuring the activities produced by the players and coaching staff
basketball
during the competition.
AccordingtoFØrsundetal.(1980)andEsteban-Garc´ıaandColl-Serrano(2003),the
estimation methods implemented to build a production frontier vary between two
types,dependingonthefunctionalform,thusrequiringthelinkofinputsandoutputs; 199
parametricornon-parametricmethods.Theformerprovideinformationontherelative
importanceofeachoneoftheinputsinobtainingoutputanditisneededtoestablish
how the error term distributes itself.
This work assumes that every team have access to homogeneous technology
and that all the professionals of the industry know it. This technology refers to
strategies,technicalresources,physicaltraining,sportsplanning,etc.Forthisreason,
theuseofnon-parametrictechniquesofoptimization–specificallythemodelknownas
dataenvelopmentanalysis(DEA)–suitsthestudymoreeffectively.Thisisduetoits
largerflexibilityandtheabsenceofspecificationerrors,sincetheadoptionofaspecific
functional form in the relation between outputs and inputs not necessary, nor is a
distribution of the efficiency.
Another advantage presented by this methodology is the possibility to manage
multi-output or multi-inputsituations and evenexpressing them in differentunits.
Deterministic frontiers assess the efficiency with regard to the best observations
of the sample, which corresponds to optimization process. Those organizations
situatedonthefrontierareconsideredefficient,whiledistancesbetweenobservations
and this isoquant are a measure of inefficiency of the corresponding firm. In both
processes – regular phase and play off – the proposed linear programming problem
is thefollowing:
Minft(cid:2)yt;xt(cid:3)
i i i
s:t
lXtpfxti i ¼1;...;m ð2Þ
lYXyt
t i
lX0
wherextand ytrepresentthevectorofinputsusedandoutputsproduced,respectively,
i i
by the unit i whose efficiency is being measured, while X is the matrix of the n
t
productivefactorsusedbyalltheteamsinthesampleand Y isthematrixofproducts
t
obtained by them. The weights of the optimum combination are represented by the
vectorofparametersl,andfinallyfistheefficiencylevelfortheteamunderanalysis
inperiodttakingintoaccounttheoptimumweights,sothatwhenf¼1,theanalysed
firm is on the isoquant and such is its efficiency that it results impossible to achieve
a bigger quantity of output given the inputs. Or dually, it is impossible to obtain
thesamevolumeofproductiondecreasingallresources.Inthesamewaywhenfo1
the firm is operating under inefficiency equal to (1(cid:2)f) since it could be possible to
attain the same output quantity by reducing the consumption of all the resources in
that proportion.
TheDEAmodelproposedisconsideringconstantreturnstoscale,sincethewhole
competitionisanalysedandnotgame-by-game,sothecompensationfactorexiststhat
SBM eliminates punctual differences, in terms of required inputs, which appear in certain
4,3 games. For instance, when a team plays against another offensive-minded team,
that style of play gives you considerably more time on attack and, as a result,
more possibilities of scoring. However, the contrary occurs when a team meets a
defensive-minded one. This model is characterized byan input orientation, in such a
waythat,givenalevelofoutput,efficiencyfirmswillbethosethatareabletoobtain
200 the same output decreasing the level of input. The adoption of one orientation or
anotherisirrelevantfromthepointofviewofidentifyinginefficienciesbutourchoice
will determine the interpretation of theresults.Otherwise, theoutput orientationwill
helpustoobtainthepotentialoutputgivensuchlevelofinputs,allowingustocompare
therealresultswiththosethatshouldhavebeenachievedbyeachinefficientteamin
order to clarify the results.
WiththeaimofassessingtrendsintotalfactorproductivityofSpanishbasketball
teams,wewillusetheMalmquistindexalsobasedonDEAresults,takingadvantage
oftheavailabilityofinformationfromseveralyears.Thisstudywillallowustodraw
conclusions about the existence of technical progress, or which is the same, the
existence of increasing returns to scale and some movement of efficient frontier.
Thereareseveralproductivityindexdecompositionsintheliterature,butamongallof
theminthispaperwewillusetheproposalofGrosskopf(1993)andCoellietal.(1998).
BothdefinetheMalmquistindexbyusingdistancefunctionsbetweentwodatapoints
and two different periods (t and tþ1) that describe a multi-input and multi-output
production technologywithoutthe needto specifyabehavioural objective:
"ft(cid:2)ytþ1;xtþ1(cid:3) ftþ1(cid:2)ytþ1;xtþ1(cid:3)#1=2
M(cid:2)yt;xt;ytþ1;xtþ1(cid:3)¼ i i i (cid:3) i i i ð3Þ
i i i i i ft(cid:2)yt;xt(cid:3) ftþ1(cid:2)yt;xt(cid:3)
i i i i i i
whereft(cid:2)ytþ1;xtþ1(cid:3)representsthedistanceortechnicalefficiencyfortheperiodtþ1
i i i
withregardtotheperiodttechnology.Inotherwords,isthedistanceofanobservation
(of input vector and output vector) in period tþ1 to the frontier in period t. Avalue
ofM greaterthanonewillindicatepositiveTFPgrowthfromperiodttotþ1,while
i
avaluelessthanoneindicatesaTFPdecline.Notethat,similarlytoCoellietal.(1998),
Malmquist indexes calculated by this way are in reality a geometric mean of two
productivity measures,coming fromone of two periodsas abenchmark.
Equation (3) could be rewritten as two components: technological change and
technical efficiencychange:
"ftþ1(cid:2)ytþ1;xtþ1(cid:3)#" ft(cid:2)ytþ1;xtþ1(cid:3) ft(cid:2)yt;xt(cid:3) #1=2
M(cid:2)yt;xt;ytþ1;xtþ1(cid:3)¼ i i i i i i (cid:3) i i i ð4Þ
i i i i i ft(cid:2)yt;xt(cid:3) ftþ1(cid:2)ytþ1;xtþ1(cid:3) ftþ1(cid:2)yt;xt(cid:3)
i i i i i i i i i
wherethefirsttermreferstothetechnicalefficiencychangeandcomparestherelative
change in technical efficiency between t and tþ1 with respect to the efficiency
frontier of the analysed unit. A value 41 indicates proximity to the production
frontier, whereas a value o1 implies divergence. The second term is a measure of
technological change or production frontier variation between the two periods
(t, tþ1), being a value 41 an indication of technological progress and a value
o1 a sign of technological recession. This way, the technical change of the sector is
reflected.
Data Professional
With the objective of evaluating the efficiency and productivity, it has been Spanish
built a panel data for 18 teams[1] taking part in ACB during the seasons 2008/2009,
basketball
2009/2010, 2010/2011 and 2011/2012. The reference database have been ACB data
statistics services which is the official web site for experts, completing with others
tools of European and American scouting[2].
The calculation of the frontier assumes that every team try to maximize their 201
production given the available inputs. The objective is to analyse the efficiency of
theteamsintheirtaskofobtainingwins,thereforetheoutputwillbethetotalnumber
of wins achieved according to Hofler and Payne (1997). Unlike the aforementioned
authors which do not consider the play-off, we take notice of during this process not
alltheteamsplaythesamenumberofgamesandthereareteamsthat,withoutvarying
their human capital, have the possibility of achieving a larger number of wins.
Duetotheneedtoanalysebothstagesasadifferentandcomplementaryoutput,itis
explained the decision of using multi-output. However, the fact that one team plays
play-off, which represents undoubtedly a sports success, does not entail necessary
an increase in its output, at the same time that it uses inputs. This fact penalizes,
from the point of view of the efficiency, teams that have achieved to complete a
remarkableregular phasequalifyingbetweeneightfirsts.Intheinterestofproviding
consistency to the study, it has been decided to increase in two the number of wins
of the eight teams in play-off, which is exactly the minimum number of extra
games they might play, avoiding this way the penalization in case of not achieving
any win. This same procedure is applied in the following qualifying rounds until
thefinals.
The selection process of inputs turns out to be the most delicate stage and at the
same time, it provides richness to the study, since they have to be consistent with
the own nature of the game and simultaneously, as anyeconomic analysis based on
production frontiers, they should help in finding reliable indicators of production
flows.Thisselectionrequiresadeepdiscussionowingtothereisnoagreementabout
quantitative and quality indicators of the basketball skills of the human capital. As
most of the sports, basketball is made of endless aspects that have influence upon
theoutcome,buttheymight notbereflectedstatistically.Butacommon aspectofall
collective sports is that the only productive factor is a group of players organized
under a style of game and other strategies introduced by a technical staff. Those
players develop a series of activities needed to achieve wins. To determine those
relevant activities it has been required theoretical foundations about the sports
discipline,whichcontribute to specify the final production function.
Apart from any proxy of the human capital (total number of player used
throughout the season), which is a production resource present in all activity,
weconsiderthatinputsinbasketballarethetotalpossessionsandthosefactorsthat
allow the teams to increase them, that is, offensive and defensive rebounds.
Fromastatisticalpointofview,whatcoachesunderstandbypossessionsistheaddition
offieldthrows(scoredormissed),receivedfaultsandturnovers.Inproductiveterms,
a possession is the opportunity used byeach team to make one basket, taking into
account that the maximum time allowed bythe sportsrules is 24seconds. Some of
these possessions finish into scored points, and those that are not, are considered
defective product, which decreases the efficiency level since it consumes inputs.
Otherwise, if two teams have achieved the same number of wins using a different
amountofpossessionsmeansthattheteamwhichgathersmorepossessions,didnot