Feature Short
Total Page：16
File Type：pdf, Size：1020Kb
Feature Short GANGAN PRATHAP UMBAI Indians won the Indian Premier Again, this year, there were nine teams 76 matches were played, but not all teams MLeague (IPL) for the first time. Were they to start with, but now Sunrisers Hyderabad played the same number of matches. To also the best team? In our July 2011 and replaced Deccan Chargers. Thus, as before, find the “best” team in the tournament we July 2012 issues of Science Reporter, we there was a full blown double round-robin shall use the same mathematical algorithm confirmed that Chennai Super Kings really tournament with a total of 72 matches, and again. deserved to win at IPL-4, and that Kolkata the four best teams at the end of this stage Knight Riders towered over the rest of the went into the playoff rounds to identify the On the night of 19 May competition at IPL-5 2012. two teams that would meet in the final. In all, 2013, each team had played the other twice, for a total of 72 matches. SCIENCE REPORTER, JULY 2013 36 Short Feature In all, 76 matches were played, Table 1: Weighted Score Rankings at the end of the 72 matches, but not all teams played the same as on 19 May 2013 number of matches. To find the Team Raw Weighted Matches Exergy “best” team in the tournament we Score Score Played shall use the same mathematical Mumbai Indians 22 23.24 16 33.77 algorithm again. Chennai Super Kings 22 21.53 16 28.97 Rajasthan Royals 20 20.54 16 26.37 Last year, on the night of 20 May 2012, when each team had played the Sunrisers Hyderabad 20 18.94 16 22.42 other twice, for a total of 72 matches, Delhi Royal Challengers Bangalore 18 17.98 16 20.21 Daredevils topped the league. This year, Kings XI Punjab 16 14.48 16 13.10 they were right at the bottom. And the winner last year, Kolkata Knight Riders did Kolkata Knight Riders 12 12.38 16 9.58 not make the cut at all, being third from the Pune Warriors India 8 8.63 16 4.65 bottom. What a reversal of fortunes! Delhi Daredevils 6 6.29 16 2.47 As before we use the Kendall-Wei scheme for tournament ranking [T.H. Wei, Total 144 144 144 161.52 The algebraic foundations of ranking theory, Cambridge University Press, London, 1952] Table 2: Exergy Rankings at the end of the 76 matches, [M.G. Kendall, Further contributions to the as on 26 May 2013 theory of paired comparisons, Biometrics 11 (1955), p. 43]. This is a process of recursive Team Raw Weighted Matches Exergy iteration; points are to be given according Score Score Played to the strengths of the team beaten. Since Mumbai Indians 26 28.45 19 42.60 this cannot be known beforehand, the raw Chennai Super Kings 24 23.81 18 31.49 scores are improved until the weighted scores are obtained, and at each stage, Rajasthan Royals 22 22.43 18 27.96 the “strength” of the team is revised until a Royal Challengers Bangalore 18 17.95 16 20.15 stable, converged value is reached. Sunrisers Hyderabad 20 18.47 17 20.08 The IPL organizers however continue to use the row-sum procedure to rank the Kings XI Punjab 16 14.12 16 12.47 teams, where 2 points are given to each Kolkata Knight Riders 12 11.71 16 8.57 team that wins, a tie or a no-result (e.g. a Pune Warriors India 8 8.57 16 4.59 match abandoned due to rain) earns 1 point and no points for a loss. In this simple Delhi Daredevils 6 6.48 16 2.63 formulation, a team got the same 2 points Total 152 152 152 170.51 for beating the best team or the worst team. The KW scheme is a weighted scheme, The KW scheme is a weighted scheme, while the IPL scheme while the IPL scheme is based on raw scores is based on raw scores obtained from adding points uniformly obtained from adding points uniformly irrespective of the strength of the team that irrespective of the strength of the team that was overcome. Further, was overcome. Further, where a variable where a variable number of matches has been played, it is possible number of matches has been played, it is to normalize the weighted scores to obtain a exergy indicator that possible to normalize the weighted scores to obtain a exergy indicator that provides the provides the fairest ranking. fairest ranking. On the night of 19 May 2013, each play another four matches at the playoff points accumulated and the number of team had played the other twice, for a total stage. matches played [G. Prathap, The Energy- of 72 matches. Table 1 shows the raw and The Kendall-Wei algorithm allows the Exergy-Entropy (or EEE) sequences in weighted scores at this stage. recursive iteration to be continued over bibliometric assessment, Scientometrics, 87 The top four teams here are the same these additional games as well. This is (2011), 515-524]. that the IPL promoters chose to go to the reflected in the final standings shown in We see indisputably that Mumbai playoff stage (Mumbai, Chennai, Rajasthan Table 2. Mumbai had played 19 games, Indians are well and truly the most deserving and Hyderabad), but not in that order. As Chennai and Rajasthan 18 games each champions of IPL-6 2013. the Net Run Rate was used in the IPL rankings and Hyderabad 17 games. The rest of the Dr Gangan Prathap is Director of the National to resolve ties (both Mumbai and Chennai teams had of course played 16 games Institute of Science Communication and Information had 22 points each), Chennai with an NRR each. To take into account the variable Resources (NISCAIR), Council of Scientifi c & of +0.530 was ranked ahead of Mumbai number of matches played, an exergy Industrial Research (CSIR), Dr KS Krishnan Marg, (NRR of +0.441). These four teams had to measure is computed from the weighted New Delhi 110012; Email: [email protected] 37 SCIENCE REPORTER, JULY 2013.