Recent Researches in Applied Mathematics and Informatics Efficiency Evaluation of Teams in IPL SANJEET SINGH Operations Management Group Indian Institute of Management Calcutta DH Road, Joka, Kolkata INDIA [email protected] http://facultylive.iimcal.ac.in/users/sanjeet Abstract:-Data Envelopment Analysis (DEA) has been used for benchmarking and efficiency evaluation of cricket teams in the Indian Premier League. Taking the data for the 2009 season, the input used by the teams is approached by the total expenses which include players' wage bill and wage of the support staff and other miscellaneous expenses. Output is measured by the points awarded, net run rate, profit and revenues. Effi- ciency scores are highly correlated with the performance in the league with a few exceptions, and when decomposing inefficiency into technical inefficiency and scale inefficiency it can be shown that the largest part of inefficiency can be explained by suboptimal scale of production and inefficient transformation of inputs into outputs. Key-Words:- DEA, Linear programming, Technical efficiency, Cricket, Indian premier league, Sports management 1 Introduction After the very successful inaugural Twenty20 level and to provide affordable family entertain- world cup cricket in South Africa in 2007, the ment. To achieve this aim, investors are entitled to popularity and economic relevance of Twenty20 hold shares of a particular team. We are, therefore, cricket has once more increased in 2008 by the dealing with entities that can be analyzed and creation of Indian Premier League (IPL), a profes- studied from the point of view of economics and sional league for Twenty20 cricket competition in are using the tools of analysis that are provided by India. The IPL was created by the Board of Con- this discipline. trol for Cricket in India (BCCI) and sanctioned by the International Cricket Council (ICC). IPL is Four years after the launch of the IPL considered to be one of the finest Twenty20 com- Twenty20 competition, time has come to evalu- petition in the world of cricket based on the lines ate the teams regarding their efficiency in terms of English Premier League (EPL) and the National of winning matches and producing the value to Basketball League (NBA). It is a very valuable their owners. Sport is not new to the mathe- product and has taken Indian cricket to a very high matical analysis [17, 18]. The efficiency of level where billions of dollars are being transacted sports teams has been measured, making use of in this event and lots of money is involved in IPL a variety of approaches and techniques (for an with big corporate and celebrities are investing in overview, see [5]) mainly focusing on the popu- this product. Its brand value was estimated to be lar U.S. team sports like baseball, hockey, and around $3.67 billion for the recently concluded basketball. Most of these studies make use of fourth season [13, 14]. IPL is a franchise based stochastic productivity and efficiency measure- competition where these franchises owns their ment methods. Such methods are based on spe- teams. Therefore, 8 franchises have been issued cific assumptions concerning the functional for the first three seasons (i.e., for the year 2008, form of the underlying production function, as- 2009, 2010) of the competition and an expansion sumptions on the distribution of the error term, to 10 teams took place for the fourth season in and a priori weighting of factors of production. 2011. Here, it may be worth noted that aim of The multitude of assumptions necessary in the BCCI, behind the launch of IPL, is not only to context of parametric and stochastic methods promote Twenty20 cricket in India but also to increases the risk of misidentification, which in create a profitable cricket league with players and turn can negatively affect the reliability of teams that are competitive on an international measurement results. In DEA no specific func- ISBN: 978-1-61804-059-6 105 Recent Researches in Applied Mathematics and Informatics tional form is required and no prior weightings has proved especially valuable in the evaluation of inputs and outputs is necessary and hence of production processes with nonmarketable offers an interesting approach for efficiency inputs or outputs and/or where correct weighting evaluation. In the context of sports, DEA has of inputs and outputs is unknown or cannot be been used by Anderson & Sharp [1] to evaluate derived [4]. As both is supposed to hold true for individual batting and running efficiency, Ja- (at least) some of the variables taken into hangir et. al. [15] to evaluate the performance of account in this article, DEA is regarded superior teams in Iranian premier football league, and by to econometric methods of efficiency Fizl & D'Itri [8] to measure individual man- measurement. Additionally, the sample is rather ager’s efficiency. small as the IPL 2009 consists of 8 teams, and in such a situation a nonparametric analysis tool In this paper, we attempt to use DEA to is superior to parametric ones where more benchmark and measure technical efficiency of observations would be required. teams in IPL. Taking the data for the 2009 season, single input is taken as the total The objective of the input-oriented DEA expenses which include players' wage bill, wage models pioneered by Charnes, Cooper and of the support staff, and other miscellaneous Rhodes [3] (also known as CCR models) is to expenses. Output is measured by points minimize inputs while satisfying at least the giv- awarded, net run rate, profit, and revenues. en output levels. These linear programming Efficiency scores are highly correlated with the models compare a test DMU (a team here) to its performance in the league with a few peers. The model searches the data set to deter- exceptions, and when decomposing inefficiency mine if some linear combination of the peer into technical inefficiency and scale inefficiency DMUs uses lower levels of inputs to produce at it can be shown that the largest part of least the level of output of the observing DMU. inefficiency can be explained by suboptimal scale of production and inefficient For each IPL team (DMU), the efficiency is transformation of inputs into outputs. measured given the 2009 season data and an This paper is organized as follows. Brief optimization will be proposed according to the description about the concepts and DEA models below indicated linear program. In DEA, the is given in Section 2. Details about the data used evaluated DMU is assigned the most favorable are presented in Section 3. Section 4, we present weighting of the inputs/outputs given the our analysis and results. The last section, i.e. constraints. The DMUs are denoted by Section 5, contains summary, some conclusions = nj .,, 2,1 Each DMU employs m inputs and suggestions for further research. L ( = L,,2,1 mi ) to produce s different 2 DEA outputs ( = L,,2,1 sr ) . Specifically, DMUj Data Envelopment Analysis (DEA) is a widely consumes amount xij of input i and produced applied non-parametric mathematical amount y of output r. It is assumed that programming approach for analyzing the rj productive efficiency of Decision Making Units xij ≥ 0 and yrj ≥ 0 and that each DMU has at (DMUs) or firms (in this paper, 8 cricket teams least one positive input and one positive output in IPL 2009 season) with the same multiple value. In DEA optimization models observed input and multiple outputs. Measurement of input and output values for all DMUs are given, efficiency of business firms is important to and a composite unit is formed with inputs shareholders, managers, and investors for any n n future course of action. Based on Farrel's[7] ∑ wx jij and outputs ∑ rj wjy for evaluated study DEA was first introduced by Charnes et. j=1 j=1 al. [3]. In recent years DEA has been applied to a wide spectrum of practical problems. For DMU0 seeking values of w j according to example, bank failure prediction [2], electric following linear programming problem (see [4]): utilities evaluation [6], commercial banks profitability [16], portfolio evaluation [19]. See Gattoufi et. al. [9, 10] for a collection of more DEA applications. Note that the DEA approach ISBN: 978-1-61804-059-6 106 Recent Researches in Applied Mathematics and Informatics m s scores with PTE scores provides deeper insight − + − + minimize f0 (θ , s , s ) =θ − α ∑si + ∑ s r into the source of inefficiency of IPL teams. i=1 r =1 3 DATA Subject to n − The data for this study has been taken from θxi0 −∑ xij w j − s i =0( i = 1,2,L , m) (1) different available and reliable sources [11,12]. j=1 n Single input considered here is total expenses + incurred by the IPL teams in 2009 season which ∑ yrj w j− s r = y r0 () r = 1,2,L , s (2) j=1 include players annual contract amounts, wages w≥0 ( j = 1,2,,) n (3) of the coaches and support staff, and other j L miscellaneous expenses. s− ≥0 ( i = 1,2,,) m (4) i L The approach to proxy the talent available s+ ≥0 ( r = 1,2,,) s (5) to a team by financial expenditures has been r L pioneered by Szymanski and Smith [18]. − Separate data for other input parameters like w denotes the weights on DMU s , and j j i rent for stadiums, travel expenses etc. would + have been of interest. These inputs have not sr are the input and output slacks and α is an infinitesimal constant. The constraint (1) implies been taken in this study due to the lack of availability and reliability of data on such that even after reduction of all inputs, inputs of parameters.