Measuring The Productivity Of NBA Players: Applications Of Data Envelopment Analysis And Malmquist Productivity Index

Data envelopment analysis(DEA),as initially proposed,is an approach for assessing the relative efficiencies of an arrangement of homogeneous decision-making units that each decision making unit utilizes the same input and output measures.Productivity measurement is of importance for both academy and industry.An exceptionally valuable measurement for productivity evaluation in DEA is the Malmquist productivity index(MPI).The MPI calculates the relative performance of a decision-making unit at various timeframes utilizing the technology of a base period.Most studies in the MPI literature are based on constant returns to scale assumption.That means any increase in inputs results in the same proportionate increase in outputs.Some studies have also mentioned the variable returns to scale assumption allowing checking different scales,increasing,decreasing and constant returns to scale.The methodology used in this thesis is MPI based on both constant and variable return to scale.The present study aims to measure the productivity of NBA players during the 2008-2009 to 2015-2016 seasons.We will employ deterministic non-parametric frontiers.Frontier functions measure the efficiency with respect to the optimal observations and correspond to optimization processes.Deterministic non-parametric frontiers disregard a specific functional form for the frontier;they are formed through linear programming techniques,such as envelopment of observed values.Firms established within the frontier are considered efficient.The use of this type of frontier has generated the DEA methodology.The proposed approach not only reveals patterns of productivity change and presents a new interpretation along with the managerial implication of each Malmquist component but also identifies the strategy shifts of an individual DMU in a particular period.This study collects the balanced panel data of 95 players covering the 2008-2009 to 2015-2016 seasons from the NBA teams.Empirical data have been obtained from the official website(www.basketball-reference.com).Given certain data constraints,the 95 players are a small part of the total number of players in the NBA(more than 400 players comprise the NBA teams).Thus,this study focuses on the 95 NBA players for several reasons.Firstly,we have acquired the data of these players over the entire study period.Secondly,the selected players are strong representatives in investigating the productivity growth of NBA players.Finally,this sample size is computationally feasible using a PC.It was found that Total Factor Productivity index growth increases when the value of the index is higher than one whereas it decreases when the value is less than one over the period.The decomposition of the Total Factor Productivity is into technical change(TC)and technical efficiency change(TEC)has also checked.An improvement in Technical Efficiency Change is considered as a shift in the "catch-up"term,while an improvement in Technological Change is the best-practice frontier.TEC is further decomposed into scale efficiency change(SEC)and pure technical efficiency change(PTEC).This decomposition provides information on the sources of the overall productivity change of NBA players.The empirical results reveal that that in the 2008-09(1st season),2011-12,2012-13,2014-15 seasons,the average Malmqui st Index for each player in each season was superior to the unit although it was not growing,whereas in the 2nd,3rd and 6th seasons,the value was less than the unit although it was growing.These values indicate that overall NBA players have experienced improvement in productivity.Regarding the growth of technology and efficiency changes during the period examined,it was seen that there was an improvement in efficiency in 2009-10,2010-11,2011-12 and 2014-15 compared to the values of the period in 2008-09,2012-13 and 2013-14.The growth of the TC average is the inverse in practically all the examined sample.When there is Progress in TC,there is a decrease in efficiency and vice versa.The way that the MPI presented average values close to the unit when its components moved in opposite direction shows that no component prevailed in the TFP variations.By decomposing the technical efficiency change(TEC),the result showed that during the study period the NBA players had experienced mainly an increment of pure technical efficiency(improvement in management practices)rather than an improvement in optimum size.Moreover,we also divide the sample players into groups by positions following the National Basketball Association classification and by the geographical regions of the world to provide more insights into how the overall growth in TFP occurred.We find that the players at small forward position and players from other countries experienced significantly higher productivity growth on average.The research study has important implications for the coaches and managers to ponder over there attention to the important concept of players productivity to make them adoptable and adjustable.Moreover,they may improve decision-making on player selections and allocation of player positions.