American Journal of Oper ations Research, 2011, 1, 180-184
doi:10.4236/ajor.2011.13020 Published Online September 2011 (http://www.SciRP.org/journal/ajor)
Measuring the Performance of Teams in the
Indian Premier League
Sanjeet Singh
Operations Management Gr o up, Indian Institute of Management Calcu tta, Kolkata, India
Received July 2, 2011; revised July 26, 2011; accepted August 17, 2011
Abstract
In this paper, using the Data Envelopment Analysis (DEA), we have measured the technical efficiency 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-
iency scores are highly correlated with the performance in the league with a few exception, and when de-
composing 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 ineffficient transformation of inputs
into outputs.
Keywords: DEA, Linear Programming, Technical Efficiency, Cricket, Indian Premier League, Sports
Management
1. Introduction
After the very successful inaugural Twenty20 world cup
cricket in South Africa in 2007, the popularity and eco-
nomic relevance of Twenty20 cricket has once more in-
creased in 2008 by the cr eatio n of In dian Pre mier Leagu e
(IPL), a professional league for Twenty20 cricket com-
petition in India. The IPL was created by the Board of
Control for Cricket in India (BCCI) and sanctioned by
the International Cricket Council (ICC). IPL is consid-
ered to be one of the finest Twenty20 competition in the
world of cricket based on the lines of English Premier
League (EPL) and the National Basketball League
(NBA). It is a very valuable product and has taken Indian
cricket to a very high level where billions of dollars are
being transacted in this event and lots of money is in-
volved in IPL with big corporates and celebraties are
investing in this product. Its brand value was estimated
to be around $3.67 billion for the recently concluded
fourth season [1,2]. IPL is a franchise based competition
where these franchises own their teams. Therefore, 8
franchises have been issued for the first three seasons
(i.e., for the year 2008, 2009, 2010) of the competition
and an expansion to 10 teams took place for the fourth
season in 2011. Here, it may be worth noted that aim of
BCCI, behind the launch of IPL, is not only to promote
Twenty20 cricket in India but also to create a profitable
cricket league with players and teams that are competi-
tive on an international level and to provide affordable
family entertainment. To achieve this aim, investors are
entitled to hold shares of a particular team. We are,
therefore, dealing with entities that can be analyzed and
studied from the point of view of economics and are us-
ing the tools of analysis that are provided by this disci-
pline.
Four years after the launch of the IPL Twenty20 com-
petition, time has come to evaluate the teams regarding
their efficiency in terms of winning matches and pro-
ducing the value to their owners. Sports is not new to the
mathematical analysis [3,4]. The efficiency of sports
teams has been measured, making use of a variety of
approaches and techniques (for an overview, see [5])
mainly focusing on the popular U.S. team sports like
baseball, hockey, and basketball. Most of these studies
make use of stochastic productivity and efficiency meas-
urement methods. Such methods are based on specific
assumptions concerning the functional form of the un-
derlying production function, assumptions on the distri-
bution of the error term, and a priori weighting of factors
of production. The multitude of assumptions necessary in
the context of parametric and stochastic methods in-
creases the risk of misidentification, which in turn can

S. SINGH
181
negatively affect the reliability of measurement results.
In DEA no specific functional form is required and no
prior weighings of inputs and outputs is necessary and
hence offers an interesting approach for efficiency evalua-
tion. In the context of sports, DEA has been used by
Anderson & Sharp [6] to evaluate individual batting and
running efficiency, Jahangir et al. [7] to evaluate the
performance of teams in Iranian premier football league,
and by Fizl & D’Itri [8] to measure individual managers
efficiency.
In this paper, we attempt to use DEA to measure tech-
nical efficiency of teams in IPL. Taking the data for the
2009 season, single input is taken as the total expenses
which include players’ wage bill, wage of the support
staff, and other miscellaneous expenses. Output is meas-
ured by points awarded, net run rate, profit, and revenues.
Efficiency scores are highly correlated with the per-
formance 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 and
outputs.
This paper is organized as follows. Brief description
about the concepts and DEA models is given in Section 2.
Details about the data used are presented in Section 3.
Section 4, we present our analysis and results. The last
section, i.e. Section 5, contains summary, some conclu-
sions and suggestions for further research.
2. DEA
Data Envelopment Analysis (DEA) is a widely applied
non-parametric mathematical programming approach for
analyzing the productive efficiency of Decision Making
Units (DMUs) or firms (in this paper, 8 cricket teams in
IPL 2009 season) with the same multiple input and mul-
tiple outputs. Measurement of efficiency of business
firms is important to shareholders, managers, and inves-
tors for any future course of action. Based on Farrel’s [9]
study DEA was first introduced by Charnes et al. [10]. In
recent years DEA has been applied to a wide spectrum of
practical problems. For example, bank failure prediction
[11], electric utilities evaluation [12], commercial banks
profitability [13], portfolio evaluation [14]. See Gattoufi
et al. [15,16] for a collection of more DEA applications.
Note that the DEA approach has proved especially valu-
able in the evaluation of production processes with non-
marketable inputs or outputs and/or where correct weight-
ing of inputs and outputs is unknown or cannot be de-
rived [17]. As both is supposed to hold true for (at least)
some of the variables taken into account in this article,
DEA is regarded superior to econometric methods of
efficiency measurement. Additionally, the sample is
rather small as the IPL 2009 consists of 8 teams, and in
such a situation a non parametric analysis tool is superior
to parametric ones where more observations would be
required.
The objective of the input-oriented DEA model (also
known as CCR models) is to minimize inputs while sat-
isfying at least the given output levels. These linear pro-
gramming models compare a test DMU (a team here) to
its peers. The model searches the data set to determine if
some linear combination of the peer DMUs uses lower
levels of inputs to produce at least the level of output of
the observing DMU.
For each IPL team (DMU), the efficiency is measured
given the 2009 season data and an optimization will be
proposed according to the below indicated linear pro-
gram. In DEA, the evaluated DMU is assigned the most
favorable weighting of the inputs/outputs given the con-
straints. The DMUs are denoted by Each
DMU employs m inputs 1,2,, .jn


,m1, 2,i to produce s
different outputs


, ,1, 2rs. Specifically, DMUj
consumes amount ij
x
of input i and produced amount
rj of output r. It is assumed that and
and that each DMU has at least one positive input and
one positive output value. In DEA optimization models
observed input and output values for all DMUs are given,
y0
ij
xy0
rj 
and a composite unit is formed with inputs 1
n
ij j
j
x
w

 and
outputs for evaluated DMU0 seeking values
1
n
rj j
j
yw


of
j
w according to following linear programming prob-
lem (see [17]):

011
minimize ,,ms
ir
ir
f
sss s 




 





Subject to

0101,2,,
n
iijji
j
x
xw sim 



 (1)

0
11, 2,,
n
rj jrr
j
ywsy rs


 


(2)


01,2,,
j
wjn (3)


01,2,,
i
s
i
m (4)


01,2,,
r
s
r
s (5)
j
w denotes the weights on DMUj i
s
, and r
s

are the
input and output slacks and

is an infinitesimal con-
stant. The constraint (2) implies that even after reduction
of all inputs, inputs of the evaluated DMU0 can not be
lower than the inputs of the composite unit. Constraint (3)

S. SINGH
182
shows that the outputs of DMU0 can not be higher than
the outputs of composite unit. In other words, DMU0 is
efficient when it is impossible to construct a composite
unit that outperforms DMU0. Conversely, if DMU0 is
inefficient, the optimal values of
j
w
1
j
form a composite
unit outperforming DMU0 and providing targets for
DMU0. As this optimization model seeks to bring ineffi-
cient DMUs to the efficient frontier by input reduction,
the model is denoted as input-oriented constant return to
scale (CRS) DEA model. To get input-oriented variable
return to scale (VRS) DEA model, we will add one addi-
tional convexity constraint to the above de-
scribed model.
1
n
j
w


In this paper, input-oriented DEA models have been
used to get the efficiency score. Assuming CRS will re-
veal a DMU’s global technical efficiency (TE). In addi-
tion to this same VRS model is used to evalu ate the local
pure technical efficiency (PTE). Comparing the TE
scores with PTE scores provides deeper insight into the
source of inefficiency of IPL teams.
3. DATA
The data for this study has been taken from different
available and reliable sources [18,19]. Single input con-
sidered here is total expenses incurred by the IPL teams
in 2009 season which include players annual contract
amounts, wages of the coaches and support staff, and
other miscellaneous expenses. The approach to proxy the
talent available to a team by financial expenditures has
been pioneered by Szymanski and Smith [4]. Separate
data for other input parameters like rent for stadiums,
travel expenses etc. would have been of interest. These
inputs have not been taken in this study due to the lack of
availability and reliability of data on such parame ters.
The outputs include the points awarded during the IPL
2009 session, team’s total revenue, profit, points awarded
in the league table, net run rate (NRR). The chosen out-
put variables aim at capturing the outputs of professional
IPL teams in a broad sense. The first two output vari-
ables, team’s total revenue and profit, reflect the eco-
nomic success of team including revenues from team
sponsors, central sponsorship, central broadcasting, and
revenues from other sources which includes In-stadia
advertising, gate receipts, merchandize sales, prize money
etc. The remaining output variables reflect team’s suc-
cess on the field, determine whether a team is qualified
for the knockout rounds or not. As these variables are
based on performance of players on the field, the first
two variables are indirectly influenced by the perform-
ance, and it therefore is appropriate to include such vari-
ables in the efficiency calculation.
The data has been collected for the IPL season 2009 as
this was the only session for which the availability of the
required data was secured. Nevertheless, it would be
valuable to have data on more than one season as the
stability of the results could be investigated. The data
collected has been shown in Table 1. In this data it may
be noted that net run rate values were negative for some
of the DMUs, to make them usable in DEA model we
have added the highest NRR (which was 0.951 for chen-
nai Superkings) to the net run rate of all DMUs. Last
column “Playoff” in Table 1 represents the playoff
round in which respective team was eliminated.
4. Analysis and Results
The efficiency scores for the IPL Teams have been calcu-
lated using DEAFrontier software [20]. The efficiency
scores for IPL teams on constant returns to scale (CRS) and
variable returns to scale (VRS) are listed in Table 2. Scale
efficiency, determined by CRS and VRS score, has also
calculated under the column “Scale Efficiency” of Table 2.
Table 1. Data for IPL teams in season 2009.
Teams Expense (Rs. Cr)Revenue (Rs. Cr)Profit (Rs. Cr) Points NRR Playoff
Chennai Super Kings 89.5 111.2 21.8 17 1.902 F
Deccan Chargers 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
Kolkata Knight Riders 85 110.8 25.8 7 0.162 BS
Mumbai Indians 99 106 7 11 1.248 BS
Rajsthan Royals 71.3 106.4 35.1 13 0.599 BS
Royal Challengers Bangalore 99.1 107.25 8.15 16 0.76 SF
Abbreviation: F = Final; SF = Semifinal; BS = Before Semifinal.

S. SINGH
183
Table 2. DEA efficiency score s with one input and four outputs.
Team (DMU No.) Rank According To
Points Table CRS EfficiencyVRS EfficiencyScale Efficiency Benchmarks DMUonVRS (weight)
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 Daredevils (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 Riders (5) 8 0.87 1 0.87 5(1)
Mumbai Indians (6) 7 0.79 0.81 0.98 1(0.498), 7(0.502)
Rajsthan Royals (7) 6 1 1 1 7(1)
Royal Challengers
Bangalore (8) 3 0.78 0.79 0.99 1(0.1), 3(0.372), 7(0.528)
Second column of the Table 2 lists the ranks of IPL
teams in season 2009 on the basis of points table and the
right most column reports the serial nos. and corre-
sponding weights of the respective efficient units in the
construction of composite reference unit when variable
return to scale is used. The composite reference unit
serves as the projected target for the inefficient DMU
and higher the weight value higher the weight of the
DMU in the construction of composite reference unit.
th
j
From the Table 2, we see that three IPL teams are
globally technically efficient: Chennai Super Kings, Delhi
Daredevils, and Rajsthan Royals. The Rajsthan Royals is
efficient because it manages to earn maximum profit
with minimum expenses among all IPL teams. Similarly,
Royal Challenger Bangalore is inefficient because of
very low profit and high expenses as compared to other
teams. At the same time Deccan Charger, champion team
of IPL 2009 season, is judged as inefficient because of its
high input and relatively low output values. Similarly,
Kolkata Knight Riders does not perform well on the field
but its performance is mainly driven by high values of
off the field outputs. Therefore, it is evident that off the
field performance of the team also play a crucial role in
determination of efficiency scores. Kings XI Punjab is
quite close to the efficient frontier but fail to actually
achieve it. On the other hand, a group of teams, consist-
ing of those with efficiency scores between 0.78 and 0.87,
are far from the efficient frontier, and a close observation
of the raw data reveals a lack of success in the field as
well as off the field in generating the revenues.
When we calculate the efficiencies on variable returns
to scale, the efficiency scores rise as the data set is en-
veloped more tightly. Efficient teams under CRS remain
efficient under VRS by definition. It is interesting to see
that Kolkata Knight Riders with efficiency score of 0.87
on CRS becomes perfectly efficient on VRS, this is be-
cause maximum value of one of its output (Revenue)
among all the IPL teams, forces this team to lie on the
efficient frontier drawn on VRS. Variability in CRS effi-
ciency scores and Scale efficiency scores indicates that
source of inefficiency for the teams is not only the
suboptimal production but also the teams are not per-
fectly efficient in transformation of inputs into outputs.
This may be due to the variability in managerial skills
employed by different franchise owners.
5. Conclusions
In this paper, we have used DEA to evaluate the effi-
ciency of teams in the IPL which was founded in 2008.
Taking the data from 2009 season, paper tries to analyze
the efficiency using playing and non playing factors as
inputs and outputs. Because on the constraint on avail-
ability of the reliable data for other inputs and outputs
such as no. of spectators, wages of the head coach and
support staff etc. stability of the results could not be
checked for different combina tions of inputs and outputs.
6. Acknowledgements
Author expresses his sincere thanks for the unknown
reviewers.
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