This is a follow-up to the bowler streaks article published last month. In addition to providing additional analysis on the topic by specifically responding to a couple of very nice queries, I have also attempted to present a new concept to get additional insights to the vexed question of "Wickets - how good are they?" In summary, akin to "Supply-side Economics" being presented as an alternate economic theory, I have tried to present this analysis as the study of bowling from the angle of the dismissed batsmen.

One often repeated query on the article centered on the number of wickets taken by the bowlers. Muttiah Muralitharan's 800 was said to contain over 160 wickets against the so-called "minnows" while Shane Warne's 708 wickets was seen to be more valuable since it contained only 17 wickets against these weaker Test teams. This argument seemed quite sound until I pointed out a fundamental error in this assumption. Is the wicket of Shakib Al Hasan less valuable than that of, say, Ishant Sharma? The former is a top batsman of a weaker team while the latter is a tail-ender of a better team. There was no response.

To solve this, I said that I would determine an index using the quality of batsman dismissed. This process will ensure that Shakib would get his due credit as a top-flight batsman with an average of 39.76, while Ishant will be accorded treatment deserving his batting average of 8.89. At one stroke this would solve all problems, including dismissals of batsmen like Bevan Congdon, Ravi Shastri or Roshan Mahanama - average batsmen from top teams.

My first idea was to accord a weight to each wicket and determine a weighted wicket value. I took some steps towards that. Then I suddenly realised that the numbers 800 and 708 are etched in the minds of cricket followers, like 6996, and it would be inadvisable for me to say that Muralitharan has 768.2 wickets or that Shane Warne has 691.1, or that Jerome Taylor has really taken 142.3 wickets, not 130. So I decided not to touch the wickets measure. Rather, I would come out with a new measure called "Weighted Wicket Index" (WWI), which would be an additional pointer.

It would be wonderful for the bowling team if Don Bradman was dismissed on 8 or Ricky Ponting was dismissed on 5. But is that information about when the batsman was dismissed, that important for me to embed in the WWI value? I should give the bowler the credit for dismissing Bradman, but at what score would overcomplicate matters and make it difficult for any follower to adopt this methodology. I have anyhow already done such an analysis when I analysed the individual spells. Moreover, context is important. I have given below two dismissals.

Sehwag c Bracken b Katich 195.

Sehwag c Clarke b Lyon 19

It would seem that the first was not such a valuable wicket for Australia since they managed to dismiss Virender Sehwag only after he reached 195. It would also seem that the latter is a great dismissal since they got him for a low score.

Unfortunately, the reverse is true. If Sehwag had got to his double-hundred in a manner other than the six he attempted, India might have won the MCG Test in 2003-04. And the latter dismissal did not do anything for Australia. That occurred while India was chasing 52 runs in Chennai in 2013 and did not mean anything.

Hence context is important. But I use context mainly in ratings work. So I decided that I would consider only the batting average for determining the WWI. In general, it is important to get the wickets of the top batsmen. However, Ricky Ponting at home had an average of 57 and away, it dropped to 46.4. Brian Lara had figures of 58.6 and 47.8 respectively. Mohammad Yousuf was king at home at 65.3 and a commoner away, at 46. It was far easier to dismiss these top batsmen, and others, away from home. Hence the average I use is location-dependent.

With this lengthy preamble, let me move on to the tables. The methodology is simple. For each bowler, add the location-based average of the batsman dismissed for all dismissals and divide by the number of wickets. Nothing can be simpler.

1. Top Weighted Wicket Index values Bowler Team Type Wickets Bow Avge W W I Mohammad Asif Pak RFM 106 24.37 36.64 N Boje Saf lsp 100 42.65 35.94 PL Harris Saf lsp 103 37.87 35.75 AF Giles Eng lsp 143 40.60 35.59 JE Taylor Win RF 130 34.46 35.57 TA Boult Nzl LM 147 29.15 35.34 Z Khan Ind LFM 311 32.95 35.13 RJ Harris Aus RF 113 23.52 34.72 M Dillon Win RFM 131 33.63 34.63 A Flintoff Eng RF 226 32.79 34.47 ..... Waqar Younis Pak RF 373 23.56 26.98 J Garner Win RF 259 20.98 26.79 Wasim Akram Pak LF 414 23.62 26.34 SCG MacGill Aus rlb 208 29.03 26.15 S Ramadhin Win rob 158 28.98 26.05 SF Barnes Eng RFM 189 16.43 25.61 JH Wardle Eng lsp 102 20.39 23.55

If anyone thought that this table would be dominated by the Muralis, Kumbles and McGraths of the world, they are in for a shock. Those leading bowlers are required to bowl right through the innings, taking wickets of batsmen of different levels. They have to capture top-order wickets, the settled batsmen in the middle order and the late-order batsmen. So this table is dominated by those bowlers who are not necessarily the leading bowlers. They take top wickets and then leave it to the others to clean up. Only one bowler in this table has crossed 300 wickets.

The table is topped by Mohammad Asif. This one-of-a-kind pace bowler from Pakistan has taken 106 wickets at a fairly low cost of 24.37 runs per wicket. He has complemented this with the quality of batsmen dismissed. His WWI is an amazing 36.64. This is some achievement. That means that the average quality of batsman dismissed by Asif is Denis Compton (away), Mohammad Azharuddin (away) or Ijaz Ahmed (home). I suggest that the readers take a minute or two to digest this fact.

Surprisingly Asif is followed by three very average spinners - Nicky Boje, Paul Harris and Ashley Giles. They have completely forgettable averages exceeding or nearing 40, but have dismissed many top batsmen, most probably those batting in the middle order. I get the feeling that when it came to the lesser and late-order batsmen, the other better bowlers in the teams came to complete the task.

Jerome Taylor, the West Indian fast bowler, is fifth in the table with a WWI of 35.57. On many occasions he was the only attacking bowler in the weakened West Indian line-up. Trent Boult, the New Zealand fast bowler comes in next. His WWI is an impressive 35.34. The low number of wickets helps a lot, in all these cases.

Then come the most important bowlers in this table: Zaheer Khan, Ryan Harris and Andrew Flintoff. They all have WWI values around the 35 mark. Each of these formed the pace-bowling spearhead of their respective teams. That means that each time these bowlers dismissed a late-order batsman, say at an average of 15, they made up with a real top-order batsman, at 55. Mervyn Dillon completes this interesting quartet of pace bowlers.

At the other end of the table, the presence of Sydney Barnes and two bowlers from the '50s, Sonny Ramadhin and Johnny Wardle, is not surprising. The quality of batsmen in the 1950s from some teams was quite low. Stuart MacGill is a surprise. He played in an era of good batsmen. My feeling is that he rarely took top-order wickets. Then comes Wasim Akram. Why should his WWI be so low? Was it the fact that, maybe, Imran Khan, Sarfraz Nawaz and Abdul Qadir took wickets of the better batsmen or that Akram dismissed a number of late-order batsmen? As did Waqar Younis, who is seventh from bottom.

As I completed this exercise I started worrying about the high placement of those average spinners. I realised that just the WWI, by itself, would not be of great value. I started going through the entries and realised that I had an excellent alternative. Since these spinners had high averages, I realised that the average could come in handy. I worked out the difference between the bowling average and WWI. This is called "Difference Index (DI). One has to be low and the other has to be high. So a high difference indicates that the bowler has contributed very well to the team. The following table lists the bowlers with very high and very low DI values, indicating the value the bowlers brought to their teams. This time there are no undeserving bowlers in the table. The comparison between the two tables is a real eye-opener.

2. Top Difference Index values Bowler Team Type Wickets Bow Avge W W I D I Mohammad Asif Pak RFM 106 24.37 36.64 12.28 RJ Harris Aus RF 113 23.52 34.72 11.20 VD Philander Saf RFM 126 22.09 31.49 9.40 MD Marshall Win RF 376 20.95 30.14 9.19 SF Barnes Eng RFM 189 16.43 25.61 9.18 GD McGrath Aus RFM 563 21.64 30.64 9.00 AK Davidson Aus LFM 186 20.53 29.32 8.79 CEL Ambrose Win RF 405 20.99 29.67 8.68 JC Laker Eng rob 193 21.25 29.90 8.66 CEH Croft Win RF 125 23.30 31.84 8.54 ..... JE Emburey Eng rob 147 38.41 30.36 -8.04 RJ Shastri Ind lsp 151 40.96 32.53 -8.43 Mohammad Rafique Bng lsp 100 40.76 32.30 -8.46 Abdul Razzaq Pak RFM 100 36.93 28.39 -8.54 CL Hooper Win rob 114 49.43 32.24 -17.19

Asif leads this table also. He had a huge difference value of 12.28. His low average and high WWI values have helped. Just think over it. Each wicket Asif dismissed cost his team 24.37 runs but he dismissed a batsman with average of 36.64.

Harris has almost similar figures to those of Asif: a low average and a high WWI means that he has an excellent DI value of 11.20. He and Asif are the only two pace bowlers with DI values exceeding 10. But for his series of injuries, Harris was a candidate for 200 wickets at a sub-25 average.

Vernon Philander is an undervalued pace bowler. His DI of 9.40 confirms that. Malcolm Marshall clocks in next at 9.19. My belief that Marshall was the best West Indian pace bowler ever keeps getting strengthened. Barnes is unique: he dismissed many batsmen with somewhat low averages, hence he has a low WWI of around 26. However his career average is also well below the 20 mark. Hence he gets a place in this table.

Glenn McGrath's DI value is 9.00. Alan Davidson's DI is just below this value and Curtly Ambrose clocks in with a value of 8.68. Jim Laker's DI value is an outstanding 8.66, for a spinner. He is the only spinner in the top-10 and is in tenth place. This is some achievement. Colin Croft completes the table.

Pause here for a minute to understand the true significance and importance of the DI.

Understandably, the spinners have all the lowest values. In truth, they occupy all the low order ten places. A relatively high average and a middling WWI sees to that. Carl Hooper is in a league by himself. The others have the difference index above -10. Hooper stands supreme with a DI of -17.19. It is difficult to conceive what value he would have brought to the West Indian side, as a bowler. After all he conceded nearly 50 runs per wicket.

Addition:

As suggested by couple of readers I have calculated the DI as a ratio instead of a difference. This will take away the problems associated with the low scoring eras such as the Pre-WW1 periods. The table is presented below. Sydney Barnes leads the table, followed by Mohd Asif, Richard Harris, Marshall and Davidson.

2a. Top Difference Index values - Ratio Bowler Team Type Wickets Bow Avge W W I DI-1(Diff) DI-2(Ratio) SF Barnes Eng RFM 189 16.43 25.61 9.18 1.56 Mohammad Asif Pak RFM 106 24.37 36.64 12.28 1.50 RJ Harris Aus RF 113 23.52 34.72 11.20 1.48 MD Marshall Win RF 376 20.95 30.14 9.19 1.44 AK Davidson Aus LFM 186 20.53 29.32 8.79 1.43 VD Philander Saf RFM 126 22.09 31.49 9.40 1.43 GD McGrath Aus RFM 563 21.64 30.64 9.00 1.42 CTB Turner Aus RM 101 16.53 23.23 6.70 1.41 CEL Ambrose Win RF 405 20.99 29.67 8.68 1.41 JC Laker Eng rob 193 21.25 29.90 8.66 1.41 ..... RJ Shastri Ind lsp 151 40.96 32.53 -8.43 0.79 S Venkataraghavan Ind rob 156 36.12 28.48 -7.64 0.79 JE Emburey Eng rob 147 38.41 30.36 -8.04 0.79 Abdul Razzaq Pak RFM 100 36.93 28.39 -8.54 0.77 CL Hooper Win rob 114 49.43 32.24 -17.19 0.65

I did another related analysis. Without worrying about the batting averages of the batsmen who were dismissed, I decided to see how the bowlers fared if I did an analysis on dismissals, classifying the batsmen into three groups: Top Order (1-4), Middle Order (5-7) and Low Order (8-11).

This is just a variation which would not differentiate between, say Ponting and Shakib. Or between Warne and Chris Martin, as batsmen. Only for this table, I have increased the cut-off to 200 wickets since I found that 100 wickets was too low a number to split into three categories. Admittedly, No. 7 is a contentious position. However, when I see that batsmen like Adam Gilchrist, Kapil Dev, Imran, Shaun Pollock, Ian Botham have all batted most of their career at No. 7, it would be unfair to the bowlers to push this pivotal position to 'Late Order'.

3. Top bowlers: by % of Top Order wickets Bowler Team Type Wickets TO-Wkts-% MO-Wkts-% LO-Wkts-% WPUJC Vaas Slk LFM 355 185-52.1% 89-25.1% 81-22.8% JA Snow Eng RFM 202 103-51.0% 43-21.3% 56-27.7% Z Khan Ind LFM 311 158-50.8% 89-28.6% 62-19.9% CS Martin Nzl RFM 233 117-50.2% 64-27.5% 52-22.3% GD McGrath Aus RFM 563 282-50.1% 139-24.7% 142-25.2% AA Donald Saf RF 330 164-49.7% 80-24.2% 86-26.1% RGD Willis Eng RF 325 161-49.5% 82-25.2% 82-25.2% Kapil Dev Ind RFM 434 214-49.3% 97-22.4% 123-28.3% JM Anderson Eng RFM 454 222-48.9% 114-25.1% 113-24.9% GD McKenzie Aus RF 246 120-48.8% 65-26.4% 61-24.8% ..... Harbhajan Singh Ind rob 417 145-34.8% 118-28.3% 150-36.0% SK Warne Aus rlb 708 225-31.8% 220-31.1% 263-37.1% LR Gibbs Win rob 309 98-31.7% 100-32.4% 111-35.9% Danish Kaneria Pak rlb 261 82-31.4% 98-37.5% 81-31.0% SCG MacGill Aus rlb 208 59-28.4% 68-32.7% 81-38.9%

It is expected that the pace bowlers would occupy all the spots in the top-10 in this table. That is logical since they have the first crack at the top order. That is how it has turned out to be. The presence of Chaminda Vaas, John Snow, Zaheer and Martin in the top four positions gives me the feeling that in two or three-pronged pace attacks, the top order wickets would be split. But then come McGrath, Donald and Bob Willis, all of whom had top-class pace bowlers operating at the other end. Kapil Dev belongs to the first category. James Anderson and Graham McKenzie complete the top ten.

The last five positions are occupied by the top spinners. Only 30% of their wickets have been those of the top-order batsmen. This also means that they had a high proportion of late-order wickets: Especially true for Warne, Harbhajan Singh and Lance Gibbs. Incidentally Muralitharan is one place above these six.

If the cut-off had been maintained at 100 wickets instead of 200, three bowlers who have captured exactly 100 Test wickets would be at the top. Richard Motz dismissed 62 top-order batsmen, Irfan Pathan dismissed 59 and Dilhara Fernando dismissed 58.

Since some of the top bowlers are missing, it is essential that I provide the relevant data for the top players. Given below are the figures for the top-20 wicket-takers. The table is self-explanatory.

4. WWI/BI for top bowlers Bowler Team Type Wickets Bow Avge TO-Wkts-% MO-Wkts-% LO-Wkts-% W W I D I M Muralitharan Slk rob 800 22.73 280-35.0% 260-32.5% 260-32.5% 28.28 5.56 SK Warne Aus rlb 708 25.42 225-31.8% 220-31.1% 263-37.1% 29.41 4.00 A Kumble Ind rlb 619 29.65 237-38.3% 181-29.2% 201-32.5% 30.30 0.65 GD McGrath Aus RFM 563 21.64 282-50.1% 139-24.7% 142-25.2% 30.64 9.00 CA Walsh Win RF 519 24.44 228-43.9% 128-24.7% 163-31.4% 29.45 5.01 JM Anderson Eng RFM 454 28.34 222-48.9% 114-25.1% 113-24.9% 32.18 3.84 Kapil Dev Ind RFM 434 29.65 214-49.3% 97-22.4% 123-28.3% 30.11 0.47 RJ Hadlee Nzl RF 431 22.30 189-43.9% 113-26.2% 129-29.9% 28.98 6.68 SM Pollock Saf RFM 421 23.12 186-44.2% 111-26.4% 124-29.5% 29.37 6.25 Harbhajan Singh Ind rob 417 32.46 145-34.8% 118-28.3% 150-36.0% 29.80 -2.66 Wasim Akram Pak LF 414 23.62 163-39.4% 106-25.6% 145-35.0% 26.34 2.72 DW Steyn Saf RF 406 22.54 173-42.6% 102-25.1% 130-32.0% 30.10 7.56 CEL Ambrose Win RF 405 20.99 192-47.4% 101-24.9% 112-27.7% 29.67 8.68 M Ntini Saf RF 390 28.83 190-48.7% 108-27.7% 92-23.6% 30.97 2.14 IT Botham Eng RFM 383 28.40 155-40.5% 110-28.7% 118-30.8% 28.67 0.26 MD Marshall Win RF 376 20.95 167-44.4% 110-29.3% 99-26.3% 30.14 9.19 Waqar Younis Pak RF 373 23.56 163-43.7% 101-27.1% 109-29.2% 26.98 3.42 Imran Khan Pak RF 362 22.81 167-46.1% 91-25.1% 104-28.7% 30.15 7.33 DL Vettori Nzl lsp 362 34.37 132-36.5% 106-29.3% 123-34.0% 30.19 -4.18 DK Lillee Aus RF 355 23.92 166-46.8% 92-25.9% 97-27.3% 30.17 6.25

The two spinners, Harbhajan and Daniel Vettori are the only two bowlers with negative DI values. Both Muralitharan and Warne have good DI values. Anil Kumble shows up on the positive side of the ledger, so to speak. Most of the modern spinners have negative DI values.

Another interesting table is the one ordered on the share of team wickets that the bowler has taken in his career.

5. Top bowlers: by Share of team wickets Bowler Team Type Wickets Team Wkts % of Team wkts M Muralitharan Slk rob 800 1986 40.3% SF Barnes Eng RFM 189 475 39.8% CTB Turner Aus RM 101 271 37.3% RJ Hadlee Nzl RF 431 1207 35.7% CV Grimmett Aus rlb 216 615 35.1% Fazal Mahmood Pak RFM 139 398 34.9% R Ashwin Ind rob 176 522 33.7% SP Gupte Ind rlb 149 442 33.7% WJ O'Reilly Aus rlb 144 436 33.0% GA Lohmann Eng RM 112 344 32.6% ..... TE Bailey Eng RFM 132 987 13.4% W Rhodes Eng lsp 127 966 13.1% R Illingworth Eng rob 122 972 12.6% JH Kallis Saf RFM 292 2725 10.7% CL Hooper Win rob 114 1553 7.3%

This table runs on expected lines. Muralitharan leads with an amazing share of 40.3% of the team wickets. He is the only bowler with a share of wickets exceeding 40%. Incidentally Bradman's share of team runs is around 25%. This bowling share percentage of Muralitharan compares favourably with Bradman's share of team runs. These are not directly comparable, of course. The team wickets, incidentally are inclusive only of the bowler wickets. Barnes is second with 39.8%. Charlie Turner, next in the table with 37.3%. A surprise is the presence of R Ashwin who has taken just over a third of the Indian wickets. The other surprise is the presence of five spinners in the top ten.

The non-bowling allrounders prop up the table.

Finally, I turn to the two requests from readers relating to the last article. Mansoor wanted me to show a table of bowlers who have reached the twin landmarks of 100-plus wickets and sub-20 averages at any time in their careers. This is distinct from my previous article in which I looked at mid-career streaks with such qualifications. This will be a career-to-date analysis. It is possible for bowlers to achieve mid-career streaks without ever reaching 20 average in their careers. For instance, Muralitharan, Warne, Kumble, McGrath and Walsh: the top five bowlers in the wickets table, have never reached 20 in their illustrious careers. So this is a special request and a special table. This time I have picked up the latest such occurrence, when there are multiple occurrences. In other words, the highest number of wickets at which they reached the sub-20 mark. The table is given below.

6. 100 wkts & sub-20 average at any time in career Bowler Wickets Avge Test# CTD-Wkts CTD-Avge SM Pollock 421 23.12 1529 210 19.87 Waqar Younis 373 23.56 1313 194 19.73 SF Barnes 189 16.43 133 175 16.93 RR Lindwall 228 23.03 392 163 19.98 IT Botham 383 28.40 885 152 19.47 AK Davidson 186 20.53 507 139 19.91 DL Underwood 297 25.84 711 132 19.92 J Briggs 118 17.75 62 115 17.76 WA Johnston 160 23.91 361 114 19.45 VD Philander 126 22.09 2122 111 18.87 J Garner 259 20.98 902 110 19.96 GA Lohmann 112 10.76 50 109 10.58 GAR Lock 174 25.58 462 106 19.99

Many bowlers who appeared in the streak tables do not appear here.

Another reader, Sukumar, had asked for a streak analysis to be done for "away" wickets. All neutral Tests are 'Away' for both teams.

7. Away streaks of 100-plus wickets at sub-20 averages Bowler Wickets Avge Start End Tests Wickets Avge GD McGrath 563 21.64 1294-1995 1620-2002 54 209 19.39 RJ Hadlee 431 22.30 786-1976 1109-1988 35 188 18.60 MD Marshall 376 20.95 884-1980 1100-1988 44 154 18.02 SF Barnes 189 16.43 65-1901 133-1914 17 126 17.96 SK Warne 708 25.42 1552-2001 1758-2005 29 143 19.76 CEL Ambrose 405 20.99 1098-1988 1239-1993 46 126 18.82 J Garner 259 20.98 862-1979 997-1984 29 110 18.09 MA Holding 249 23.69 779-1976 971-1983 31 120 19.64 AA Donald 330 22.25 1291-1995 1538-2001 24 101 19.58 M Muralitharan 800 22.73 1648-2003 1822-2006 26 101 19.65 R Benaud 248 27.03 431-1956 487-1960 20 100 19.94

In important tables, we seem to always see those bowlers who do matter. Look at the top-three bowlers here. They would be in anybody's shortlist of the top bowlers. Both Warne and Muralitharan find a place here. The surprise is Richie Benaud. In the mid-fifties, Benaud was devastating in India, South Africa and Pakistan.

This article attempts to respond to the statement: There are wickets and wickets just as there are batsmen and batsmen. Of course, wickets and bowling averages are the pillars of the bowler career analysis workspace. However, this article conclusively proves that there is life beyond wickets and averages.