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, INDIA [email protected] http://facultylive.iimcal.ac.in/users/sanjeet

Abstract:-Data Envelopment Analysis (DEA) has been used for benchmarking and efficiency evaluation of teams in the . 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 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-

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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

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m s scores with PTE scores provides deeper insight +−  − +  ),,( minimize 0 θ ssf ),,( −= αθ  i + ∑∑ ss 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 θ i0 ∑ ijij ( ==−− L,,2,10 miswxx ) (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 ∑ rrjrj 0 ()==− L,,2,1 sryswy (2) j=1 include players annual contract amounts, wages =≥ njw 2,1(0 ),, (3) of the coaches and support staff, and other j L miscellaneous expenses. − =≥ mis 2,1(0 ),, (4) i L The approach to proxy the talent available + =≥ srs 2,1(0 ),, (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. the evaluated DMU0 cannot be lower than the The outputs include the points awarded inputs of the composite unit. Constraint (2) during the IPL 2009 session, team's total reve- shows that the outputs of DMU0 cannot be nue, profit, points awarded in the league table, higher than the outputs of composite unit. In net run rate (NRR). The chosen output variables other word, DMU0 is efficient when it is aim at capturing the outputs of professional IPL impossible to construct a composite unit that teams in a broad sense. The first two output outperforms DMU0. Conversely, if DMU0 is variables, team's total revenue and profit, reflect inefficient, the optimal values of w j form a the economic success of team including reve- nues from team sponsors, central sponsorship, composite unit outperforming DMU and 0 central broadcasting, and revenues from other providing targets for DMU0. As this optimization sources which includes In-stadia advertising, model seeks to bring inefficient DMUs to the gate receipts, merchandize sales, prize money efficient frontier by input reduction, the model is etc. The remaining output variables reflect denoted as input-oriented constant return to scale team's success on the field, determine whether a (CRS) DEA model. To get input-oriented team is qualified for the knockout rounds or not. variable return to scale (VRS) DEA model, we As these variables are based on performance of will add one additional convexity constraint players on the field, the first two variables are n to the above described model. indirectly influenced by the performance, and it ∑ w j = 1 j =1 therefore is appropriate to include such variables in the efficiency calculation. The data has been In this paper, input-oriented DEA models collected for the IPL season 2009 as this was the have been used to get the efficiency score. As- only session for which the availability of the suming CRS will reveal a DMU's global techni- required data was secured. Nevertheless, it cal efficiency (TE). In addition to this same would be valuable to have data on more than VRS model is used to evaluate the local pure one season as the stability of the results could be technical efficiency (PTE). Comparing the TE investigated.

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Table 1. Data for IPL teams in season 2009 Teams Expense Revenue Profit Points NRR Playoff ( Rs. Cr) (Rs. Cr) (Rs. Cr) 89.5 111.2 21.8 17 1.902 F 94.7 109.5 14.8 14 1.154 Champion Delhi Daredevils 84.1 107.4 23.3 20 1.262 SF Kings XI Punjab 80.5 106.6 26.1 14 0.468 BS 85 110.8 25.8 7 0.162 BS Indians 99 106 7 11 1.248 BS 71.3 106.4 35.1 13 0.599 BS Royal Challengers 99.1 107.25 8.15 16 0.76 SF Bangalore Abbreviation: F = Final; SF = Semifinal; BS = Before Semifinal

The data collected has been shown in table 1. In this the same time Deccan Charger, champion team of data it may be noted that net run rate values were IPL 2009 season, is judged as inefficient because of negative for some of the DMUs, to make them its high input and relatively low output values. usable in DEA model we have added the highest Similarly, Kolkata Knight Riders does not perform NRR (which was 0.951 for Chennai Superkings) to well on the field but its performance is mainly the net run rate of all DMUs. Last column ‘Playoff’ driven by high values of off the field outputs. in table 1 represents the playoff round in which Therefore, it is evident that off the field perform- respective team was eliminated. ance of the team also plays a crucial role in deter- mination of efficiency scores. Kings XI Punjab is 4 Analysis and results quite close to the efficient frontier but fail to actu- ally achieve it. On the other hand, a group of teams, The efficiency scores for the IPL Teams have been consisting of those with efficiency scores between calculated using DEAFrontier software [20]. The 0.78 and 0.87, are far from the efficient frontier, efficiency scores for IPL teams on constant returns and a close observation of the raw data reveals a to scale (CRS) and variable returns to scale (VRS) lack of success in the field as well as off the field in are listed in Table 2. Scale efficiency, determined generating the revenues. by CRS and VRS score, has also calculated under the column ``Scale Efficiency" of Table 2. Second When we calculate the efficiencies on variable column of the Table 2 lists the ranks of IPL teams returns to scale, the efficiency scores rise as the data in season 2009 on the basis of points table and the set is enveloped more tightly. Efficient teams under right most column reports the serial nos. and CRS remain efficient under VRS by definition. It is corresponding weights of the respective efficient interesting to see that Kolkata Knight Riders with units in the construction of composite reference unit efficiency score of 0.87 on CRS becomes perfectly when variable return to scale are used. efficient on VRS, this is because maximum value of one of its output (Revenue) among all the IPL The composite reference unit serves as the teams, forces this team to lie on the efficient projected target for the inefficient DMU and higher frontier drawn on VRS. Variability in CRS the weight value higher the weight of the j th DMU efficiency scores and Scale efficiency scores in the construction of composite reference unit. indicates that source of inefficiency for the teams is From the Table 2, we see that three IPL teams are not only the suboptimal production but also the globally technically efficient: Chennai Super Kings, teams are not perfectly efficient in transformation Delhi Daredevils, and Rajasthan Royals. The Ra- of inputs into outputs. This may be due to the jasthan Royals is efficient because it manages to variability in managerial skills employed by earn maximum profit with minimum expenses different franchise owners. among all IPL teams. Similarly, Royal Challenger Bangalore is inefficient because of very low profit and high expenses as compared to other teams. At

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Table 2. DEA Efficiency Scores with One Input and Four Outputs Team Rank CRS VRS Scale Benchmarks (DMU No.) Ac- Efficiency Efficiency Effi- DMU on VRS (weight) cording ciency To Points Table Chennai Super Kings (1) 2 1 1 1 1(1) Deccan Chargers (2) 4 0.84 0.87 0.97 1(0.496), 5(0.146), 7(0.34) Delhi Dare- devils (3) 1 1 1 1 3(1) Kings XI Punjab (4) 5 0.91 0.91 1 1(0.014), 3(0.135), 7(0.851) Kolkata Knight Rid- ers (5) 8 0.87 1 0.87 5(1) Mumbai In- dians (6) 7 0.79 0.81 0.98 1(0.498), 7(0.502) Rajasthan Royals (7) 6 1 1 1 7(1) Royal Chal- lengers Bangalore(8) 3 0.78 0.79 0.99 1(0.1), 3(0.372), 7(0.528)

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