Optimization Model IPL using DEA

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Optimization Model

Model: DEA

Measurement of efficiency of IPL teams of all three

seasons.

Submitted by: Akshat Gupta

Roll Number: 09DM011



Table of Contents

1. IPL ( Introduction)1.1. First Season

1.2. Second Season

1.3. Third Season

2. The Teams

2.1. Performance of teams (Analysis)

3. Introduction to DEA

4. Objective of the Report

5. Methodology

6. Calculations

6.1. Calculation of Team Ratings

6.2. Calculation of Net Run Rate

6.3. Calculation of Primal Efficiency

6.4. Dual Mode

6.5. Variable Slack

7. Conclusions

8. Bibliography



IPL: Indi n Premier League

The Indian Premier League (of ten abbreviated as IPL), is a domesti professional Twent cr icket competition in India. It was initiated by the Board of Control for Cr icket in India (BCCI) headquar tered in Mumbai and supervised by BCCI Vice

President Chirayu Amin, chairman & commissioner for IPL, and C O, Sundar R aman. It presently includes 10 teams (franchises) consisting of players fromdifferent countr ies. It was star ted af ter an altercation between the BCCI and the Indian Cr icket League.

In 2010, IPL became the f irst spor ting event ever to be broadcast live on the popular video shar ing website YouTube. Its brand value was estimated to be around$4.13 billion (over 18,000 crore (US$4.05 billion)) the same year. According toglobal spor ts salar ies review, IPL is the second highest- paid league, based on f irst-team salar ies on a pro rata basis, second only to the NBA. It is estimated that theaverage salary of an IPL player over a year would be £2.5 million.

First season

The inaugural season of the tournament star ted on 18 Apr il 2008 and lasted for 4days with 59 matches scheduled, out of which 58 took place and 1 was washed out due to rain. The f inal was played in DY Patil Stadium, Nerul, and Navi Mumbai.Every team played each other both at home and away in a round robin system. The topfour rank ing sides progressed to the knockout stage of semi-f inals followed by a f inal.

R ajasthan R oyals defeated Chennai Super K ings in a last ball thr iller and emerged asthe inaugural IPL champions.



Second Season

The venue was shifted to South Africa. The format of the tournament remained same

as the inaugural one. Deccan Chargers, who finished last in the first season, came out

as eventual winners defeating the Royal Challengers Bangalore in the final.

Relocating the tournament posed extreme logistical challenges for the BCCI sincemore than 10,000 cricketers and other staff members needed to be flown from India to

South Africa within a span of a few weeks. The IPL in jected approximately US$100

million into South Africa's local economy. In addition, the BCCI signed a Rs. 8,200

crores (US$1.63 billion) contract with Multi Screen Media to broadcast matches live

from South Africa to India.

Third Season

The third season opened in January 2010 with the auction for players. 66 players wereon offer but only 11 players were sold. Four teams qualified for the semi finals. The

first semi final was won by Mumbai Indians who defeated Bangalore Royal

Challengers by 35 runs. Chennai Super Kings defeated Deccan Chargers in the second

semi final. The final was played between Chennai Super Kings and Mumbai Indians.

Chennai Super Kings won by a margin of 22 runs.



The Teams

Performance of Teams



DEA

Data envelopment analysis (DEA) is a nonparametric method in operations research

and economics for the estimation of production frontiers. It is used to empiricallymeasure productive efficiency of decision making units (or DMUs). Non parametric

approaches have the benefit of not assuming a particular functional form/shape for thefrontier; however they do not provide a general relationship (equation) relating outputand input. There are also parametric approaches which are used for the estimation of

production frontiers. These require that the shape of the frontier be guessed beforehand by specifying a particular function relating output to input. ne can alsocombine the relative strengths from each of these approaches in a hybrid methodwhere the frontier units are first identified by DEA and then a smooth surface is fittedto these. This allows a best practice relationship between multiple outputs andmultiple inputs to be estimated.

"The framework has been adapted from multi input, multi output production functions

and applied in many industries. DEA develops a function whose form is determined by the most efficient producers. This method differs from the rdinary Least Squares( LS) statistical technique that bases comparisons relative to an average producer.Like Stochastic Frontier Analysis (SFA), DEA identifies a "frontier" on which therelative performance of all utilities in the sample can be compared: DEA benchmarksfirms only against the best producers. It can be characterized as an extreme pointmethod that assumes that if a firm can produce a certain level of output utilizingspecific input levels, another firm of equal scale should be capable of doing the same.The most efficient producers can form a 'composite producer', allowing thecomputation of an efficient solution for every level of input or output. Where there isno actual corresponding firm, 'virtual producers' are identified to make comparisons"(Berg 2010).

Data envelopment analysis (DEA) is a linear programming methodology to measurethe efficiency of multiple decision making units (DMUs) when the production process

presents a structure of multiple inputs and outputs.

Some of the advantages of DEA are:

y no need to explicitly specify a mathematical form for the production functiony proven to be useful in uncovering relationships that remain hidden for other

methodologiesy capable of handling multiple inputs and outputsy capable of being used with any input output measurementy the sources of inefficiency can be analysed and quantified for every evaluated

unit



Objective of the Report

The prime ob jective of this report is to measure the efficiency of each IPL team¶s

performance on the basis:

Input Data

y Matches Played

y Matches Won

y Net Run Rate (Runs/over scored ± Runs/over conceded)

Output Data

y Team Ratings

This research can be used to

y Calculate odds of one team against the other and can be used for betting on

mathematical grounds.

y To measure the performance of one team against the other.

y To improve the rankings of a team on the basis of input factors.

For more accurate measurement of performance data like Batting average, bowling

average, individual players output with respect to money invested on that player can be considered as input data.

Here to explain the few factors through which performance can be measured, I have

taken into account only 3 input data and 1 output data.

Methodology

The data is a secondary data available on IPL¶s website. Team¶s ratings have been

calculated as per ICC¶s norm of calculation of ratings in a multi tournament involving

more than 4 teams. In this case I have taken the ratings calculation based on World

Cup ratings system as it involves 8 teams. Also the ratings have been measured over

the period of all three seasons with a team playing a maximum of 47 matches and a

minimum of 42 matches.



Calculation of Team Ratings (Output)

As the data for team¶s rating was unavailable on the website, the rating is calculated

on the basis of ICC¶s world cup rating system

y For every match won a team gets 2 points.y If a team wins in a semi final it gets 4 times the 2 points in addition to the 2

points it won for winning a match. If it does not win a semi final it does not get

any point.

y If a team wins the final it gets 6 times the 2 points in addition to the 2 points it

won for winning a match. If it does not win the final it gets 2 times the 2 points.

Calculation of Net Run Rate (Input)

Net run rate is a simple process. It is the total runs scored by the team in all the

matches divided by the total number of over¶s it took in all the matches subtracted by

the total runs it conceded divided in all the matches divided by the total number of

over¶s it bowled in all the matches.

The table below shows the input in red and output in dark blue.

Here we can see that ratings of Delhi Daredevils (DD) and Royal Challengers

Bangalore (RCB) are same despite of huge difference in their net run rate.



Calculation of efficiency (Primal)

Below I have given an example of Chennai Super Kings efficency.

v1, v2, v3 are the inputs and u is the output

Its efficiency is 96.91%. This shows that the output ratings of Chennai Super Kings is

less and the matches they won against the matches they played. The net run rate does

not play a role in their ratings.

b jective Function is the ratings (output) that is 4.7 and Z is the sumproduct of the

ob jective function and the inputs and outputs.

Changing cells of the solution are the input coefficients.

Likewise for other teams it is calculated on the excel sheet.



Dual Model

This is done to find how the efficiency on one team is affected by the performance of

other teams.

In the above example what we see is that Chennai Super Kings has to keep Ra jasthan

Royal and Kolkatta Knight Riders as their benchmark for efficiency

Similarly,

Deccan Chargers: Ra jasthan Royals & KKR

Mumbai Indians: Ra jasthan Royals & KKR

Delhi Dare Devils: Ra jasthan Royals, KKR & RCB

Kings XI Punjab: Ra jasthan Royals, KKR & RCB



Slack

In this what we can see is that output slack is s4, and is always zero for all the cases

Whereas, in the input the slack is non negative. Now the input when multiplied by

efficiency subtracted by the slack gives us the figure of appropriate amount of input

that should exist to make the efficiency 100%.

This is done to check back in the primal efficiency is coming correct or not. Slack will

show how much to reduce it by so that the efficiency will become 100%. In the case

of CSK the Matches played f reduced to 40 and matches won reduced to 19 or 20 and

run rate even if dipped to as low as 0.6 will bring up their efficiency to 100%

Similarly it can be done for the rest of the teams too.



Conclusion

It has been noted that how the input factors affect the efficiency of a team and slack

helps to determine what is extra in those inputs. Now in the case of games played, the

matches played and won cannot be reduced, but the efficiency can be increased by

varying the net run rate and the winning rate of the team.

Further, in the research by taking into account the batting and bowling average as

inputs we can determine efficiency with team ratings as output. This can help in

calculating accurate odds of a team against another, and can be used in betting on

games.

Bibliographyhttp://www.iplt 20.com/stats.php

http://www.deazone.com/t utorial/index.htm

http://www.icc-cricket.com/icc/handbook/ 2005-06 /Pages-7 3-80.pdf

http://en.wikipedia.org/wiki/Ipl

http://en.wikipedia.org/wiki/ 2008_Indian_Premier_Leag ue

http://en.wikipedia.org/wiki/ 2009 _Indian_Premier_Leag ue

http://en.wikipedia.org/wiki/ 2010 _Indian_Premier_Leag ue

http://en.wikipedia.org/wiki/Data_en velopment_analysis

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Optimization Model IPL using DEA