Malaya Journal of Matematik, Vol. S, No. 1, 46-56, 2021

https://doi.org/10.26637/MJMS2101/0009

Performance evaluation & rankings of players in IPL 2019 by DEA & SEM

Arijit Ghosh1, Munmun Dey2, Banhi Guha3, Subrata Jana4 and Anirban Sarkar5

Abstract The quantitative study of sports data, especially team sport is an interesting field. This paper investigates the efficiency of batsmen, bowlers and all-rounder who participated in the competition 2019. First, input data and output data were validated using Structural Equation Modeling (SEM) and then Data Envelopment Analysis (DEA), a Linear Programming (LP) based technique was used for evaluating the efficiency measurement of the batsmen, bowlers and all-rounder by ranking them on the basis of DEA Scores. The Auction Price was also taken as a parameter for evaluating the value for money spent on each player. The ranking without auction price is based solely on Cricketing parameters. Cricketing parameters along with Auction price depicts the ranking from the context of value for money. The results assist the decision makers in figuring out the position of the players on the basis of Cricketing performance as well as Cricketing return based on the money invested. This is the first study applying DEA and SEM to rank batsmen, bowlers and all-rounder in IPL 2019. This model has been validated with Structural Equation Modeling (SEM). The uniqueness of the study lies in the fact that both cricketing performance on the ground by the players and the return on money invested on those players have been taken into consideration individually and collectively for ranking. Keywords Quantitative study, Efficiency, Modeling, IPL Competition, Skill.

1 St. Xavier’s College (Autonomous), Kolkata. 2 Department of Commerce, Vivekananda Mission Mahavidyalaya, West Bengal, India. 3Amity University, Kolkata. 4Seacom Engineering College, Howrah. 5Department of Commerce & Management, West Bengal State University, Barasat. 1 [email protected]; [email protected]; [email protected]; [email protected]; 5anirban [email protected]. Article History: Received 01 December 2020; Accepted 28 January 2021 c 2021 MJM.

Contents 6.3 Analysis of Performance of All-rounder...... 54 7 Conclusions, Limitations & Future scope...... 55 1 Introduction...... 46 1.1 ICC Player Rankings...... 47 References...... 55 1.2 IPL Player Rankings...... 48 2 Literature Survey...... 48 1. Introduction 3 Novelities...... 49 Indian Premier League (IPL) is a franchise-based T-20 cricket competition launched by BCCI on 13th September, 2007 with 4 Methodology...... 49 a grandiloquent celebration in April, 2008. Lots of money, 4.1 Structural Equation Model (SEM)...... 49 big corporate and celebrities are involved in this tournament. 4.2 Data Envelopment Analysis...... 49 Eight teams play one another twice in a home and away for- 5 Data...... 50 mat. Eventually, the top ranking teams of round robin league qualify for the play offs. From the league phase the highest 6 Results & Analysis...... 51 ranking two teams play against each other, which is called first 6.1 Analysis of Performance of Batsmen...... 51 qualifying match, the winner of this match goes to the IPL 6.2 Analysis of Performance of Bowlers...... 53 final and the loser gets second chance to qualify for the IPL Performance evaluation & rankings of players in IPL 2019 by DEA & SEM — 47/56

final by playing another match called second qualifier. From • The level of run-scoring in the match- If both teams league phase the 3rd and 4th team play against each other score 500runs in respective innings, then the computer and the winner plays the loser of the first qualifying match. rates it as a high scoring match, and hence 100 runs Eventually in the IPL final match the two winners from the scored by a player in this innings is worth lesser than second and the first qualifying match play the final and the 100 runs scored in a low scoring match in which both winner receives the IPL trophy. teams score just 150 runs. Similarly, if a team scores The IPL auction is a gala event every year garnering a lot of 500runs in the first innings and 200runs in the second enthusiasm among the worldwide cricket fans. Each of the innings, a century in the second innings will get more eight teams is given a budget of Rs.85 crore to complete their credit than in the first innings as the general level of run squads with a maximum of 25 players including a maximum scoring was higher in the first innings. of 8 overseas players. Before the auction begins, the teams are given an opportunity to retain the players from last season. • The result of the match- If a player has scored more The budget that remains after the retention process is then runs in a match, in which his team wins then he gets spent in the auction. A team can retain a maximum of five bonus points. Further, bonus points will be more if players through a combination of pre-auction retention and the victory is against a strong team. For example, win ‘Right To Match’ (RTM) Cards. A maximum of three capped bonus against the present Australian team is higher than India players and two capped overseas players can be retained the bonus against Bangladesh team. by each team. The RTM allows a player’s previous team • Out or -A not out innings receives a bonus as in to match any winning bid for the player that they have just Test match matter more than in ODI. released. Often teams releases a player with the intention of signing him back at a cheaper price using a ‘Right To Match’ • At which juncture the runs are scored- If a player score card. runs when his team is in crisis, then player gets more The players that go under the hammer are first grouped by rating points. their specialty into categories of batsmen, all-rounder, - keepers, fast bowlers and spinners who are auctioned sepa- For a bowler, the factors that are important to decide his rately. Players who sign up for the auction, set their base price, ranking include: and are bought by the highest bidder. The unsold players go • Wickets taken and runs conceded. back and can be brought back in the final phase of the auc- tions if the franchises want them. Final unsold players at the • Ratings of the batsmen dismissed- For example, at auction are eligible to be signed up as replacement signings present Kohli holds the number one rank in the Test, so either before or during the tournament. his wicket will carry more rating points to bowlers than the wicket of Jaspreet Bumrah. 1.1 ICC Player Rankings • The level of run-scoring in the match- Consider in an in- The ICC Player Rankings uses a complicated moving average nings, the Australian team has scored 350 runs and Bhu- where the players are rated on a scale of 0 to 1000 points. vneshwar Kumar took three wickets for 50 runs (3-50) If a player’s performance improves over his past record, his and in another innings, Australian team scored 180 runs points increase and if his performance declines against his and Hardik Pandya took 3-50. So Bhuvneshwar Ku- past accomplishment he loses his points. The value of each mar will get more rating points than Pandya because he player’s performance within every match is calculated using has conceded 50 runs in a high scoring match whereas a pre-programmed algorithm, based on objective evaluation Pandya has spent 50 runs in a low scoring match of just of various circumstances in the match. The Test ratings are 180 runs. updated within 12 hours after each Test match and ODI ratings are updated at the end of each ODI series. Each individual • Heavy workload - bowlers who bowl a large number player’s performance is given a different score for every single of overs in the match get some credit for the heavy match. workload, even if they take no wickets; Test Match Rankings • The result of the match-Bowlers who take a lot of wick- For a batsman, the following factors are considered while ets in a match in which his team wins, receive a bonus. calculating the total points: That bonus will be higher if it is against a highly rated • Runs scored i.e., more runs means more bonus points opposition teams. • Bowlers who do not bowl in a high-scoring innings are • Strength of the opposing bowling attack- the higher the penalized. combined ratings of the opposition’s bowling attack, proportionately more value is given to the batsman’s The players’ ratings are calculated by combining their weighted innings. performance in the latest match with their previous rating.

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This new ‘weighted average’ is then converted into points. points for each player will be calculated. However, there is Though recent accomplishments have more weightage than lack of evidence on selection of the few chosen parameters earlier performances in his career, all his performances are and the basis of determination of the points allocated for each taken into account while calculating the rating points. Players parameters. Hence, there is a need to devise a simplified and who miss a Test match for their country, for whatever reason, logical model for ranking the performance of the cricketers lose one per cent of their points. in the IPL. The model suggested in this paper is a simplified New players start at zero points, and need to establish them- structure for measuring the player’s performance in one of the selves before they get full ratings. For example, a batsman biggest league of the sub-continent. who has played 10 Test innings gets 70 per cent of his rating (i.e. his rating will be between 0 and 700 points). He gets 100 2. Literature Survey per cent only after he has played 40 Test innings. Similarly, a bowler who has taken 30 wickets also gets 70 per cent of his Kimber and Hansford (1993) analyzed batting in cricket sta- full rating. He gets 100 per cent only after he has taken 100 tistically. This study was expended by Barr and Kantor (2004) Test wickets. This means that successful new players need to by suggesting a method to compare and select batsmen in play a considerable number of test matches to be counted in cricket. Swartz et al. (2006) projected a simulation procedure the world top five. for optimal batting order in One Day Cricket. This work was expanded by Swartz et al. (2009) by modeling and simula- One-Day Rankings tion for one day cricket. Karnik (2009) derived the hedonic The objectives behind the ODI Ratings are similar to the Test price equations to estimate a bid price for all the cricketers Ratings, with the following significant differences: in the Indian Premier League (IPL) auction. He proposed a • Batsmen gain bonus for rapid scoring. Unlike test price model using the data from the 2008 season and fruitfully matches they do not get much credit for being not out as tested next to the data from the 2009 season. The variables a not out batsman is, by definition, batting at the latter in the equations were the regular playing factors such as runs part of the innings when the value of his wicket is low scored, wickets taken and age. Van Staden (2009) proposed a graphical technique for comparison of cricketers’ bowling • Bowlers gain bonus for economy. A bowler who con- and batting performances. Singh (2011) made an effort for cedes just 26 runs in 10 overs will have his rating measuring the performance of teams in the IPL using DEA. improve significantly, even though he hasn’t taken a He took both playing and non-playing factors to analyze the wicket. efficiencies of the teams in 2009 season. Lenten et al. (2012) used various playing and non-playing factors of the athletes • Unlike test match, players lose only a half per cent of cricket sport that determine their biding value in the auc- (1/2%) of their points for missing a match for their tion of IPL. Sharma (2013) applied Factor Analysis approach country. All ODI matches are given equal weights, in performance measurement of T20 cricket. Gholam et al. except for ICC Cricket World Cup matches, where good (2014) applied DEA for cricket team selection. Sankaran S performances earn bonus points. (2014) explored the association between player performance • Big scores or wicket hauls against very weak teams get and valuation. He developed a new performance metrics and much less credit than the same performances against applied K-means cluster analysis to identify distinct groups of the strong ODI teams. bowlers. Lin et al. (2016) applied window analysis technique of Data Envelopment Analysis (DEA) on Chinese Profes- 1.2 IPL Player Rankings sional Baseball League teams to measure offense, defense and We can see that the ICC cricket ranking is a complex and integrated efficiency from 2007 to 2014. Zambom-Ferraresi rigorous ranking structure with varied weightage given to et al. (2015) applied DEA to measure technical efficiency of the different circumstances of each match. The ICC does teams UEFA Champions League. Choudhury et al. (2019) not consider the IPL performance in calculating the ranking used DEA model to select Cricketers for Indian Cricket team. points. In IPL, the Most Valuable Player Award is given to In 1918, Wright used the first application of path analysis, the player who contributes most to his team in all the areas which modeled the bone size of rabbits. Pearl (1998) argues like batting, bowling and fielding. The parameters taken into that SEM allows us to test out theories with non-experimental consideration for calculation of the players points are number data under the assumption that a causal model is true. Accord- of 4s and 6s hit, number of wickets taken, number of dot ing the Ullman (2006), SEM is used to estimate the population balls bowled, number of catches taken or stumping done by covariance matrix and then compare the estimated population each player. The points added to the player for this award covariance matrix with the sample covariance matrix. If these are: 2.5 points will be given for each four 3.5 points will be two matrices turn out to be similar, it means that the structural given for each six 3.5 points will be given for each wicket model best fits with the data. Hershberger 2003 explored the taken 1 point for each dot ball bowled by a player 2.5 points growth of SEM. Manhas 2013 studied the role of SEM in the- for each catch or stumping by a player After adding all the ory testing. Teo T 2010 applied path analysis in educational points from the above aspects from every match, the total context. Lemmer et al. 2013 discussed techniques for team

48 Performance evaluation & rankings of players in IPL 2019 by DEA & SEM — 49/56 selection after short cricket series. De Stobbeleir et al. (2011) 4. Methodology studied the complex relationship among variables. Saikia et al. (2019) has summarized the application of Statistics and In this research DEA has been carried out to find out the Data Mining based noteworthy works on various dimensions most efficient IPL batsman, bowler and all-rounder and then of cricketing data. ranking them keeping in mind the auction price and other attributes. The validity of inputs and outputs in DEA has been carried out using SEM in two stages, first the validity of inputs 3. Novelities and outputs was checked, whether the research can be carried Cricket is an important component of entertainment in India as out with the chosen inputs and output, and secondly, validity well as the rest of the cricket playing countries. It is generally of efficiency, which was found out from DEA, was checked agreed that the main roles of cricketers are batting and bowl- with the chosen sets of inputs and outputs of the production ing. Various parameters may be used to rank the players. The using SEM. most frequent parameters are batting average, striking rate for batsmen and Economy rate, number of wickets for bowlers. 4.1 Structural Equation Model (SEM) All rounder are also gaining importance in this new format SEM is a statistical modeling technique which is used for of the game. Hence we cannot overlook their performance confirmation of research model through fit statistics. In other in both these areas. The ranking method used by ICC is too words, researchers use this technique to validate their con- sophisticated and that used by IPL is unscientific. Hence there struct by using statistical technique using structural equation is a need to develop a ranking method that can be applied model having a structure of the covariance between observed with ease to scientifically rank the players as per the important variable. cricketing parameters. In our study CB-SEM was used using AMOS. Firstly, inputs & Structure of the paper: outputs have been validated and then the structured model was validated taking the efficiency score, which is found out from DEA, with the available inputs and output of the proposed study. In SEM, validation means fitting the proposed model to the data which involves solving sets of equations. Here convenient framework was developed for a statistical test and compared with the tabulated results to validate the model. CB-SEM has different goodness of fit like Hoelter, Parsimony- Adjusted Measures, AIC, etc., which are some functions of the chi-square and degree of freedom. Using SEM in research, the testing of the model is authenticated by data, based on path significance values (Hair et al. 2006).

4.2 Data Envelopment Analysis Data Envelopment Analysis (DEA), is a linear programming (LP) based technique to measure the relative performance of Decision-Making Units (DMU) in the presence of multiple inputs and outputs. In 1978, DEA was developed by Charnes, Cooper and Rhodes, following works by George Bernard Dantzig in 1951 and Farrell in 1957. The popularity of DEA is due to its ability for measuring efficiencies of multiple-input Figure 1. Flow chart for the proposed study and multiple-output DMUS. Mathematical model of DEA Here Structural Equation Modeling (SEM) has been used The input-oriented measurement of technical efficiency of a to validate the input output model and subsequently Data firm under VRS requires the solution of the following LPP Envelopment Analysis (DEA) has been applied to rank the due to Banker, Charnes, Cooper in1984. In the input oriented players. DEA has become a well-liked performance measure- model we try to minimize the inputs while maintaining the ment for peer evaluation. In this paper efficiency estimation same level of outputs. An efficient firm is one in which the of the batsmen, bowlers and all-rounder in IPL 2019 has been inputs cannot be minimized further. However, an inefficient done using DEA & SEM. This paper is the first of its kind firm is one in which there is still scope of further decreasing since validation has been done using SEM. The paper is also the inputs for the same level of outputs.Ghosh et al. (2014) first of its kind to rank the players based on auction values. It applied DEA super efficiency model for efficiency measure- helps to evaluate whether the performance of the players is at ment in Indian automobile companies. par with the money that has been invested on them. Minθ j

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Subject to be calculated by using the above input oriented linear pro- gramming. The process is repeated p times to calculate the p operational efficiency scores of all DMU’s. The input and ∑ λ jxm j ≤ θx jm;(m = 1,2,3,...1),( j = 1,2,3,...p) j=1 output weights selected such that it maximises the efficiency ∞ value. In general, a DMU is considered efficient, if it scores a ∑ λ jym j ≥ y jm;i( m = 1,2,3,...k),(j = 1,2,3,...n) value 1, otherwise it is inefficient. j=1 p 5. Data ∑ λ j = 1; j=1 The data of IPL 2019 for this study has been taken mainly

λ1 ≥ 0( j = 1,2,3,...,p) from www.iplt20.com. The data for batsmen who have played minimum 10 matches & scored minimum 100 runs were con- Assume a set of p DMU’s, such as: DMU1,DMU2,...,DMUp. sidered. So the total number of batsmen taken into considera- Every DMUj,( j = 1,2,..., p), produces k outputs y jm(m = tion is 43. The data for bowlers who have played minimum 10 1,2,...,k) by the xm j(m = 1,2,...,l). Suppose the input matches & taken minimum 5 wickets has been taken for this weights use of l inputs and output weights are denoted as analysis. So the total number of bowlers taken into considera- λ j( j = 1,2,..., p). The efficiency of individual DMUj can tion is 32.

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6. Results & Analysis

6.1 Analysis of Performance of Batsmen The figure-1 shows the path diagram of the model with auction price for the batsmen The figure-2 shows the path diagram of the model without auction price for the batsmen From the table 4. it is clearly evident that the goodness of fit statistics is within the tolerance limit (p ¿ 0.05) and statistically insignificant, i.e. the proposed model fits the data. Goodness of Fit Index (GFI) which is the measure of fit be- tween the proposed model and the observed covariance matrix is above the recommended value of 0.85 hence it indicates that the proposed model is the best fit. Normed fit index (NFI) is the difference between the null model’s chi-square and the proposed model’s chi-square, divided by the null model’s chi- square and Comparative fit index (CFI) compares the fit of the

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rate despite being hugely low on the Auction Price. Shane Watson has been given the lowest rank since he has a very poor batting average of 23 in 14 matches played. Suresh Raina is also placed lower down the list due to a terrible batting average of 24. Hardik Pandhya has been given the 16th rank on the basis of runs scored by IPL ratings. In our analysis he has received the 1st place because along with scoring 402 runs, he has the highest strike rate of 191.42. David Warner being the winner of the orange cap has a strike rate of 143.86 and an average of 69.20. MS. Dhoni has the highest batting average of 83.20 with 416 runs and strike rate of 134.62. Though he has a rank of 13 in the list of batting leaders, he has secured the 1st position in our analysis. This shows that our analysis is a holistic one which focuses on every aspect of the batting performance and not only on runs scored. proposed model to the fit of independent or null model.NFI Table 6: Batsmen Ranking according to DEA Score and CFI in baseline comparisons are also greater than the considering Auction Price recommended value of 0.9. Hoelter at 5% and 1% values are also greater than the number of DMU’s(Decision making Unit) i.e. 43. This suggests that the efficiency values are being validated. Table 5: Batsmen Ranking according to DEA Score without considering Auction Price

Table 6 depicts the ranking of batsmen based on Auction Price (Cr), No of Matches played, the total number of runs scored, the highest runs scored by batsman, batting average, and Strike Rate. Hardik Pandya, M.S.Dhoni, Ravindra Jadeja, David Warner, Jonny Bairstow, Dinesh Karthik, , , Mandeep Singh, David Miller, Moeen Ali, ranked high for their all round batting performance and rea- Table 5 depicts the ranking of batsmen considering No of sonable valuation. They have the same efficiency score hence, Matches played, the total number of runs scored, the highest the same ranks. Similarly, equality of ranks has been done for runs scored by batsman, batting average, and Strike Rate all such cases. without considering Auction Price (Cr). Interestingly, the ranks are toppled as we include auction Hardik Pandya, M.S.Dhoni, , David Warner, Jonny Bairstow, price into the analysis. David Warner, Hardik Pandhya and Andre Russell, David Miller, Marcus Stoinis ranked high MS. Dhoni continue to enjoy the 1st position due to their according to this analysis and have the same rank. Their superior performance justifying the high auction price claimed efficiency score is the same hence the ranks are the same. by them. The highest paid player of IPL2019, Similarly equality of ranks has to be done for all such cases. with a whooping Rs. 17Cr auction price is pushed to the 17th has a higher rank as compared to Shreyas position from the previously enjoyed 8th position as he too has Iyer since the former has great batting average and strike failed to justify his auction price with superior performance.

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On the other hand, Ravinder Jadeja who had a performance rank of 15 moves up to secure the 1st position with an auction price of Rs. 7Cr. Moen Ali with a pay packet of only Rs.1.7Cr has scored 220 runs for his side with a strike rate of 165.41. Moreover, Pollard with 4th rank has performed exceptionally well at Rs.5.4Cr. with a performance rank of 15 in table 5. On the other hand, being the highest paid oversees batsman in our list has been pushed down from the 4th to the 14th rank because his strike rate and batting average are lower than all others in his price bracket. Ambati Rayudu continue with the low rank as at rs.2.2 Crores, he has a poor batting average of 24 only.

6.2 Analysis of Performance of Bowlers The figure-3 shows the path diagram of the model for the bowlers with Auction Price of balls bowled per wicket taken i.e. Strike rate; without considering the Auction Price. Table 8: Bowlers Ranking according to DEA Score without Auction Price

Kagiso Rabada secured the first rank. Besides, Ravindra Jadeja, Rashid Khan, Shreyas Gopal, Deepak Chahar and Imran Tahir are the top 5 bowlers due to their overall excellent performance. Among them, Imran Tahir was the winner of the purple cap with the highest number of wickets of 26. In our analysis due importance have been given to all aspects of the bowling performance including average, strike rate and economy rate. Hence, we find that not Imran Tahir, but Rabada, has secured the 1st position due to the best and bowling strike rate. The figure-4 shows the path diagram of the model for the Interestingly, among spinners, Ravichandran Ashwin with 15 bowlers without Auction Price wickets has the 8th rank whereas Ravindra Jadeja with same From the table 7. it is clearly evident that the goodness of fit number of wickets has the 3rd rank. The superior rank of statistics is within the tolerance limit (p ¿ 0.05) and statistically Jadeja is attributable to a better bowling average and better insignificant, i.e. the proposed model fits the data. economy rate. Similarly among fast bowlers, Mohammed This ranking of bowlers depicted in table 8 is based only Shami has a rank of 13 and Jasprit Bumrah has secured a on Cricketing parameters, No of Matches played; The number rank of 7, though both have taken 19 wickets each. Hence, of balls bowled; The number of runs conceded; The number we may conclude that wicket taking is an important but not of wickets taken; The average number of runs conceded per the sole consideration for judging the bowler’s performance. wicket i.e. Bowling average; The average number of runs Dhawal Kurkarni and has the lowest ranks due to only 6 conceded per over i.e. Economy rate; The average number wickets taken and a high bowling average and high strike rate.

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Jaydev Unadkat with 10 wickets has got the 21st rank as he has a very high bowling average. Table 9: Bowlers Ranking according to DEA Score with Auction Price

Table 9 depicts the ranking of bowlers based on Auction Price (Cr); No of Matches played; The number of balls bowled; The number of runs conceded; The number of wickets taken; The average number of runs conceded per wicket i.e. Bowling average; The average number of runs conceded per over i.e. Economy rate; The average number of balls bowled per wicket taken i.e. Strike rate. Shreyas Gopal with his twenty wickets haul and better econ- omy rate has surpassed Rabada (Auction Price of Rs.4.2 Cr.) to secure the 1st position due to a very low auction price of Rs.0.2 Cr.. Efficiency score is the same for few players hence they been given the same ranks. Equality of ranks has to be done for all such cases. with 10 wickets has the lowest rank as his overall performance does not commen- surate the high auction price. In fact there was a lot of buzz after Unadkat, being an uncapped player bagged a whopping Rs.8.4 Cr. in the auction. Hardik Pandhya with the highest auction price of Rs. 11 Cr. has a rank of 16 which clearly highlights his poor performance. Bhuvaneswar Kumar and Sunil Narine both auctioned for Rs. 8.5 Cr. and have secured 17th and 18th rank respectively due to their not so impressive performance. Table 11: All rounder Ranking according to DEA Score 6.3 Analysis of Performance of All-rounder without Auction Price The figure-5 shows the path diagram of the model for the bowlers with Auction Price The figure-6 shows the path diagram of the model for the all-rounders without Auction Price From the above table it is clearly evident that the goodness of fit statistics is within the tolerance limit (p ¿ 0.05) and statistically insignificant, i.e. the proposed model fits the data. This ranking depicted in table 11of all rounders is based only on Cricketing parameters, No of Matches played; The average number of runs conceded per wicket i.e. Bowling average; The average number of balls bowled per wicket taken i.e. Strike rate; batting average and Strike Rate without considering the Auction Price.

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Andre Russell, Kagiso Rabada and Shreyas Gopal have 7. Conclusions, Limitations & Future received the 1st rank based on their overall excellent perfor- scope mance in both the areas of bowling and batting. Andre Russell has secured the 1st rank among batsmen and with a bowling In this research paper, SEM and DEA have been applied to average of 26 and 11 wickets, he was impressive with the measure the efficiency of batsmen, bowlers and all-rounder ball too. Russell was the top most player in the IPL players’ participating in the Indian Premier League 2019. Cricketing points table with 369 points. Hardik Pandhya with 342 points parameters along with auction price depicts the ranking from closely follows Russell and in our analysis too he has secured the context of value for money. The ranking without auction a high rank of 4 due to his all round performance. Ravinder price is based solely on Cricketing parameters. Since the Jadeja with 3rd rank among the bowlers had done well with a ranking of Players in IPL is done using an unsophisticated batting average of 35 and strike rate of 120.45, thus enabling method, the analysis based on DEA will provide greater clarity him to be ranked 2nd among the all-rounder. Sunil Narine and and a scientific base to the ranking of players in IPL. The though reckoned as best All-rounder in the ranking used by ICC is again too complicated to be applied in world arena have failed to impress with 16th and 17th rank a sub-continental tournament. respectively. Bravo has a batting average of 16 and Narine has The inputs and outputs included in the study are exten- a poor batting average of 18 only and a high bowling average sively researched. Though the analysis has been conducted of 35. on a small sample of players to show its efficacy, it can be Table 12: All rounders Ranking according to DEA easily extended to the entire set of players if required. The Score with Auction Price ranking with only cricketing parameters changes after inclu- sion of auction price as an input, highlighting the importance of performance to commensurate the money being paid. It is obvious to expect superior performance from highly paid players and hence their ranking falls when they fail to perform as par excellence. On the other hand the ranking of low paid players improve when they perform beyond expectation. This ranking will help team owners in identifying utility of players and formulate strategy for the next season auction. However, choice of inputs and outputs affects efficiency sores. We have set a filter to short-list the players who have been included in the study. A study with different sets of play- ers may be undertaken. We can further extend the analysis to measure the performance of overseas players and domestic players separately. The study covers the IPL 2019 data only. We can extend the study to compare the players’ performance Table 12 denotes the ranking of all-rounder is based on, No in different seasons of the tournament. A continuous assess- of Matches played; the average number of runs conceded ment across seasons will enable to provide due importance to per wicket i.e. bowling average; the average number of balls past performance in the analysis. Window analysis & compar- bowled per wicket taken i.e. Strike rate; batting average and ative analysis of each player assuming each year as a separate Strike Rate along with considering the Auction Price. Andre Decision Making Unit can be done in the future. Russell continues to enjoy the 1st rank after including auction price into the analysis. His performance has commensurate the auction price of Rs.7 Crore. Sreyas Gopal with an impres- References sive bowling average of 17.35 has secured the first position [1] Banker, R. D., Charnes, A., & Cooper, W. W., Some mod- with fees of only Rs.0.2 Crore. Hardik Pandhya has been els for estimating technical and scale inefficiencies in data pushed to the 6th position after including auction price. This envelopment analysis. Management science, 30(9)(1984), highlights that a better performance was expected from him 1078-1092. against the payment of Rs.11 Crores. Krunal Pandhya has [2] Barr, G. D. I., & Kantor, B. S., A criterion for comparing also not performed well with Rs.8.8 Crores. He has a poor and selecting batsmen in limited overs cricket. Journal of batting average of 17. Bravo and Narine with high auction the Operational Research Society, 55(12)(2004), 1266- prices have disappointing performances. The highest paid 1274. all-rounder, at Rs.12.5 Crores has secured the [3] Chames, A., Cooper, W. W., & Rhodes, E., Measuring 10th rank with poor batting and bowling averages of 20.5 and the efficiency of decision making units. European journal 31.5 respectively. of operational research, 2(6)(1978), 429-444. [4] Chaudhary, R., Bhardwaj, S., & Lakra, S., A DEA Model for Selection of Indian Cricket Team Players. In 2019

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