Munich Personal RePEc Archive Evaluating professional tennis players’ career performance: A Data Envelopment Analysis approach Halkos, George and Tzeremes, Nickolaos University of Thessaly, Department of Economics September 2012 Online at https://mpra.ub.uni-muenchen.de/41516/ MPRA Paper No. 41516, posted 24 Sep 2012 20:02 UTC Evaluating professional tennis players‘ career performance: A Data Envelopment Analysis approach By George E. Halkos and Nickolaos G. zeremes University of Thessaly, Department of Economics, Korai 43, 38333, Volos, Greece Abstract This paper by applying a sporting pro uction function evaluates 229 professional tennis players$ career performance. By applying Data Envelopment Analysis (DEA) the paper pro uces a unifie measure of nine performance in icators into a single career performance in ex. In a ition bootstrap techni,ues have been applie for bias correction an the construction of confi ence intervals of the efficiency estimates. The results reveal a highly competitive environment among the tennis players with thirty nine tennis players appearing to be efficient. Keywords: .rofessional tennis players/ Data Envelopment Analysis/ 0port pro uction function/ Bootstrapping. %EL classification: 114' 129' 383. 1 1. Introduction The economic theory behin sporting activity is base on the wor4 of Rottenberg (1952). 7owever, 0cully (1984) was the first to apply a pro uction function in or er to provi e empirical evi ence for the performance of baseball players. 0ince then several scholars have use frontier pro uction function in or er to measure teams$ performance an which has been escribe on the wor4s of 9a4, 7uang an 0iegfrie (1989), .orter an 0cully (1982) an :izel an D$Itri (1992, 1998). 0imilarly, Dawson, Dobson an Gerrar (2000a) applie stochastic frontier approach (0:A), measuring managers$ efficiency for a panel of managers in English :ootball (soccer) .remier league. The stu y by 7aas (2003a) was one of the first stu ies which applie ata envelopment analysis (DEA) in or er to measure team efficiency of twenty English .remier 3eague clubs. More recently, Barros an 3each (2002a, 2002b, 2008) applie a stochastic 1obb-Douglas pro uction frontier an DEA in or er to measure the performance of football clubs in the English :.A. .remier 3eague. Even though several stu ies have use DEA metho ology to evaluate mostly football teams$ efficiency levels, there are not any stu ies proposing a similar pro uction function approach for evaluating professional tennis players$ efficiency levels. Recently a stu y by R?mon, Ruiz an 0irvent (2012) propose a DEA mo el with no inputs an a common set of weights in or er to evaluate professional tennis players$ efficiency levels. In contrast to the pre-mentione stu y this stu y uses a sports pro uction function approach in a DEA framewor4 in or er to evaluate 229 professional tennis players$ career efficiency levels. In that respect our paper 2 contributes to the existing literature by provi ing a DEA base multi-criteria in icator of tennis players$ performance evaluation. The structure of our paper is the following. 0ections two an three present respectively a brief literature review an the ata an the metho ology a opte in the stu y respectively. 0ection four iscusses the erive empirical results, whereas the last section conclu es the paper. 2. Literature review The pro uction function in professional team sports is base on full technical efficiency in a sense that output can be maximize given a level of inputs or the inputs can be minimize given a set of outputs1. 7owever, accor ing to Dawson, Dobson an Gerrar (2000b) professional teams are not behaving as profit maximisers ue to the existence of principal-agent relationships an therefore, fail to minimize costs an thus to be technical efficient. Accor ing to Rottenberg (1952) the @pro uctA in sporting pro uction function is the a mission revenue generate by the sporting contest but, accor ing to Dawson, Dobson an Gerrar (2000b) the mo eling i ea of treating revenues as an output have not been supporte by researchers in the fiel of sport economics. 7owever, 0cully$s (1984) specification of treating as input in ivi ual players performance an team performance as output became an acceptable mo eling strategy of the sporting pro uction function. Accor ing to Dawson, Dobson an Gerrar (2000a, 2000b) there are two important limitations for the stu ies following this approach. :irst, the use of O30 regression analysis represents the average efficiency rather than the absolute creating 1 :or an extensive analysis an literature review of sports pro uction function see Dawson, Dobson an Gerrar (2000b) an 3ee an Berri (2008). 3 several measurement problems for policy evaluation2. 0econ ly, 0cully$s pro uction function exclu es the impact of coaches which accor ing to several stu ies play a maCor role of teams$ performance (9ech, 1981/ 1armichael D Thomas, 1995). 7owever, to our opinion still there are other aspects affecting irectly teams$ performance an can not be capture ue to lac4 of information. These may well be the history of the team, the spirit or other capital an labor relate factors such as the physiatrists, octors, training staff, training centers an their explicit personnel, youth aca emies an their personnel, etc. 0everal stu ies have applie efficiency analysis on sport teams$ performances3. Though the economic framewor4 of professional sporting activity is base on the wor4s of Rottenberg (1952), Eeale (1924), Fones (1929) an 0loane (1929, 1981, 1982). In a ition the first empirical evi ence in an average pro uction function framewor4 was foun in the wor4 of 0cully (1984) who investigate the performance of baseball players. By using the percentage of matches won in or er to mo el teams$ output an management, capital an team spirit as inputs, 0cully$s empirical wor4 was the first to apply a pro uction function in or er to provi e empirical evi ence. The sporting pro uction process has been mo ele by several others in a similar way (among others 9ech, 1981/ At4inson, 0tanley D Tschirart 1988/ 0chofiel , 1988). The application of frontier pro uction function in or er to measure teams$ performance has been ate bac4 on the wor4s of 9a4, 7uang an 0iegfrie (1989), .orter an 0cully (1982) an :izel an D$Itri (1992, 1998). A itionally, over the last 2 Dawson, Dobson an Gerrar (2000b) suggest that stochastic frontier approach (0:A) is more suitable for measuring teams$ performance compare to O30 approach. 7owever as note by 3ee an Berri (2008) the time-varying stochastic frontier mo els with the i entical temporal pattern assumption cannot be use in the analysis of team efficiency in sports. 3 :or a literature review on the subCect matter see Barros an Garcia- el-Barrio (2008). 4 two eca es several scholars have been applying parametric an nonparametric frontier analysis to establish football teams$ performance an their eterminants. Dawson, Dobson an Gerrar (2000a), applying stochastic frontier approach (0:A), measure managers$ efficiency for a panel of managers in English soccer$s .remier league using as output the percentage of matches won an as inputs several player ,uality variables, for the time perio of 1992 to 1998. 7aas (2003b) applie a ata envelopment analysis (DEA) measuring team efficiency of the U0A MaCor 3eague 0occer (M30). In a DEA setting an for the year 2000, 7aas use hea coaches$ an players$ wages as inputs an revenues, points awar e an number of spectators as outputs. In a ition 7aas (2003a) in a similar DEA setting performe an efficiency analysis for twenty English .remier 3eague clubs for the year 2000-2001. :urthermore, Barros an 3each (2002a, 2002b, 2008) applying a stochastic 1obb-Douglas pro uction frontier an DEA measure the performance of football clubs in the English :.A. .remier 3eague for the time perio s 1989-1990 to 2002-2003. They applie a combination of sport an financial ata in or er to measure football clubs$ efficiency levels. :ric4 an 0immons (2008) by applying 0:A on ata for German premier soccer league (Bun esliga) showe that managerial compensation impact positively on team success. In a ition using the recent evelopments of efficiency measurement Barros, Assaf an 0?-Earp (2010) by applying 0imar an Gilson$s (2008) DEA bootstrap proce ure analyze the performance of the Brazilian first league football clubs. 0imilarly, Barros an Garcia- el-Barrio (2011) measure the efficiency of the 0panish football clubs for the seasons 1992H1998 an 2003H2004 by applying the two-stage proce ure (0imar D Gilson, 2008). 5 In terms of professional tennis relate stu ies, several of them have concentrate on pre icting tennis matches$ outcomes. :or instance, el 1orral an .rieto-Ro rIguez (2010) by estimating probit mo els an applying bootstrapping techni,ues using Gran 0lam tennis match ata from 2005 to 2008 test whether the ifferences in ran4ings between in ivi ual players are goo pre ictors for Gran 0lam tennis outcomes. 0everal other pre icting mo els for tennis matches outcomes have been also presente over the years (Boulier D 0te4ler, 1999/ 1lar4e D Dyte, 2000/ Klaassen D Magnus, 2003/ 0cheibehenne D Bro er, 2008/ Mc7ale D Morton, 2011). Moreover, in a ifferent stu y 1oate an Robbins (2001) haven$t foun any evi ence that top-ran4e male tennis professionals are more e icate to their careers compare to the top-ran4e female professionals. In a ition Goznia4 (2012) by using ata from the International Tennis :e eration (IT:) provi es evi ence that gen er ifferences are smaller in a very competitive setting an that the effects of previous performance are epen ent on gen er an the time the previous competition too4 place.