Efficiency Measurement And Decomposition In Data Envelopment.Analysis

Data Envelopment Analysis(DEA)has been recognized a known methodology for evaluating the efficiency of Decision Making Units(DMUs)in a wide range of areas since it was originally developed almost four decades in the past.Earlier,performance or efficiency has been evaluated by various economic approaches,but none of these approaches were found satisfactory in measuring the efficiency and productivity in service and public sector or non-profit organizations.Presently,an excessive range of applications of DEA has been offered.These DEA applications have used DMUs in several procedures to assess the performance of units such as countries,universities,hospitals,regions,cities and business organizations as well.In the sports industry,DEA has been applied recently in measuring the efficiency of teams and players.Several DEA methodologies were developed and applied to access the performance in the sports industry.Basketball is a tactical game.Players are hired based on team needs and a player's strengths.Most of the players always try their best to contribute to their game and professional carrier during the progression of their playing and placed themselves in history.However,the most technically efficient players in basketball considering their performance in the game has not yet been recognized and accredited.In an application like NBA,we decomposed the efficiency of all-time NBA leaders into pure technical and scale efficiencies using Black box DEA models with output orientation.These models are applied to evaluate the technical and scale efficiency of all-time leaders(N=1160).The average scale efficiency(0.9326)is highest among all the three efficiencies,i.e.,technical efficiency(0.8360)and pure technical efficiencies(0.8955).The results illustrate that 81 players are scale efficient(SE=1)whereas 21%of players have a high scale efficiency score.This was also observed that most of the players are placed in high-efficiency score intervals.The scores of scale efficiency as compared to Technical and Pure technical efficiency specified the stability and high competition among the players.The results also affirm that the proportion of the players in case of scale efficiency is the maximum.Also,output projections for the inefficient DMUs were presented.Significant outcomes concerning the efficiency together with efficiency frontier projections were analyzed in this study.This feature of DEA is helpful for the future predictions of inefficient players.Conventional data envelopment analysis(DEA)models only consider the inputs provided to the system and the outputs produced from the system in measuring efficiency,ignoring the operations of the internal processes and settings of the DMUs under study.The results thus obtained sometimes are ambiguous.The issue with inefficient DMUs is of great concern that what aspects can cause the inefficiency.Sources of inefficiency can be identified by decomposing the overall efficiency in components.Efficiency decomposition empowers decision makers to recognize the stages that cause the inefficiency of the system,and to improve the performance of the system efficiently.Consistent with these perspectives,we presented the efficiency decomposition of parallel DEA models in nonhomogeneous settings.Continuing to our work,the performance of a sports player is considered an important contributing factor to the player's salary.In this research work,a systematic application procedure of several DEA models(in different versions and formulations)is demonstrated.We introduced a framework to study the relationship between the salary and efficiency of the players as NBA has been the highest paid professional sports league in the world.The salaries of the players in the sports industry are the important determinant for efficient performance in any game.The empirical literature regarding the significant variables for salary determinants is deficient in sports industry specifically the NBA.These approaches were applied to estimate the efficiency of the National Basketball Association(NBA)players.First,we present data envelopment analysis(DEA)models for a nonhomogeneous parallel network of National Basketball Association(NBA)games.To outline the relationship between salary and players'efficiency,we applied the suggested methodology to the panel data set of the NBA players from 2005-2016.The identification of variables that are most likely to contribute to NBA player efficiency and performance is also a contribution of this study.Each player consumes the minutes played as shared inputs in two parallel subsystems,namely,offensive and defensive games.The efficiency is decomposed into two subsystems.The overall efficiency of NBA players with their offensive and defensive efficiencies are evaluated.Also,the maximum and minimum of the efficiency for each subsystem have been measured.Furthermore,it was proved that these two efficiency values(maximum and minimum)are identical if and only if each of the subsystems is efficient.Results indicated that,during the last decade,the overall average efficiency of all the players is low(0.57%).Our findings suggest that,in general,there exists an increasing trend in overall efficiency,whereas mixed trends are found for offensive and defensive efficiencies.Additionally,all three efficiencies are found to have a significant association with the salary.Standardized coefficients show that offensive efficiency has a positive effect on the salary,while the defensive efficiency has a negative association with the salary and is considered the least important type.Moreover,we estimated the effect of the salary for the three efficiencies(overall,offensive and defensive)by taking only the players whose overall efficiencies are greater than the average(0.57%).Only the offensive and defensive efficiencies have a significant association with the salary.Interestingly,the defensive efficiency predictor plays the most important role compared with the offensive efficiency.The players' defensive efficiencies are only associated with the salary and the relationship between the salary,and defensive efficiency is still highly significant.In recent years,there have been some prominent sport-related subjects on the public policy plans,specifically the wages and the performance of the players.The decision-makers must address several issues to fulfilling the demands of their organization's components.This research work will be helpful in developing theoretical foundations and provides potential benefits not only for sports management practitioners but for such organizations and industries as well.