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GANGAN PRATHAP Feature Short quality of performance (batting average) and quantity of performing opportunities (number of innings played). Sachin is probably the most N Boxing Day 2012, Kumar Sangakkara joined a select successful when quantity of performing opportunities is taken into O club of Test batsmen who had reached the extraordinary account. On quality of performance, when measured by the batting milestone of 10,000 runs. The players in this league are: average (we depart from the usual cricketing practice and here take Is Sachin the greatest in this club? Or is it Bradman, who had an average nearly double that of all in the list above? And, who of this galaxy, was the most consistent? The Exergy-Consistency map shows Tendulkar ahead Readers of Science Reporter might remember an exercise of the competition to find the most “consistent” batsmen from a select list of iconic batsmen (September 2011). “Consistency” was defined to go beyond Sachin Tendulkar India 15,645 Ricky Ponting Australia 13,378 Rahul Dravid India 13,288 Jacques Kallis South Africa 12,980 Brian Lara West Indies 11,953 Allan Border Australia 11,174 Steve Waugh Australia 10,927 Shivnarine Chanderpaul West Indies 10,696 Mahela Jayawardene Sri Lanka 10,674 Sunil Gavaskar India 10,122 Kumar Sangakkara Sri Lanka 10,045 SCIENCE REPORTER, FEBRUARY 2013 30 Short Feature This is a composite that combines quality and consistency along with quantity. If such an indicator is an acceptable measure for batting performance, then Tendulkar is once again ahead of the rest of the competition. Sachin is probably the most successful when quantity of performing opportunities is taken into account. On quality of performance, when measured by the batting average, Bradman ranks foremost. Statistics for the league of 10000 Test runs batsmen and Don Bradman Innings Runs Average Energy Exergy Consistency çX Tendulkar 320 15645 48.89 1605477 764893.8 0.476 364416.66 Kallis 268 12980 48.43 1238194 628658.2 0.508 319183.54 Bradman 80 6996 87.45 1212502 611800.2 0.505 308700.10 Dravid 286 13288 46.46 1276202 617380.9 0.484 298666.83 Ponting 287 13378 46.61 1333720 623591.9 0.468 291565.62 Lara 232 11953 51.52 1514553 615837.1 0.407 250407.44 Border 265 11174 42.17 905558 471163.3 0.520 245147.04 Chanderpaul 249 10696 42.96 874188 459455.5 0.526 241480.49 Sangakkara 196 10045 51.25 1163491 514806.3 0.442 227784.72 Gavaskar 214 10122 47.30 1012946 478761.1 0.473 226282.77 Waugh, Steve 260 10927 42.03 974265 459228.2 0.471 216461.16 Jayawardene 230 10674 46.41 1202774 495366.4 0.412 204018.28 this as the ratio of runs scored to total number of innings played), I, R, E and X. In quality terms, as expressed by the average number of Bradman ranks foremost. But among the limited sample we examined runs scored for the opportunities one has had at the crease, Bradman then, it was Kallis who turned to be more consistent than the others. is far ahead with a record that may never be equalled. But when it We shall now apply the same protocol used earlier to see who comes to consistency with the bat, we find that Chanderpaul and among these eleven is the most consistent. Again, we use data Border are actually ahead of Kallis. from the Cricinfo website (www.espncricinfo.com/). For purposes of At this stage we introduce one more indicator, η X. This can also comparison, we also collect the information about Bradman. be expressed as η 2E or as η q2I. This is a composite that combines Second Table displays the salient figures. Some mathematical quality and consistency along with quantity. If such an indicator is an preliminaries are required here. acceptable measure for batting performance, then Tendulkar is once For any batsman who has played I innings, let the innings by again ahead of the rest of the competition. Hopefully, this settles all r i I innings batting sequence be represented by i, = 1 to . The batting arguments about who the greatest batsman was? Figure 1 is a display R Σ r i I total is then = i, = 1 to . A batting average can then be of these findings on an Exergy-Consistency map. q = R/I E Σ r 2 computed as . We also define an energy term = i . Another energy like term, which we shall call exergy X is obtained from qR. The consistency of batting performance is simply η = X/E. Dr Gangan Prathap is Director of the CSIR National Institute of Science We see from Table above that Tendulkar ranks above the rest Communication and Information Resources, New Delhi 110 012; Email: gangan. [email protected] when performance is measured by any one of the following indicators, 31 SCIENCE REPORTER, FEBRUARY 2013.

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