Inernaional Journal of Spors Science 2014, 4(5): 152-164 DOI: 10.5923/j.spors.20140405.02 Improving he Tournamen Performance of ATP Players from he Perspecive of Efficiency Enhancemen Chia-Hui Tsai 1, Duen-Yian Yeh 2,*, Ching-Chyuan Chang 3 1 Spors Teaching and Research Cener, Transworld Universiy, Yunlin 640, Taiwan 2 Deparmen of Informaion Managemen, Transworld Universiy, Yunlin 640, Taiwan 3 Office of Physical Educaion Affairs, Taipei Medical Universiy, Taipei 110, Taiwan Absrac This sudy analysed efficiency changes in he ineremporal ournamen performance of ennis players in he Associaion of Tennis Professionals (ATP) and proposed improvemen suggesions o assis hese players in improving heir ournamen performance from he perspecive of efficiency enhancemen. Nine ournamen performance indices were used o evaluae he daa colleced from 45 ATP players beween 2007 and 2010. Daa envelopmen analysis approach and Malmquis producion index were adoped o deermine efficiency measures. We used a sraegic managemen map o locae he players in various characerisic groups according o heir efficiency measures and provided inefficien players wih a disincive proposal for improving heir ournamen performance. The proposal had he characerisics of benchmarking learning, hierarchy (including macro-level and micro-level) and cusomizaion (for each inefficien ATP player). Keywords Tennis, ineremporal efficiency evaluaion, Sraegic managemen map, Evaluaion index 1. Inroducion I has been well-known ha a ennis player could successfully improve his/her ournamen performance from several perspecives, including echnical skill, physiology, psychology, acics, ec. [1-7]. In pracice, ennis players who had poor rankings (or poor performance) would cusomarily ry o enhance heir experience and ranking by paricipaing in more ournamens. Thus, he achievemen of higher ATP poins or ranking migh come from he high number of ournamen paricipaion, no compleely come from he improvemen of ournamen performance. In fac, hidden in his siuaion was he perspecive of he efficiency regarding player s ournamen performance. The aemp proceeding from he managerial perspecive-efficiency enhancemen was rarely ried, bu migh be an alernaive way o improve he ournamen performance of ennis players. Acually, business enerprises have conduced efficiency enhancemen of heir saff for many years. Efficiency is defined as he comparison of wha is acually produced or performed wih wha can be achieved wih he same consumpion of resources. Efficiency enhancemen consiss of wo pars, efficiency evaluaion and performance improvemen proposal [8-9]. In pracice, mos of decision-makers wan o know how far a saff can be * Corresponding auhor: yeh@wu.edu.w (Duen-Yian Yeh) Published online a hp://journal.sapub.org/spors Copyrigh 2014 Scienific & Academic Publishing. All Righs Reserved expeced o produce or perform more oucomes wih no furher resources wased by efficiency enhancemen [10-12]. Basically, he evaluaion resuls provide he enerprise wih subsanial benefis regarding saff s job performance [8, 13]. On he oher hand, numerous sudies have explored he applicaion of efficiency evaluaions in he field of spors, for example, applicaions of evaluaing he efficiency of naions a summer Olympics [14], of major league baseball players [15], of baskeball players [16] and of professional golfers on he PGA, LPGA and SPGA ours [17-18]. In fac, among hese pas sudy works, only a few ones proposed concree suggesions regarding efficiency enhancemen for he objecs evaluaed. For example, in he research of Cooper e al. [16], one of he inefficien ceners was advised o raise he number of rebounds per game for enhancing his game efficiency and, however, anoher was advised o raise he number of free hrow goals per game. In ennis compeiion, each player will enaively employ various bale sraegies o display his srengh(s) and hide his weakness(s) and hen ry o bea his opponen. Alhough opponens may differ, each player usually follows a specific paern of bale, which is designed o make full use of his own srenghs. For his reason, idenifying he srenghs and weaknesses of ennis players is vial, paricularly for op ennis players. However, from one perspecive, he srenghs or weaknesses of a ennis player are relaive o his opponen and, accordingly, should no be idenified barely from his own raw ournamen saisics. From anoher perspecive, i is noed ha wih he raw saisics a given player canno know eiher how or how much o improve his ournamen in order o perform efficienly. For example, a given player in
Inernaional Journal of Spors Science 2014, 4(5): 152-164 153 he Associaion of Tennis Professionals (ATP)can compare himself wih Berdych regarding he maximum percenage of 1s Serve Poins Won (79%), wih Nadal regarding he maximum percenage of Break Poins Saved (70%), wih Roddick regarding he maximum percenage of firs serve (69%), wih Hewi regarding he maximum percenage of Break Poins Convered (49%), ec., bu his would mean o use as benchmark a player ha in each dimension of he game performs like he bes, which is very unrealisic and is no a feasible opion for achieving efficien performance. More specifically, in respec of ascerain exen, efficien performance is a relaive viewpoin [8, 19]. Each ennis player may have his own way o achieve he efficiency of ournamen performance. Unil recen years, efficiency evaluaion of ournamen performance was applied o appraise he ournamen saisics of professional ennis players by using several famous mehods, including saisical mehods, daa envelopmen analysis (DEA) and 2-uple fuzzy linguisic compuing model [20-24]. However, he resuls of exan lieraure have given rise o numerous issues ha require furher invesigaion. Firs, because he skills of ennis players improve or deeriorae over ime, assessing changes in ineremporal ournamen performance is essenial when conducing comprehensive efficiency evaluaions of he ournamen performance of ennis players. According o Färe, Grosskopf, Norrisand Zhang [25], he following hree efficiency measures for ennis players can be assessed based on changes in heir ineremporal ournamen performance: (1) shif in echnology (SIT), (2)caching-up in efficiency (CIE)following he player s echnical (shif) improvemen, and (3) he Malmquis produciviy index (MPI) of ineremporal ournamens. Unforunaely, invesigaions relaed o changes in he ineremporal ournamen performance of ennis players are lacking. In addiion, o improve he ournamen performance of ennis players, curren exan lieraure only provides players wih micro-perspecive daa references, for example, efficien or no and efficiency ranking. Few sudies have been conduced ha provide players wih macro-perspecive suggesions, for example, sraegic informaion and deerminans of winning. Thus, his is anoher issue requiring furher research. Using he sraegic managemen experiences of business enerprises, such as a usage of sraegic managemen maps [26], we can develop and enhance he provision of efficiency sraegies and assis ennis players in more rapidly idenifying soluions for improving heir ournamen performance. Under his conex, we endeavored o enhance he fundamenal research of ournamen performance improvemens for ennis players by analyzing he wo highlighed issues in he hopes of conribuing academically o he field of ennis and providing ennis coaches and players wih an alernaive percepion. I is well-known he ATP official webpage provides inegral saisics regarding he ournamen performance of players. Therefore, according o he previously menioned research background and moivaions, we invesigaed he single-year and ineremporal ournamen performance of ATP players respecively using he DEA approach and he MPI. Subsequenly, we used he obained resuls o formulae micro- and macro- improvemen sraegies o enhance he efficiency of ournamen performance of ATP players. 2. Lieraure Review As far as we know, he sudies regarding he ournamen performance improvemen of ennis player were quie rare. By using he daa of Wimbledon Open, Klaassen and Magnus [27] developed a model ha explores boh he quesions of wheher op ennis players in a op ournamen employed an opimal (efficien) service sraegy and wheher economic agens were successful opimizers. They found ha he answers are no posiive. Tsai [20] used he DEA and super-efficiency models o evaluae efficiency of he 2007-season ournamen performance of 50 ATP players by adoping one inpu and eigh oupu measures as evaluaion indices. The auhor conduced a series of analyses and discussions regarding he ATP players evaluaion resuls, including efficiency score, reurns of scale, peer reference, efficiency caegorizaion and grade, slack analysis, sensiiviy analysis. In addiion, many suggesions were also proposed for fuure improvemen. In Tsai & Chao [21], he auhors evaluaed he efficiency of ournamen performance of professional players of he Women's Tennis Associaion (WTA) by using he basic DEA models and six inpu and oupu evaluaion measures. Of 50 WTA players, 4 players were evaluaed o be overall efficien, 11 players o be echnical efficien and 5 players o be scale efficien. Indoor game se win raio and hree se game win raio were he wo measures ha mosly affec he performance of WTA players. In addiion, Ruiz, Pasor and Pasor [23] assessed he performance of ATP professional ennis players using DEA. In heir work, he DEA benchmarking analysis allowed idenifying srenghs and weaknesses of he game of he players and ranking he players wih help of cross-efficiency evaluaion. On he oher hand, using logisic model and longiudinal daa beween 1991 and 2008, Ma e al. [24] examined facors ha lead o winning maches in men s singles Grand Slam ennis. 16 variables were classified ino hree caegories, player skills and performance, player characerisics and mach characerisics, o predic mach oucome. In summary, hey recommended more raining in reurning skills; o avoid overesimaion of he posiive impac of saure, lef hand and professional experience; and a male player begins his professional ennis career by paricipaing in he US Open or Wimbledon. Being differen from adoping he objecive mehods in he aforemenioned sudies, Tsai [22] aemped invesigaing he ournamen performances of ATP players by using a subjecive evaluaion mehod. In her work, nine evaluaion measures, expers assessmen and2-uple fuzzy
154 Chia-Hui Tsai e al.: Improving he Tournamen Performance of ATP Players from he Perspecive of Efficiency Enhancemen linguisic compuing consiue he evaluaion model required. The wo evaluaion measures, 1sserve and 2nd serve poins won, were assessed as he key ones significanly affec he performance of ATP players. Of he 11 players evaluaed, Nadal had he bes performance, while Lu had he wors. In summary, he exan lieraure missed wo main asks, i.e., efficiency enhancemen proposal and analysis of ineremporal ournamen performance of players. Based on he consideraion ha more applicaion sudies and experiences regarding he efficiency enhancemen in he ennis field have o be coninuously accumulaed, his sudy would ry o complee hese wo asks. 3. Mehods 3.1. Research Paricipans Based on he research in Tsai [20], we seleced 45 ATP players as he sudy paricipans. The complee scores and saisical daa of hese 45 ATP players were colleced from he official ATP Webpage. We colleced daa from 2 years, specifically 2007 and 2010. The main idea was o examine he performance changes of ennis players in a hree-year period. 3.2. The DEA Approach The DEA analysis of relaive efficiency provides very useful informaion regarding he srenghs and weaknesses of each player, which may help hem o improve heir ournamen performance oward he efficien level. The DEA approach is widely employed and has he following significan characerisics [9, 28]: (1) can simulaneously process muliple inpus and oupus, faciliaing he use of various measuremen unis; (2) produces efficiency froniers and comprehensive indices insead of mean values, and can evaluae efficiencies under varying environmens; (3) he produced efficiency measures are relaive efficiency indices; hese indices show he subjec s resource usage condiions and can be provided as a reference for sraegy formulaors; (4) he weighed inpus and oupus are produced hrough linear programming and are no affeced by subjecive facors, hus, conform o fairness principles for each players evaluaed; (5) quaniaive and qualiaive facors can be simulaneously processed; and (6) daa regarding an insufficien inpu or excessive oupu of relaive inefficien measures can be provided. The wo DEA-based models used in his sudy are as follows [28-29]: 3.2.1. The Charnes, Cooper, and Rhodes (CCR) Model The DEA-based CCR model is a model ha assumes consan reurns o scale (CRS) and is used o calculae echnical efficiency (TE) measures. Farrell [30] defines he CCR model as a model ha can mainain exising producion combinaions when all inpus are reduced o he lowes raio combinaion. Tha is, when TE is 1 and all oher slack variables are 0, he player evaluaedis considered echnically efficien; conversely, when TE is less han 1, he player evaluaedis considered echnically inefficien and a porion of he inpu resources is wased. 3.2.2. The Banker, Charnes, and Cooper (BCC) Model The DEA-based BCC model is a model ha assumes he variable reurns o scale (VRS). Tha is, i loosens he CRS consrains assumed for he CCR model, changing hese assumpions o VRS and subsequenly faciliaing he measuremen of pure echnical efficiency (PTE). 3.3. The Malmquis Produciviy Index (MPI) Mehod The DEA approach can only compare he efficiencies of a single year or period, and canno longiudinally analyze efficiencies across several consecuive years. Using he exended MPI mehod, we can furher measure he changes in overall efficiency in various periods. The MPI mehod was proposed by Caves, Chrisensen and Diewer [31]. Subsequenly, Färe e al. [25] exended he MPI mehod by employing a geomeric means model as a supplemen, and esablished a DEA-based model ha could measure ineremporal efficiencies. Färe e al. [25] furher decomposed MPI ino numerous source variaions. In his sudy, we adoped he efficiency variaion model developed by Färeand Grosskopf [32] o analyze ineremporal efficiency variaions. Efficiency variaions are comparisons of changes in he producion possibiliy ses for various periods. According o he example of measuring MPI shown in Figure 1, when he producion fronier F of period shifs oward period +1 and resuls in producion fronier +1 F, he MPI would be he variaions ha lead o he relaive performance evaluaion resuls. The relevan definiions are as follows: T = { ( X, Y ) Y 0 where X 0} represens he producion possibiliy ses (wih producion variables X and Y) in period. Under he echnical condiions of CRS, he producion possibiliy ses T can be presened as follows: ( ) m, ;0 s, ; j j ji j j jk j 0, 1, P X = Y X λ X Y λ Y λ j= n i 1 k 1 = = which is he echnical variaion measuremen of a subjec (i.e., Poin A); n is he number of he players evaluaed; m and s are respecively he numbers of inpus and oupus; λ is he inensiy vecor. Iniially, he producion disance funcions for period and period +1 were defined as follows [33]: D ( X, Y ) = max Z : ZY P ( X ), Z > 0 { } { } D + 1 ( X + 1, Y + 1 ) = max Z : ZY + 1 P + 1 ( X + 1 ), Z > 0
Inernaional Journal of Spors Science 2014, 4(5): 152-164 155 { } { } D + 1( X, Y ) = max Z : ZY P + 1( X ), Z > 0 D ( X + 1, Y + 1) = max Z : ZY + 1 P ( X + 1), Z > 0 where Z is a lower bound parameer. According o he sudy by Färeand Grosskopf [32], MPI is he produc of a shif in echnology (SIT) and caching-up in efficiency (CIE). Eqns (1-3) respecively define SIT, CIE, and MPI (See Figure 1); 1. SIT is represened by he geomeric means of EG/EF and BD/BC, and is defined in eqn (1). SIT>1 represens echnical advancemen, SIT<1 represens echnical deerioraion, and SIT=1 represens invariance. In shor, SIT>1 means ha he ennis player achieved a echnology breakhrough. 1/2 1/2 1 1 1 1 BD EG + + + + D (X,Y ) D (X,Y ) BC EF + 1 + 1 D (X,Y ) D(X,Y) SIT = = (1) 2. CIE is he efficiency comparison beween he producion froniers of period and period +1, and he produced raio is he cach-up degree. CIE is defined in eqn (2). CIE>1 represens cach-up efficiency improvemen following he player s echnical (shif) improvemen, CIE<1 represens cach-up efficiency deerioraion, and CIE=1 represens cach-up efficiency invariance. + 1 BA + 1 + 1 + 1 D ( X, Y ) CIE = BD = (2) EA D ( X, Y ) EF Y 3. The ineremporal efficiency change of an individual subjec from period o period +1 should cover he echnical shif and efficiency cach-up degree facors. The produc of he wo facors is used o measure MPI. MPI>1 represens overall performance improvemen, MPI<1 represens overall performance deerioraion, and MPI=1 represens overall performance invariance. MPI = SIT CIE + 1 + 1 + 1 + 1 D ( X, Y ) D ( X, Y ) D ( X, Y ) = 1 1 + + (, ) 1 1 1 D ( X, Y ) D X Y + + + D ( X, Y ) + 1 D ( X, Y ) D ( X, Y ) = + 1 + 1 + 1 + 1 + 1 D ( X, Y ) D ( X, Y ) Supplemened wih he conceps shown in Figure 1, we can deermine ha eqns (1-3) are appropriae for calculaing ineremporal efficiency changes in any wo periods [31]. 3.4. The Sraegic Managemen Map (SMM) Referencing he imporance-performance analysis (IPA) framework proposed by Marillaand James [34], his sudy adoped he marix conceps o formulae an analyical framework wih wo dimensions. In view of heir respecive unique significance, he SIT was aken as one dimension (verical axis), while he CIEaken as he oher dimension (horizonal axis) (see Figure 2). According o he performance of hese wo ineremporal efficiencies, ennis players can be caegorized ino he four relevan quadrans o forma marix for sraegic managemen. From he resuls of his marix, we can deermine he srenghs and weaknesses of a ennis player s ineremporal efficiencies, and veriably provide improvemen suggesions a a macro-level. (3) Z + 1 Y + 1 1 Y + Z Y G F D + 1 ( X D (X,Y,Y D C ) ) D A + 1 + 1 +1 + 1 ( ( X D ( X X + 1 + 1,Y,Y,Y 1 F + + 1 + 1 F ) ) ) Y A (X,Y ) E B X Figure 1. An example of measuring MPI [32]
156 Chia-Hui Tsai e al.: Improving he Tournamen Performance of ATP Players from he Perspecive of Efficiency Enhancemen 3.5. The Inpu and oupu Evaluaion Indices Because differen evaluaion indices produce varying evaluaion resuls, follow-up analyses, suggesions, and feedback, index selecion mus be a core focus, and he seleced indices should reflec curren issues. In addiion, based on experiences of implemening efficiency evaluaions in business enerprises, he principle ha The evaluaion is according o he records has been esablished. Therefore, regarding managemen conen, he screening of indices was based on exising record sysems [10]. The evaluaion indices used in his sudy were primarily screened from he ATP Webpage. In a previous sudy, Tsai [20] adoped a rigorous screening process o obain one inpu and eigh oupu indices (game performance), which comprised he following: 1. Inpu index: he number of ATP ournamens played (Tourn Played) 2. Oupu indices: ATP poins (Poins), 1s Serve, 1s Serve Poins Won, 2nd Serve Poins Won, Break Poins Saved, 1s Serve Reurn Poins Won, 2nd Serve Reurn Poins Won, and Break Poins Convered. In he work of Tsai [20], hese evaluaion indices were esablished based on he recorded saisics of ennis players on he ATP official Webpage, and by he consideraion of oher published lieraure, he conen validiy was also esablished. In addiion, correlaion analysis was conduced o deermine indices independence, where indices such as Aces, Double Fauls, Break Poins Faced, Service Games Played, Service Games Won, Service Poins Won, Break Poins Opporuniies, Reurn Games Played, Reurn Games Won, Reurn Poins Won, Toal Poins Won, Forced Errors, and Unforced Errors were disregarded because of excessively high levels of correlaion. A significan correlaion was no observed beween he remaining nine indices. In fac, all he nine evaluaion indices have been used in he work of Ma e al. [24]. 3.6. The Mehods and Designs for Efficiency Evaluaion 3.6.1. Single-year Efficiency Evaluaion To simulae he ournamen performance of ATP players, his sudy adoped oupu-oriened CCR and BCC models o evaluae he 2010 ournamen performance daa. The evaluaion resuls included he following hree saic efficiency measures: 1. TE: Obained hrough he CCR model under he assumpion of CCR. 2. PTE: Obained hrough he BCC model under he assumpion of VCR. 3. Scale efficiency (SE): Scale-efficien (SE=1) exiss when he inpu and oupu daa vary proporionally. Conversely, scale-efficien (SE<1) does no exis when variaions are unproporional. Defined by Akison [35], TE comprises PTE and SE. Thus, SE can be obained by calculaing TE over PTE. 3.6.2. Variaion Analysis for Ineremporal Tournamen Performance To focus he analysis, his sudy only shows variaions in he ineremporal ournamen daa in2007 and2010. The MPI, CIE, and SIT measures (hereafer referred o as he hree ineremporal efficiency measures) were calculaed using eqns (1-3). 3.7. Daa Analysis Originaing from a managemen conen perspecive, we employed he following 4-level daa analysis mehod: 1. Single-year ournamen performance analysis: Discussing and analyzing he hree saic efficiency measures obained hrough he CCR and BCC models. 2. Ineremporal ournamen performance variaion analysis: Discussing and analyzing he ineremporal ournamen performance variaion daa calculaed using eqns (1-3). 3. Ploing he SMM: Because his sudy aimed o elucidae he ineremporal performance variaions of ATP players, of he hree ineremporal efficiency measures, MPI was he synergisic measure beween he oher wo measures. Thus, we regarded he SIT and CIE of he ATP players as he verical and horizonal axes, respecively. Consequenly, according o he performance resuls for hese wo measures, we ploed he ATP players in heir relevan quadrans o faciliae furher sraegy managemen proposals. 4. Hierarchical and cusomized improvemen proposals: From he resuls obained in he hird-level analysis, we formulaed and proposed macro-level (comprehensive) improvemen sraegies based on he resuls obained from he SMM. Furhermore, we provided micro-level (individual) improvemen suggesions o he comparaively weaker ATP players based on he resuls obained from he DEA model. All he proposals of ournamen performance improvemen were conduced by originaing from he perspecive of efficiency enhancemen. 4. Resuls and Discussion 4.1. Single-year Descripive Saisics Tables 1(a) and 1(b) show he descripive daa for he nine evaluaion indices of he 45 ATP players for 2007 and 2010, respecively. The saisical variables in he daa comprise he minimum (Min), maximum (Max), mean, sandard deviaion (SD), and coefficiens of variaion (CV). Only he mean of he ATP poins index in 2010 (2011.9 poins) and 2007 (1435.6 poins) differed significanly (repeaed-samples = 2.32, p =.031), achieving a growh rae of over 40%. The remaining eigh performance indices showed no significan differences.
Inernaional Journal of Spors Science 2014, 4(5): 152-164 157 4.2. The Saic Efficiency Measures and Ineremporal Efficiency Measures Table 2 shows he resuls of he hree saic efficiency measures for 2010 and he comparaive resuls of he hree ineremporal efficiency measures for 2007 and 2010 of he 45 ATP players. 4.2.1. The Three Saic Efficiency Measures for 2010 4.2.1.1. TE Table 2 shows ha only Nadal and Moya were echnically efficien, and he efficiency froniers are deermined by hese wo players. The mean value for he 45 ATP players was.5130, he sandard deviaion was.1662, and he coefficien of variance was.3240, which implies ha he TE performance of he players varied considerably. 4.2.1.2. PTE Table 2 shows ha 18 ATP players were efficien in PTE performance. The 45 ATP players exhibied a mean value of.9695, exremely close o 1. To a cerain exen, his daa se reflecs he skill level of professional ennis players. In addiion, he sandard deviaion was.0343, and he coefficien of variance was.0354. This shows an exremely small difference in PTE performance. 4.2.1.3. SE Table 2 shows ha only Nadal and Moya were scale-efficien. The mean value for he 45 ATP players was.5268, he sandard deviaion was.1598, and he coefficien of variance was.3033, which implies ha he SE performance of he players varied considerably. In summary, he PTE performance of he 45 ATP players in 2010 was more consisen and closer o efficiency. According o he definiions proposed by Akison [35], PTE represens he skill-level performance efficiency of he players. Therefore, because he 45 ATP players were op professional, consisency beween heir PTE values was a ypical resul. Subsequenly, SE and TE showed invered performance rends, ha is, inefficien players accouned for he majoriy, and efficiency measures were low and differed subsanially. Based on hese resuls, we could deermine ha he inefficiency of ATP players primarily resuled from low or no scale-efficien, which explores he phenomenon all he 43 ATP players (excluding Nadal and Moya) had an asymmeric performance beween heir game inpus and oupus. More specifically, all he 43 ATP players paricipaed in many ATP ournamens (inpu index) bu heir game performances (oupu indices) were unable o mach he upgrade. Accordingly, reducing he number of ournamens played may be he simples mehod han he upgrade in performance. Furhermore, Nadal and Moya possessed perfec performance on he hree saic efficiency performance measures and, accordingly, were he mos ousanding players in 2010. I especially deserves o be menioned ha Moya was no a op ATP player and was ranked only 507 in 2010. He achieved he efficien saus of he compeiions by means of he leas number of ournamens played (8 ournamens). Therefore, i was found ha each player has a differen way o achieve he efficiency of ournamen performance, which will depend obviously on his own characerisics or need. Table 1. Single-year performance descripive daa for he nine evaluaion indices of he 45 ATP players for 2007 and 2010 Evaluaion Indices Saisical Variables Tourn Played Poins 1s Serve (%) 1s Serve Poins Won (%) 2nd Serve Poins Won (%) Break Poins Saved (%) 1s Serve Reurn Poins Won (%) 2nd Serve Reurn Poins Won (%) Break Poins Convered (%) (a) 2007 Min 17 442 50 64 46 48 22 43 31 Max 33 7715 69 80 62 71 35 58 62 Mean 23.7 1435.6 60.2 72.4 52.2 61.6 29.8 51.1 42.2 SD 3.5 1294.3 4.5 3.9 3.3 5.0 3.5 3.3 6.4 CV 14.6% 90.2% 7.4% 5.4% 6.4% 8.1% 11.7% 6.5% 15.2% (b) 2010 Min 8 55 51 64 44 45 25 43 31 Max 34 12025 69 79 60 70 36 58 49 Mean 23.5 2011.9 60.5 72.0 51.4 61.1 29.7 50.9 40.2 SD 5.0 2282.4 4.0 3.9 3.1 5.5 2.8 2.9 4.3 CV 21.1% 113.4% 6.7% 5.4% 6.1% 9.1% 9.3% 5.7% 10.8%
158 Chia-Hui Tsai e al.: Improving he Tournamen Performance of ATP Players from he Perspecive of Efficiency Enhancemen Table 2. Saic efficiency measures for 2010 and ineremporal efficiency measures for 2007 and 2010 of he 45 ATP players The hree saic efficiency measures for 2010 The hree ineremporal efficiency measures Player TE PTE SE MPI CIE SIT Federer 0.7525 1.0000 0.7525 0.6665 0.4514 1.4765 Nadal 1.0000 1.0000 1.0000 1.0260 1.0043 1.0216 Roddick 0.6147 1.0000 0.6147 1.3712 1.6623 0.8249 Davydenko 0.5289 1.0000 0.5289 1.0122 0.9754 1.0377 Gonzalez 0.4991 0.9894 0.5044 1.0212 0.9909 1.0306 Robredo 0.3857 0.9366 0.4118 0.9322 0.9063 1.0285 Blake 0.4841 0.9420 0.5139 0.9212 0.8902 1.0349 Haas 0.6683 1.0000 0.6683 1.0217 1.0439 0.9787 Djokovic 0.7524 1.0000 0.7524 1.0623 1.0115 1.0502 Nalbandian 0.7160 1.0000 0.7160 0.3333 0.1116 2.9858 Murray 0.7768 1.0000 0.7768 1.1452 1.0505 1.0901 Ferrer 0.5541 0.9928 0.5581 0.9854 0.9568 1.0299 Berdych 0.5481 1.0000 0.5481 1.0349 1.0101 1.0245 Gasque 0.3821 0.9620 0.3972 0.9669 0.9556 1.0118 Youzhny 0.5590 0.9771 0.5721 1.0195 0.9803 1.0400 Baghdais 0.4037 0.9626 0.4194 0.9865 0.9695 1.0175 Hewi 0.5114 1.0000 0.5114 0.9778 0.9146 1.0692 Chela 0.3989 1.0000 0.3989 1.0556 1.0557 0.9999 Sepanek 0.4623 0.9403 0.4917 0.8846 0.7778 1.1374 Soderling 0.5830 1.0000 0.5830 1.0474 1.0190 1.0279 Melzer 0.4577 0.9464 0.4836 1.0381 0.9862 1.0527 Malisse 0.3867 0.9492 0.4074 0.9630 0.9526 1.0109 Moya 1.0000 1.0000 1.0000 3.2710 10.255 0.3189 Verdasco 0.4881 1.0000 0.4881 1.0636 1.0451 1.0178 Almagro 0.4008 0.9615 0.4168 1.0025 0.9869 1.0157 Acasuso 0.8543 1.0000 0.8543 1.0716 1.0993 0.9748 Simon 0.4200 0.9810 0.4281 1.0518 1.0386 1.0127 Benneeau 0.4164 0.9669 0.4307 1.0260 1.0043 1.0216 Gicquel 0.4547 0.8999 0.5053 0.9769 0.9493 1.0291 Ginepri 0.4395 0.9323 0.4714 0.9855 0.9556 1.0314 Becker 0.2976 0.9652 0.3083 0.9811 0.9686 1.0129 Mayer 0.3820 0.9267 0.4122 1.0120 0.9879 1.0243 Monfils 0.4281 0.9523 0.4495 1.0440 1.0183 1.0252 Vliegen 0.4737 0.8542 0.5546 0.9257 0.8888 1.0415 Massu 0.4039 1.0000 0.4039 1.0760 1.0581 1.0169 Clemen 0.2980 0.9221 0.3232 0.9878 0.9697 1.0187 Monaco 0.4442 1.0000 0.4442 0.9697 0.9409 1.0306 Kohlschreiber 0.4091 0.9749 0.4196 1.0597 1.0377 1.0212 Del Poro 0.6157 0.9772 0.6301 0.9995 0.9757 1.0244 Serra 0.3407 0.9335 0.3650 1.0640 1.0216 1.0415 Koubek 0.4208 0.9397 0.4478 1.0112 0.9870 1.0245 Korolev 0.4290 0.9375 0.4576 1.0357 1.0036 1.0320 Querrey 0.4659 1.0000 0.4659 0.9951 0.9645 1.0318 Gabashvili 0.3777 0.9857 0.3832 1.0351 1.0353 0.9998 Lu 0.4085 0.9196 0.4442 0.9941 0.9793 1.0151 Mean 0.5130 0.9695 0.5268 1.0469 1.1744 1.0614 SD 0.1662 0.0343 0.1598 0.3647 1.3977 0.3218 CV 0.3240 0.0354 0.3033 0.3484 1.1901 0.3032
Inernaional Journal of Spors Science 2014, 4(5): 152-164 159 4.2.2. The Three Ineremporal Efficiency Measures 4.2.2.1. SIT Overall, he mean value was 1.0614, he sandard deviaion was.3218, and he coefficien of variance was.3032. These values indicaed ha significan performance differences exised for he SIT of ATP players. Table 2 shows ha 39 ATP players achieved echnical advancemen, wih SIT measures greaer han 1. Of hese 39 players, Nalbandian scored 2.9858 for an improvemen magniude of 198.6%, followed by Federer, who scored 1.4765 for a magniude of 47.7%, and Sepanek, who scored 1.1374 and achieved a magniude of 13.7%. Conversely, six ATP players presened echnical deerioraion, wih SIT measures of less han 1. Of hese six players, Moya scored.3189 for a deerioraion magniude of 68.1%, followed by Roddick, who scored.8249 for a magniude of 17.5%. 4.2.2.2. CIE Overall, he mean value was 1.1744, he sandard deviaion was 1.3977, and he coefficien of variance was 1.1901. These resuls indicaed ha significan performance differences exised among he CIE of ATP players. Table 2 shows ha 19 ATP players achieved CIE measures greaer han 1. Of hese 19 players, Moya scored 10.2550, for an efficiency enhancemen magniude of 925.5%, followed by Roddick, who scored 1.6623 for a magniude of 66.2%. Conversely, 26 players scored CIE measures of less han 1. Of hese 26 players, Nalbandian scored 0.116, for a deerioraion magniude of 88.8%, followed by Federer, who scored 0.4514 for a magniude of 54.9%. 4.2.2.3. MPI MPI is he synergisic measure of SIT and CIE. Overall, he mean value was 1.0469, he sandard deviaion was.3647, and he coefficien of variance was.3484. These resuls indicaed ha he overall performance of he players differed significanly. Table 2 shows ha 26 players achieved an MPI measure greaer han 1. Of hese 26 players, Moya scored 3.2710, for an overall performance improvemen magniude of 227.1%, followed by Roddick, who scored 1.3712 for a magniude of 37.1%. Conversely, 19 players scored MPI measures of less han 1. Of hese 19 players, Nalbandian scored.3333, for an overall deerioraion magniude of 66.7%, followed by Federer, who scored.6665 for a magniude of 33.3%. In summary, he 45 players mean values of he hree ineremporal efficiency measures for 2007 and 2010 were greaer han 1, indicaing an overall improving condiion. However, he performance differences beween he players were considerable due o he large values of hree coefficiens of variaion. On he oher hand, regarding individual ATP players, several ATP players exhibied performance exremiies. For example, Moya showed he bes performance in CIE and MPI, and achieved efficien levels in all hree saic efficiency measures in 2010. However, he scored he wors for SIT; whereas Nalbandian exhibied he opposie performance condiion o Moya. If we were o disregard Nalbandian and Moya, and recalculae he hree ineremporal efficiency measures, we would find ha he significan differences among he players resuled from he exreme performance measures of hese wo players. In addiion, Roddick and Federer have criical ye similar performance deerioraion condiions, which confirmed he presen siuaions ha Roddick has reired and Federer has los he championshipaura. Nadal presens he bes and mos sable performance. 4.3. The Sraegic Managemen Map Figure 2 shows he disribuive resuls of he SMM for he 45 ATP players, where CIE=1 and SIT=1 were used as he horizonal and verical dividing boundaries. These boundaries divided he SMM ino four quadrans. The characerisics of he four quadrans and he number of ATP players disribued among hese quadrans are explained below. 1. Quadran I: Technical advancemen and improved CIE; he ineremporal ournamen performance of 13 ATP players was ploed in his quadran. 2. Quadran II: Technical advancemen bu deerioraing CIE; he ineremporal ournamen performance of 26 ATP players was ploed in his quadran. 3. Quadran III: Technical and CIE deerioraion; no ATP players were ploed in his quadran. 4. Quadran IV: Technical deerioraion bu improving CIE; he ineremporal ournamen performance of 6 ATP players was ploed in his quadran. Figure 3 shows he SMM for he 45 ATP players. We provided an alernaive sraegic group name o each of he four quadrans. These quadrans were named according o he performance of he CIE and SIT indices for he 45 ATP players. The relevan explanaions are as follows: 1. Quadran I: Comparing daa from 2007 and 2010, boh he SIT and CIE indices showed improving resuls. Thus, his quadran was named Peak-Period. 13 ATP players were ploed in his quadran. The seven represenaional players and heir forward ATP ranking variaions were as follows: Nadal (2-1), Djokovic (10-2), Murray (12-4), Soderling (28-5), Berdych (15-7), Verdasco (33-8), and Monfils (46-15) 1. The remaining six players presened backward ATP ranking variaions. 1 The firs number in he parenheses denoes he player s ATP rank for 2007; he second number denoes heir ATP rank for 2010.
160 Chia-Hui Tsai e al.: Improving he Tournamen Performance of ATP Players from he Perspecive of Efficiency Enhancemen Figure 2. Disribuive resuls of he sraegic managemen map for he 45 ATP players Low High CIE Pursuing-Efficiency-Growh (26 players) Peak-Period (13 players) High Ready-To-Reire (0 player) Seeking-Technology-Breakhrough (6 players) S I T Low Figure 3. The sraegic managemen map for he 45 ATP players 2. Quadran II: Comparing daa from 2007 and 2010, he SIT index showed significan improvemen. If he CIE also improves, each player in his quadran may have a Peak-Period performance in he fuure. Thus, his quadran was named Pursuing-Efficiency-Growh. 26 ATP players were ploed in his quadran. The seven represenaional players and heir improved MPI measures (MPI>1) were as follows: Davydenko (1.0122), Gonzalez (1.0212), Youzhny (1.0195), Melzer (1.0381), Almagro (1.0025), Mayer (1.0120), and Koubek (1.0112). The remaining 19 players presened deerioraing MPI measures. 3. Quadran III: Comparing daa from 2007 and 2010, boh he SIT and CIE indices showed deerioraing resuls. Thus, his quadran was named Ready-To-Reire. In his sudy, no ATP players were ploed in his quadran. 4. Quadran IV: Comparing daa from 2007 and 2010, he SIT measure shows deerioraing resuls. Players can mainain an appropriae CIE and MPI level hrough exensive ournamen experiences and hen seek echnology breakhroughs. Thus, his quadran was
Inernaional Journal of Spors Science 2014, 4(5): 152-164 161 named Seeking-Technology-Breakhrough. Six players were ploed in his quadran, all of whom presened backward ATP rankings as follows: Roddick (3-10), Haas (9-251), Chela (25-39), Moya (32-507), Acasuso (37-248), and Gabashvili (71-99). However, he MPI measures for hese players indicaed improving resuls. he players in his quadran, we found ha mos were former celebriies. Thus, we sugges adoping a sraegy where hese players can frequenly compee and obain more revenue, paricularly Roddick, who was ranked enh in he ATP rankings in 2010, which demonsraes his compeiiveness. Parially adoping improvemen sraegies may also benefi hese players comebacks. 4.4. Hierarchical and Cusomized Improvemen Proposals 4.4.1. Macro-level Improvemen Sraegy Proposals Considering he 45 ATP players ploed in he hree quadrans, we adoped sraegic managemen conceps and proposed he following improvemen sraegies: 1. For ATP players in he Peak-Period quadran: We sugges adoping ypical conservaive sraegies (paradigm proecion)and coninuing each player s curren raining program and game syle o mainain opimal condiions. The SIT and CIE performance of ATP players in his quadran improved only slighly (0%-9%), specifically Simon, Benneeau, Monfils, Kohlschreiber, Serra, and Korolev. These six players showed no efficiency for he hree saic efficiency measures for 2010 and backward ATP rankings from 2007 o 2010. Thus, he players in his quadran should aim o surpass heir personal bes o improve performance. 2. For ATP players in he Pursuing-Efficiency-Growh quadran: We sugges adoping CIE improvemen sraegies, specifically Nalbandian, Federer, and Sepanek. These hree players exhibied relaively low MPI performances and should adjus heir individual compeiion condiions. The possible plans for his quadran are explained in he following chaper. 3. For ATP players in he Seeking-Technology- Breakhrough quadran: According o previous ournamen performance resuls and ATP rankings for 4.4.2. Micro-level Inpu-oupu Performance Improvemen Suggesions This sudy proposed micro-level inpu-oupu performance improvemen suggesions o furher and more comprehensively provide improvemen plans for inefficien ATP players. This process involvedemploying 2010 daa obained from he CCR model using he DEA approach. The research paricipans were hree inefficien ATP players ploed in he various quadrans explained in he previous chaper, specifically Serra (lowes TE) in he Peak-Period quadran, Nalbandian (lowes MPI) in he Pursuing-Efficiency-Growh quadran and Haas from he Seeking-Technology-Breakhrough quadran. 4.4.2.1. Serra Table 3. Inpu-oupu performance improvemen suggesions for Serra Serra was considered a Peak-Period player, bu had he lowes TE (.3407). Table 3 shows he inpu-oupu performance improvemen suggesions for himo enhance his efficiency (TE = 1.0000). From Table 3, besides he arge ATP poin (2054 poins), which can be obained by winning good scores in maches, he remaining arge oupu values are no easy o obain (arge value = 100). As shown in Table 3, Serra should break hrough he echnology of reurn of serve. To be specific, alhough he hree oupu indices, 1s Serve Reurn Poins Won, 2nd Serve Reurn Poins Won and Break Poins Convered, belong o moderae performance, Serra should acively seek a echnology breakhrough for improve he performance in he hree indices. TE Value 0.3407 Moya s I/OE valuaion Indices Original Daa Projecion Difference % Indices Tourn Played 31 31 0 00.0% 8 Poins 700 2054 1354 193.4% 55 1s Serve (%) 60 100 40 66.6% 59 1s Serve Poins Won (%) 66 100 34 51.5% 66 2nd Serve Poins Won (%) 52 100 48 92.3% 49 Break Poins Saved (%) 62 100 38 61.3% 52 1s Serve Reurn Poins Won (%) 29 100 79 272.4% 29 2nd Serve Reurn Poins Won (%) 50 100 50 100.0% 43 Break Poins Convered (%) 43 100 57 132.6% 34 Benchmarking Players Nadal (0.0423) and Moya (0.9577)
162 Chia-Hui Tsai e al.: Improving he Tournamen Performance of ATP Players from he Perspecive of Efficiency Enhancemen On he oher hand, in he process of enhancing efficiency, he DEA model suggesed ha Serra could selec Nadal and Moyaas his benchmarking players, among whom Moya was he mos suiable learning objec. Also shown in Table 3 were he performance indices of Moya. For Serra, he performance indices of Moya were he arges easy o achieve, as compared wih he arge values of 100 s. In fac, he main consideraion involved in performance improvemen suggesion was he number reducion of ournamens played. 4.4.2.2. Nalbandian Nalbandian was considered a Pursuing-Efficiency-Grow h player. Table 4 shows he inpu-oupu performance improvemen suggesions for Nalbandian (TE=.7160) o enhance his efficiency (TE = 1.0000). Excluding he arges of four service game-relaed indices (a arge value close or equivalen o 100), he arges for he remaining hree reurn game-relaed indices are obainable. Crucially, as shown in Table 4, Nalbandian should enhance his serve echnologies or bale sraegies o improve his CIE condiions. More specifically, he should mainly improve he performance on he four oupu indices, including 1s Serve, 1s Serve Poins Won, 2nd Serve Poins Won and Break Poins Saved. In addiion, he DEA model suggesed ha Moya could be he mos suiable learning objec for him. 4.4.2.3. Haas Haas was considered a Seeking-Technology-Breakhrou gh player. His hree saic efficiency measures were TE=.6683, PTE=1.0000, and SE=.6683, while his hree ineremporal efficiency measures were MPI=1.0217, CIE=1.0439, and SIT=.9787.Table 5 shows he inpu-oupu performance improvemen suggesions for him o enhance his efficiency (TE = 1.0000). Basically, Haas had mediocre performance on he four service game-relaed indices, 1s Serve, 1s Serve Poins Won, 2nd Serve Poins Won and Break Poins Saved, while had very bad performance on he hree reurn game-relaed indices, 1s Serve Reurn Poins Won, 2nd Serve Reurn Poins Won and Break Poins Convered. Specifically, besides he arge ATP poin (277 poins), which can be obained hrough effor, he remaining arge oupu values are no easy o achieve (a arge value close or equivalen o 100). In sum, for efficien ournamen performances, Haas mus consider how o improve his overall echnology. In he process of enhancing efficiency, he DEA model suggesed ha Moya could be he mos suiable learning objec for him. Table 4. Inpu-oupu performance improvemen suggesions for Nalbandian TE Value 0.7160 I/O Evaluaion Indices Original Daa Projecion Difference % Tourn Played 17 17 0 00.0% Poins 1325 1851 526 39.7% 1s Serve (%) 58 100 42 72.4% 1s Serve Poins Won (%) 70 100 30 42.9% 2nd Serve Poins Won (%) 50 95 45 90.0% Break Poins Saved (%) 58 100 42 72.4% 1s Serve Reurn Poins Won (%) 35 56 21 60.0% 2nd Serve Reurn Poins Won (%) 58 85 27 46.6% Break Poins Convered (%) 48 67 19 39.6% Benchmarking Players Nadal (0.0758) and Moya (0.9242) Table 5. Inpu-oupu performance improvemen suggesions for Haas TE Value 0.6683 I/O Evaluaion Indices Original Daa Projecion Difference % Tourn Played 16 16 0 00.0% Poins 185 277 92 49.7% 1s Serve (%) 59 100 41 69.5% 1s Serve Poins Won (%) 71 100 30 42.9% 2nd Serve Poins Won (%) 51 100 49 96.1% Break Poins Saved (%) 62 100 38 61.3% 1s Serve Reurn Poins Won (%) 27 83 56 207.4% 2nd Serve Reurn Poins Won (%) 49 100 51 104.1% Break Poins Convered (%) 31 99 68 219.4% Benchmarking Players Nadal (0.0071) and Moya (0.9929)
Inernaional Journal of Spors Science 2014, 4(5): 152-164 163 Regarding he previous analysis, he reason ha he inpu improvemen suggesions were zero was because we adoped an oupu-oriened DEA model in his sudy. However, an analyical process similar o ha for he hree ATP players can also be employed for he remaining players, hereby cusomizing he oupu improvemen suggesions and benchmarking learning for each inefficien ATP player. 4.5. The Transformaion of Managemen and Training The inference concep of DEA approaches adops mahemaical linear programming and is par of managemen science. Specifically, he series of daa analyses conduced in his sudy originae from a managemen science perspecive. Therefore, he resuls obained from hese analyses mus be ransformed ino a raining perspecive for acual implemenaion; for example, he suggesions formulaed for Nalbandian regarding increasing his oupu indices, and hose formulaed for Serra and Haas regarding improving heir echnology of reurn of serve (he same recommendaion was also proposed for ATP players by MA e al. [24]). The mehods for ransforming hese suggesions ino acual raining aciviies o improve ournamen performance depend on he knowledge and experience of he ATP players and heir coaches. According o previous experiences, viable opions include benchmarking learning, applying spors science and compuer-aided echnology, or coach replacemen. 5. Conclusions Based on he oucomes of he above, his sudy conduced a disincive proposal for ATP players o improve heir ournamen performance from he perspecive of efficiency enhancemen. The proposal had he characerisics of hierarchy (including macro-level and micro-level), cusomizaion (for each inefficien ATP player) and benchmarking learning. In he saic efficiency analysis, reducing he number of ournamens will be he mos simple and effecive mehod for many of inefficien ATP players owards enhancing heir efficiency of ournamen performance. In he process of proposing micro-level inpu-oupu performance improvemen suggesions, many of he arge values for inefficien players regarding oupu evaluaion indices are close or equivalen o 100or he degree of effor exceeds 100%. For his group of inefficien players, he condiion of heir games indispensably needs a comprehensive exploraion, which could include echnology breakhrough and efficiency caching-up. On he oher hand, his sudy also found ha Moya was a unique ATP player by means of his own way o achieve he efficiency of performance and was a suiable learning objec. The suggesion of reducing he number of ournamens played would boher par of he coaches and players. However, his sudy emphasized ha he perspecive of efficiency enhancemen provides an alernaive opporuniy for he coaches and players o carefully consider how o improve heir ournamen performance. On he oher hand, as a benchmarking analysis model, he DEA approach was in a special posiion ha he analysis resuls obained in his sudy were expeced giving reference values only for he ATP players in his sudy. Therefore, when using he DEA approach, he arge player and his major compeiors should ogeher be included ino assessmen. In he fuure, ournamen daa for he 45ATP players afer 2010 should be coninuously recorded o invesigae and verify he long-erm ournamen resuls of hese players. Furhermore, similar ineremporal performance invesigaions can be conduced on female players of he Women s Tennis Associaion. 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