April 4, 2012

Consistency in Test bowlers: a new look

An improved way of analysing consistency across the career of Test bowlers statistically

Bob Willis was remarkably consistent through the course of his Test career © Getty Images

This is based on an idea given by Prashanth. After giving the idea and participating in a discussion or two, he disappeared off the radar. However I thank him for providing the spark. Couple of years back Gabriel Rogers did a similar article. However that wonderful article was based on complex statistical methodology and would not have been out of place in an Annual Conference of Statisticians. Mine is simpler, more common-sense based and is aimed at everyone who comes into this blogspace, irrespective of his statistical knowledge.

The relevant points are explained below.

1. For this purpose five-Test slices are considered. This is a reasonable number and normally covers 2-3 months of Test cricket. Tests, rather than innings are used as the basis so that both bowling and batting can be covered in an equitable manner.
2. Five tests means that batsman can go through a Test or two of limited opportunities to bat or non-batting because of emphatic wins etc. There will be enough opportunities within the five-Test slice to catch up. Normally the bowlers do not have this problem since they do a higher share of a team's work and have to capture 20 wickets for a win.
3. There is enough time to get over short duration loss of form.
4. To measure consistency, only runs scored and wickets captured will be used. The fundamental cricket dictum that batsmen should score runs and bowlers should take wickets is followed. Averages are important mainly over a career and for comparisons across players.
5. Why not average? Let us take couple of examples to understand why not. McGrath and Trueman have career averages around 22.0 and WpT values of around 4.5. In a 5-Test period, match context being comparable, McGrath captures 25 wickets at 25.0 and Trueman, 15 wickets at 20.0. Who has performed closer to his career figures and for that matter, better. Certainly McGrath, despite the higher slice average. Similarly for batting.
6. Let us not forget that we remember numbers like 46 (Laker) and 41 (Alderman) rather than the specific averages. Similarly 774 (Gavaskar) and 688 (Lara) without being aware of the averages.
7. The career slices should be non-overlapping and equal, other than the last one. Gooch's 456 in one test should be part of one career slice only. Similarly Laker's 19 wickets. Hence the concept of rolling number of Tests is not valid.
8. Five Tests might seem arbitrary but represents a long enough career slice. It represents a long Test series.
9. The keyword is consistency with reference to the player's own career performance levels. It may happen that a bowler has a rather high WpT value: e-g, Barnes at 7.00, Muralitharan at 6.02 et al., and what is perfectly acceptable for another bowler might not be, for such bowlers. That is acceptable since they have set high benchmarks and we are interested in seeing how often they went off these benchmarks.
10. We are not looking about high and low values but only relative to the concerned player's career figures. Over a five-Test stretch Murali is expected to take 30 wickets and Kallis is expected to capture nine wickets. This will be the basis. If Murali captured 20 wickets in the Test slice, it is well below average and the same 20-wickets performance for Kallis, way above average.
11. I know that a bowler like Imran Khan who did not bowl at all in 3 slices at the end of his career would be slightly affected by this methodology. However there is no clear method of handling this. I do not want to exclude Tests where a bowler did not bowl. Then the number of slices would not be dependent on the number of Tests played. Also I don't want someone later on asking me to exclude batsman's Test where there has been an innings win for loss of few wickets. These are minor quirks and may only reduce the accuracy from 100% to 95%.
12. Adjustment is made for the last career slice if the same is fewer than five Tests.
13. The criteria for selection is 100 or more Test wickets. 160 bowlers qualify. The only bowlers of note who are missing are Shane Bond and Frank Tyson (Adrian, happy !!!).
14.The Standard Deviation (SD) of the slice ratios is used to determine consistency.

I had initially thought that I would combine the batsmen and bowlers together in a single article. However the introduction of six tall graphs meant that the article would have become very long and I have separated this into two articles. The graphs are also special purpose ones showing the slice plotting of up to 10 players per graph.

The following 5 groups are formed for purposes of determining consistency. For each career-slice of 5-tests, a ratio is formed between that concerned slice's runs/wickets and the career-average runs/wickets for 5 tests. This ratio is called SPF (Slice Performance Factor). Suppose the bowler has captured 17 wickets and his 5-Test career-WpT value is 24, the SPF value is 0.71. If he captured 30 wickets, the SPF is 1.25.

A. SPF  below 0.67:  Well below average - Falls into the inconsistent bracket.
B. SPF 0.67 - 0.90:  Below average
C. SPF 0.90 - 1.10:  Around average
D. SPF 1.10 - 1.33:  Above average
E. SPF  above 1.33:  Well above average - Falls into the inconsistent bracket.

Groups B, C and D are considered to be well within the average levels. Standard Deviation is also used to determine the consistency.

First some data tables. The first one is the core table of bowlers who have captured over 300 wickets in their Test career. The tables and graphs are presented with least comments. Let me allow the erudite readers to come out with their own comments.

BowlerTestsWktsAvgeWpTMeanStdDevMid3%C-SlicesGrp AGrp BGrp CGrp DGrp E
Muralitharan M13380022.736.01.000.27474.127451053
Warne S.K14570825.424.91.000.29569.02946955
Kumble A13261929.654.71.000.27574.12737584
McGrath G.D12456321.644.51.000.26672.02535854
Walsh C.A13251924.443.91.010.32870.42738745
Kapil Dev N13143429.653.30.990.39048.12777337
Hadlee R.J8643122.305.01.030.28383.318131022
Pollock S.M10842123.
Wasim Akram10441423.624.00.990.33766.72143653
Harbhajan Singh9840632.224.10.990.26185.02033680
Ambrose C.E.L9840520.994.11.000.28770.02028424
Ntini M10139028.833.91.000.35561.92128236
Botham I.T10238328.403.81.010.42952.42164254
Marshall M.D8137620.954.60.990.29270.61733452
Waqar Younis8737323.564.31.000.43055.61847124
Imran Khan8836222.814.10.980.46455.61851453
Vettori D.L11035833.873.31.000.41068.22246363
Lillee D.K7035523.925.11.000.24371.41422622
Vaas WPUJC11135529.583.21.000.37669.62346463
Donald A.A7233022.
Willis R.G.D9032525.
Lee B7631030.824.11.000.26687.51609232
Gibbs L.R7930929.093.90.990.27568.81633442
Trueman F.S6730721.584.60.990.30071.41424512

To clarify the table contents. WpT mean Wickets per test. Mean is the mean of the SPF values and is close to 1.0 for all bowlers. StdDev is the Standard Deviation for all the SPF values. Mid3% is the % of the Groups B, C and D over the total number of Career Slices, which is the next column: C-Slices. Grp A to Grp E are self-explanatory. The complete file is available for downloading. The link is provided at the end.

Amongst the top wicket-takers, only Hadlee and Harbhajan Singh have the Mid3% values exceeding 80, indicating a high level of consistency. Then comes Donald, with 86% and Willis, with a very high 94%.

Consistency is determined in two ways. The first is statistical. The Standard Deviation (SD) is determined for all the ratios. Low SD values indicate consistent players and high SD values indicate inconsistent players. The usual method of using the Coefficient of Variation is not required since the means for almost all players is around 1.00. Shown below are the SD tables with the low-20 SDs indicating very consistent bowlers.

BowlerTestsWktsAvgeWpTMeanStdDevMid3%C-SlicesGrp AGrp BGrp CGrp DGrp E
O'Reilly W.J2714422.605.31.000.120100.0601410
Morkel M3913930.
Adcock N.A.T2610421.
Dilley G.R4113829.763.40.980.169100.0903420
Kasprowicz M.S3811332.883.00.990.17187.5802411
Willis R.G.D9032525.
Snow J.A4920226.674.11.000.19490.01003511
Collinge R.O3511629.
Lohmann G.A1811210.766.21.020.200100.0401120
Old C.M4614328.
Saeed Ajmal2010726.705.31.000.210100.0401120
Danish Kaneria6126134.804.30.990.21184.61313621
Umar Gul4315732.483.71.000.21988.9903321
Johnson I.W4510929.
Steyn D.W5427223.195.00.990.22381.81112521
Hughes M.G5321228.384.00.990.22490.91113160
Donald A.A7233022.
Statham J.B7025224.853.61.000.23078.61422631
Johnson M.G4719031.
Edmonds P.H5112534.

Now for the tables with the high-SD values indicating a very low level of inconsistency.

BowlerTestsWktsAvgeWpTMeanStdDevMid3%C-SlicesGrp AGrp BGrp CGrp DGrp E
Rhodes W5812726.972.21.000.88733.31251213
Hooper C.L10211449.431.11.010.72723.82194017
Briggs J3311817.753.60.970.67957.1721211
Hogg R.M3812328.453.20.990.56975.0815101
Bracewell J.G4110235.812.51.130.56355.6922122
Illingworth R6112231.202.00.990.55561.51335212
Kallis J.H15227632.451.81.000.54738.731106249
Sobers G.St.A9323534.
Giffen G3110327.103.30.980.52342.9721202
Shastri R.J8015140.961.91.000.51262.51636313
Verity H4014424.383.61.000.51162.5821311
Noble M.A4212125.
Underwood D.L8629725.843.51.060.49633.31862226
Mushtaq Ahmed5218532.973.61.000.48554.51124113
Intikhab Alam4712535.952.71.010.48130.01031114
Greig A.W5814132.212.40.990.47958.31233402
Giles A.F5414340.602.60.990.47345.51132303
Abdul Qadir6723632.813.51.000.46550.01433314
Imran Khan8836222.814.10.980.46455.61851453
Bailey T.E6113229.

The alternate method is common-sense-based. The two extreme group numbers, A and E, are considered significant departures from the career levels. The middle three group numbers are added and divided by the total number of slices to get the Mid3%. This reflects the consistency of the players. Shown below are the SD tables with the high-10 Mid3% values.

BowlerTestsWktsAvgeWpTMeanStdDevMid3%C-SlicesGrp AGrp BGrp CGrp DGrp E
O'Reilly W.J2714422.605.31.000.120100.0601410
Old C.M4614328.
Morkel M3913930.
Dilley G.R4113829.763.40.980.169100.0903420
Lohmann G.A1811210.766.21.020.200100.0401120
Saeed Ajmal2010726.705.31.000.210100.0401120
Adcock N.A.T2610421.
Willis R.G.D9032525.
Hughes M.G5321228.384.00.990.22490.91113160
Snow J.A4920226.674.11.000.19490.01003511

Now for the tables with the low Mid3% values indicating a very low level of inconsistency.

BowlerTestsWktsAvgeWpTMeanStdDevMid3%C-SlicesGrp AGrp BGrp CGrp DGrp E
Hooper C.L10211449.431.11.010.72723.82194017
Intikhab Alam4712535.952.71.010.48130.01031114
Bailey T.E6113229.
Underwood D.L8629725.843.51.060.49633.31862226
Rhodes W5812726.972.21.000.88733.31251213
Pathan I.K2910032.263.40.990.36333.3620202
Boje N4310042.652.30.990.42933.3932103
Benaud R6324827.033.90.990.44238.51343024
Kallis J.H15227632.451.81.000.54738.731106249
Yadav N.S3510235.

Not surprisingly there is a strong negative correlation between the two methods. Understandably the correlation is negative since low SD and high Mid3% values indicate consistency. The correlation coefficient is a fairly high -0.73.

Now for some special graphs.

Graph of consistency for top wicket-takers
© Anantha Narayanan

The top-10 bowlers are featured. It can be clearly seen that most of these bowlers do not exhibit a high level of consistency. The only exception seems to be Hadlee, during the first half of his career.

Most consistent: Based on low SD values

Most consistent bowlers (based on low SD values)
© Anantha Narayanan

Look at O'Reilly. An SD a low as 0.12 indicates a very consistent career. This is borne out by his placement in the next graph also. Willis is the only one amongst this lot with over 85 Tests. The others have all played below 50 Tests. Amongst the modern bowlers, Kasprowicz and Steyn have been fairly consistent. Especially look at Steyn's last five slices.

Most consistent: Based on high Middle-3-group % values

Most consistent bowlers (based on high middle-3 % values
© Anantha Narayanan

These are the bowlers with high middle three group % values. There are four bowlers, led by O'Reilly who have all their groups in the middle. This is amazing. This means that not once did these bowlers go below 66.7% or above 133.3% of their career values. That is some consistency. It can be seen that three of these bowlers, O'Reilly, Dilley and Adcock also occupy the top three positions in the SD table, indicating the very high degree of correlation between the two methods. Old is there in the top-10. However in terms of consistency, Willis takes the plum position. Look at his graph. Out of 18 career slices only once has he gone into the two extreme groups.

Least consistent: Based on high SD values

Least consistent bowlers (high SD values)
© Anantha Narayanan

These graphs look like the dying person's cardiograph. These players have had moves up and down throughout their career. Most of them are also batting all-rounders. It is also possible that these players might have had stretches in which they bowled very little. However that means that they were very inconsistent as bowlers.

Least consistent: Based on low Middle-3-group % values

Least consistent bowlers (low middle-3 % values)
© Anantha Narayanan

Almost the same bowlers. However now Underwood and Benaud come in. Look at Pathan's graph. Most of these bowlers have around a third of the slices in the middle.

Bowlers with top averages

Graph of bowlers with top averages
© Anantha Narayanan

Just to complete the analysis I have given here the charts for the top bowlers - by average., since most of them would have missed the first chart: by wickets captured. Again inconsistency seems to be the trend here. But look at Adcock. High consistency, coupled with low average. And look at Barnes's chart. One nice long position just under the mean, made up at the end. Marshall and Ambrose seem to have alternating low and highs. Note Laker's huge spike, obviously during 1956.

I think mention must be made of two bowlers, Bill O'Reilly and Bob Willis. O'Reilly never went off the middle three groups. That is some consistency. Willis, for someone who played 85 Tests, went off the middle radar just once. That is again the definition of consistency.

To download/view the Excel sheet containing the complete data for 160 bowlers, please click/right-click here.

I will do a similar analysis for Batsmen next.

Anantha Narayanan has written for ESPNcricinfo and CastrolCricket and worked with a number of companies on their cricket performance ratings-related systems

Comments have now been closed for this article

  • testli5504537 on April 21, 2012, 2:31 GMT

    @ Ananth I too used to be very obsessed with these stats, centuries/50s 5-wicket, 10-wicket hauls, landmarks etc. but that was only till I was not even 15, after that I started realizing about how some people are keeping the interest of the team above and how some people are fighting with opposition to get their 100, even though there is nothing left in the match and is about time when captains can agree to draw the match. Hadlee took 9 10-wicket hauls against Garner's NIL, what does it prove? For centuries! why not 200 be counted as 2 centuries? 300 as three? Bradman would have had a total 43 in 52 tests! Its just that people have decided that whether you score 100 or 501, it will be counted as one century! What difference it makes if it was counted as 5 tones? The difference between 99 and 100 is just 1, and there is just one test, which was won/lost by 1 run, nobody scored a hundred in that or even a 99. [[ By now you would be aware that I am the least respecter of the 100, as a landmark. To me it is nothing more than the run taken when you are on 99. The media and the statisticians (to which set I do not belong) have made such landmarks bigger than what they are. Of course Murali would take more 5/10-wkt hauls than any one. He was Sri Lanka's 50% bowler. Same with Hadlee. Of course the four West indies pacemen would take fewer 5/10-wkt hauls. They were lions hunting in the same forest. You would notice I never use the number of hundreds or 5-wkt hauls as a performance measure. But I use the number 100 itself in batting and 4 wkts in bowling as a convenient cut-off. I could as well use 99 for this but will show me as a silly person, which I hope I am not. The sorry saga of the 100th 100 must prove this. The media obsession which unfortunately affected the great man himself is a lesson for us. Ananth: ]]

  • testli5504537 on April 20, 2012, 7:09 GMT

    wher is speed buster s hoaib akhter man????????????????? and saqlain also both pakistani atar ones

  • testli5504537 on April 20, 2012, 2:39 GMT

    Kemar Roach has finally taken a 10-wicket haul for Windies, only the third a Windies bowler has done it in last 17 years, in contrast, Indian bowlers have taken 18 times 10-wicket hauls in this period! In fact Kumble has as many 10-wicket hauls as Roberts/Holding/Croft/Garner/Marshall put together! Muralitharan has 22 10-wicket hauls as against 27 by Windies in their entire test history! [[ I did not know about 27. Amazing. They had only 5 more than Murali. And out of the 27, Marshall had 4 and Ambrose/Walsh 3 each. A clear indication that the hunters hunted in a pack. One reason why I do not put in too much importance over such personal landmarks. I have more time for the bowling landmarks because the fifth wicket is 10% of the wickets available. The 100th run, for me, is only the run after the 99th run. However I use the 100 as good cut-off point. Ananth: ]]

  • testli5504537 on April 19, 2012, 16:33 GMT

    Funny how a lot of people are talking about the most consistent not being stars etc. Well, Bill O'Reilly was certainly the star bowler in his team, so I don't know what they're talking about. [[ That discussion was more on Bob Willis. Ananth: ]]

  • testli5504537 on April 15, 2012, 3:15 GMT

    @shrikanth - interesting stuff on Verity vs Bradman. Can you let me know how you came by those figures?

    I googled it. Found it in some article on Verity. Not in a database.


  • testli5504537 on April 13, 2012, 4:06 GMT

    Not only are the West Indies not producing taller faster quicks, they are not having enough African origin batsmen. I wonder when the Fredericks, Greenidges and Lloyds will come. Last year, during India's series, Tony Cozier remarked that in schools, where once many cricket matches would be going on in a single ground, these days girls were playing hop-scotch. Perhaps that will be the real contribution of the Keiron Pollards - give a glimpse of real rewards that await successful cricketers and inspire more youngsters to take to the game. [[ The Pollards of the world will move on to IPL, BPL. BB, XPL, YPL and ZPL and leave the Braithwaites to play Test cricket. So West Indies cricket will not gain. Ananth: ]]

  • testli5504537 on April 12, 2012, 13:41 GMT


    Aussie win is similar to India's win ag. Zimbabwe at delhi in 2000. On last day Zimbabwe batted for 44 overs and then India score 190/3 in 37.3 overs to win. Lots of similarities.. Hilfenaus did exactly what srinath did 12 years ago. ganguly was in his 1st year of captaincy similar to clarke. [[ Many similarities. Two scores over 400. India declares just 36 ahead. Zimbabwe losing three for 25. Fourth day end 115 for 5. Then wickets fell but every one of the last four batsmen went past double figures. Then India scored at 5 RpO and won with very few overs to spare. Dodgy light again at Delhi in November. This match was 1515, just six matches before the Pakistan-England match I had referred to. Spare a thought for Andy Flower, 253 runs for once out. Ananth: ]]

  • testli5504537 on April 12, 2012, 12:27 GMT

    @Ananth - yeah, a wonderful game of cricket. Sorry I couldn`t get to watch more of it, but the 11pm-6am (Japan time) - (12-7 Aus I think) hours make it pretty tough during a working week. [[ Less of a problem in India. But still tough to watch the complete day's play. I was falling off the chair at 29 for no loss and had to move my base to the bedroom. Then after an hour I checked on my mobile and saw 61 in 22 overs and gave up on an Aussie win. This win reminded me of the England win over Pakistan during December 2000 (Test # 1521). I was visiting Wisden in England at that time for discussions on the Wisden-100 and somehow managed to locate a commentary. I remember the running around at lunch time during the last 30 minutes. I liked Hick a lot and for a change he contributed. Imagine Atherton scoring 26 in 33, against Waqar. Ananth: ]] Sammy, once again, seems to be copping a lot of criticism on the forums and in the press for field placement/negativity/bowling changes et al. I only caught the first hour and last hour and a half of Day 5, so I`m probably not qualified to comment, but...I think he`s a v.good captain, a limited cricketer in some ways, but he keeps taking wickets at a very decent average, and bats capably. Most importantly though, he seems to have been able to mould a team who play for each other and obviously respect him. If we remember the circumstances under which the job was thrust upon him, after so many (more talented) others had failed, often dismally, I think he`s done a remarkable job.

    I`m sure I wasn`t the only Aussie supporter this morning who wouldn`t have been too unhappy to see the Windies win it.

  • testli5504537 on April 12, 2012, 6:01 GMT

    @ Ananth: Another excellent point you made was about Clarke as a captain. The Aussies never cease to amaze me with their choice of captains and the way the captains are groomed and how players bite their egos for team cause. A lesson for most Asian teams. Every captain since AB have always had a successful stint, 95% attributed to the excellent group of players and 5%, to excellent captaincy. Yet to find a bad captain in Australia. Well, someone could still say,"With such a team, Boycott's mum could captain Oz" but the reality is that everyone comes into ANY international team with some potential, but the way the potential is groomed (be it player or captain) talks volumes of the cricketing system. Though the Oz team cant be compared to 99-2008 team, they are still THE Team to beat. They are doing it consistently, unlike Eng/SAF who are not that consistent. [[ Over the past four months, Clarke has demonstrated his top-drawer credentials three times as captain. First he trashed his own classic innings of 151 as useless since the team lost. Second when he declared at 329, caring very little not just for 400 but even Australia's pinnacle of 334. Of course he was aware of the significance of 334. Third when he declared an over after a drinks break, when West Indies least expected and gave himself only 5 overs, But what overs were they. Ultimtely match winning overs. If he had natted on until tea and declared, West Indies might have been 50 for 3 and might have saved the match easily. Ananth: ]]

  • testli5504537 on April 12, 2012, 5:43 GMT

    Wonderful observation Ananth! To me, Sammy is one of the better captains I hav seen. He always gets into a test with his place under scrutiny, but delivers overall, competing and challenging the best. India was lucky to have narrowly NOT LOST to WIndies. I feel Test Cricket should be popularized rather than ODI/T20, which sell on their own. In the 50s, 60s and 70s, when we had no other dominant format in the world stage, test cricket had no competitions. But since the introduction of shorter versions, busier people and paucity of time, test cricket has to be promoted much more than any other format. Not that test cricket has lost its sheen, but beyond a few die hard fans, test cricket has become an academic exercise (with plethora of 2 test series). Televising FC cricket is a good move, but A Tours and Youth tours should be promoted and advertised as well. Consistent good cricket shall definitely draw crowds or TV viewership! [[ Sammy in 22 Tests has captured 62 wickets at 30 and a s/r of just over 60 at an RpO value of 2.83. Other than RpO these are better figures than Venkataraghavan. He is a very useful cricketer. May not be a world class all-rounder. However the world class all-rounders like Gayle and Bravo prefer coloured clothes. So, the bottomline is that, over the past three years, Sammy has done more for West Indian cricket than the so called super stars. Ananth: ]]

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