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Greatest Bowler: Statistical Analysis


Greatest!

By Shwetabh
June 27 2005

Who are the best bowlers to have terrified, bamboozled, flummoxed, or simply intimidated batsmen in more than a century of test cricket? Whatever their means, their goal has been singular-to send the batsman in front of them back to the pavilion. It is a question, which was on cricket lovers’ lips when Harold Larwood floored the Aussies in their backyard, when Lillee and Thomson dominated cricket, when the Indian spin quartet spun webs like spiders, when the Windies pace quartet made batsmen quiver and shiver, when Akram and Waqar sent down toe crunching swinging yorker after yorker, when Kumble made the ball spit like a cobra, when Warne and Murali made the ball spin like a political story, and when McGrath almost seemed to be getting wickets by boring the batsman.

Bowling is an art and no amount of objectivity can satisfy the eternal purist. However, an attempt can surely me made to put all the different tricks perfected with a five and a half ounce leather ball over more than a hundred years into numbers and try to answer who has been the most successful exponent of the craft of bowling. Mind you, not who has been the best, but strictly who has been the most successful.

In what is to follow, we deal strictly with statistics and keep aesthetics out. The plan is to come up with an objective ranking of the best bowlers in test history taking into account their productivity, fire power, and short and long term success. We start with the top 50 wicket takers in test cricket. The list can be found here [1]. As we go through the somewhat tedious process we try to explain all assumptions, but put some details in a short appendix, so as to not test the patience of the reader.

In order to make the first shortlist, three broad criteria were chosen viz. the total number of wickets taken, the average, and the number of five wicket hauls:

  1. The ability to consistently perform at the highest level of cricket is reflected through the number of wickets.
  2. Bowling average is a good indicator of the effectiveness of the performance.
  3. The number of five wicket hauls a good proxy for the match effectiveness of the performance.
As we start to use these parameters to compile the first shortlist, we notice a common trend of spinners generally having higher averages than fast bowlers. For a fair comparison, we compare the spinners’ averages amongst themselves (Group S) and likewise for the fast bowlers (Group F). For details see [2]. A bowler was part of the first shortlist if two of the following three criteria were true:

  1. Bowler has more than 200 wickets.
  2. Bowlers’ average is less than the mean average in Group S or Group F depending on whether the bowler is a spinner or fast bowler.
  3. Bowler has more than 15 five wicket hauls.
We proceed to assign points in order to quantify the bowlers’ success. On a scale of 1-8, points were assigned as follows:

  1. 200-249 wickets=1 point, 250-299 wickets=2 points etc. up to a maximum of 8 points [3]
  2. 1 point for every 0.5 lower average than the mean average of Group S or Group F depending on whether the bowler is a spinner or a fast bowler. The mean average of Group S is 27 and of Group F is 24. In Group F an average of 23.5-24=1 point, 23-23.49=2 points etc. up to a maximum of 8 points. In Group S 26.5-27=1point, 26-26.49=2 points etc. up to a maximum of 8 points.
  3. 15-19 five wicket hauls=1 point, 20-24 five wicket hauls=2 points etc. up to a maximum of 8 points.
We get the following shortlist and associated points:

Table 1
Bowler Wickets Wicket Points Average Ave. Points 5 Wicket Hauls 5 Wicket Points Total
Warne 583 8 25.51 3 29 3 14
Muralitharan 532 7 22.86 8 44 6 21
Walsh 519 7 24.44 0 22 2 9
McGrath 499 7 21.22 6 26 3 16
Kumble 461 6 28.23 0 29 3 9
Kapil 434 5 29.64 0 23 2 7
Hadlee 431 5 22.29 4 36 5 14
Akram 414 5 23.62 1 25 3 9
Ambrose 405 5 20.99 7 22 2 14
Botham 383 4 28.40 0 27 3 7
Pollock 377 4 22.09 4 16 1 9
Marshall 376 4 20.94 7 22 2 13
Younis 373 4 23.56 1 22 2 7
Imran 362 4 22.81 3 23 2 9
Lillee 355 4 23.92 1 23 2 7
Donald 330 3 22.25 4 20 2 9
Willis 325 3 25.20 0 16 1 4
Gibbs 309 3 29.09 0 18 1 4
Trueman 307 3 21.57 5 17 1 9
Underwood 297 2 25.83 3 17 1 6
Garner 259 2 20.97 7 7 0 9
Statham 252 2 24.84 0 9 0 2
Holding 249 1 23.68 1 13 0 2
Gillespie 248 1 25.72 0 8 0 1
Benaud 248 1 27.03 0 16 1 2
McKenzie 246 1 29.78 0 16 1 2
Chandrasekhar 242 1 29.74 0 16 1 2
Bedser 236 1 24.89 0 15 1 2
Qadir 236 1 32.80 0 15 1 2
Grimmett 216 1 24.21 6 21 2 9
Roberts 202 1 25.61 0 11 0 1
Harbhajan 199 1 28.17 0 16 1 2

The point system was chosen to reward the truly outstanding performance in each category with 8 points and move down in equal slabs from there. There are no negative points. As an example, Donald has 330 wickets @ 22.25 and 20 five wicket hauls. He gets 3 points for taking between 300-349 wickets, 4 points for an average between 22.0-22.49 (fast bowler’s mean average is 24), and 2 points for 20-24 five wicket hauls. The list has 22 fast bowlers and 10 spinners.

A cut off of 7 points was chosen for future analysis and we are left with 4 spinners and 15 pacers in the next list. We have verified that none of the other bowlers make it to the final top ten spots, so for simplicity we shall restrict future analysis to the second shortlist. After taking into account, a bowlers’ ability to take lots (number) of cheap (average) wickets with many performances of high impact (five wicket hauls), we analyze a bowler’s destructive ability. For this, the strike rate, number of ten wicket hauls in a match, and the number of wicket per innings were the chosen criteria for the following reasons:

  1. Strike rate best describes a bowlers’ wicket taking ability in a short spell.
  2. Number of 10 wicket hauls gives an indication of his impact on a match.
  3. Number of wickets per innings points to his ability to consistently take wickets over his entire career.
Strike rate comparison also suffers from the same problem as average between spinners and fast bowlers. Spinners tend to have worse strike rates than fast bowlers in general. For example, in the remaining group of bowlers, the spinners have a mean strike rate of 62 as opposed to 52 for the pacers. We adopt the same strategy as earlier and compare the groups separately in the strike rate criteria.

The points criteria was chosen as follows:
  1. 1 point for every 2 balls higher strike rate than the mean strike rate in Group S or Group F depending on whether the bowler is a spinner or pacer. The mean strike rate of Group S is 62 and of Group F is 52. In Group F, a strike rate of 50-51.99=1 point, 48-49.99=2 points etc. In Group S, a strike rate of 60-61.99=1 point, 58-59.99=2 points etc. Lower strike rates in the respective groups carry no point value. A maximum of 8 points can be awarded.
  2. 2-3 ten wicket hauls (1 point), 4-5 ten wicket hauls (2 points) etc. up to a maximum of 8 points.
  3. 2.3-2.4 W/I (1 point), 2.4-2.5 W/I (2 points) etc. up to a maximum of 8 points [4].
The updated points tally of our champion bowlers is:

Table 2
Bowler Strike Rate SR Points 10 Wicket Haul 10 W points Wickets/Innings W/I points Total
Muralitharan 58.5 2 13 6 3.33 8 37
McGrath 51.1 1 3 1 2.33 1 19
Warne 59.0 2 8 4 2.46 2 22
Hadlee 50.8 1 9 4 2.76 5 24
Ambrose 54.5 0 3 1 2.23 0 15
Marshall 46.7 3 4 2 2.46 2 20
Walsh 57.8 0 3 1 2.13 0 10
Kumble 65.7 0 7 3 2.63 4 20
Akram 54.6 0 5 2 2.21 0 11
Pollock 56.5 0 1 0 2.12 0 10
Imran 53.7 0 6 3 2.28 0 12
Donald 47.0 3 3 1 2.44 2 15
Trueman 49.4 2 3 1 2.40 2 14
Garner 50.8 1 0 0 2.33 1 11
Grimmett 67.1 0 7 3 3.04 8 20
Kapil 63.9 0 2 1 1.89 0 8
Botham 56.9 0 4 2 2.13 0 9
Younis 43.4 6 5 2 2.33 1 16
Lillee 52.0 1 7 3 2.67 4 15

As an example, Donald with a strike rate of 47, 3 ten wicket hauls, and 2.44 wickets/innings gets 3 points for having a fast bowler’s strike rate between 46-48, 1 point for taking 2-3 10 wicket hauls, and 2 points for taking between 2.4-2.5 wickets per innings. These 3+1+2=6 points added to his earlier tally of 9 points gives him a total of 15 points.

For further analysis, we chose a cut of 15 points or above. This leaves the final playing field with 11 bowlers of which 7 are pacers. We have verified that none of the omitted make the final 10 and choose to omit them for simplicity. In particular, Imran and Trueman come very close. The next part of the analysis rewards the bowlers for extraordinary bowling performances in an innings and/or match. We look at the number of times a bowler has picked up 8 or more wickets in an innings and 12 or more wickets in a match. This section aims to reward flair, followed by the final section, which is based on consistency. The points criteria was chosen as:
  1. 8 W/I=1 point; 9/10 W/I= 2 points.
  2. 12-13 W/M=1 point; 14+ W/M=2 points.
After incorporating these points the updated table is:

Table 3
Bowler Points for 8+ W/I Points for 14+ W/M Total
Muralitharan 5 5 47
Warne 1 1 24
Kumble 3 4 27
Marshall 0 0 20
Grimmett 0 3 23
McGrath 2 0 21
Younis 0 2 18
Ambrose 1 0 16
Imran 2 3 17
Donald 1 1 17
Trueman 1 1 16
Lillee 0 0 15

We do not make another cut to the list at this point. Since there are only 11 bowlers left in the fray, we present their results on consistently good performances next. The two criteria chosen are:
  1. The number of innings per five wicket haul.
  2. The difference between the home and away averages of a bowler.
The number of innings per five wicket haul is an excellent indicator of the bowler’s ability to produce performances of impact regularly. The difference between the home and away bowling averages shows how skilled a bowler is in different bowling conditions. Unlike batsmen, however, its not obvious why home conditions would be better than away. We choose to examine only the difference without giving any weight to which is better. The point criteria for the final round is:
  1. 6-7 innings/5 wicket haul=1 point, 5-6 innings/5 wicket haul=2 points etc. up to a maximum of 4 points.
  2. Difference between away and home average 0-1=6 points, 1-2=5 points etc. up to a minimum of 0 points.
The final table is as follows:
Table 4
Bowler Innings per 5 W/I 5 W/I points Home Average Away Average Difference HA-AA points Total
Muralitharan 3.63 4 20.61 26.91 6.30 0 51
Hadlee 4.33 3 22.96 21.72 1.24 5 33
Kumble 6.03 1 23.75 35.76 12.01 0 28
Warne 8.17 0 26.24 24.93 1.31 5 29
Grimmett 3.38 4 24.59 23.86 0.73 6 33
McGrath 8.23 0 21.84 20.63 1.21 5 26
Marshall 6.95 1 20.06 21.57 1.515 26
Younis 7.27 0 20.29 26.06 5.77 1 19
Imran 6.91 1 19.20 25.76 6.56 0 18
Donald 6.75 1 21.64 22.96 1.32 5 23
Trueman 7.52 0 20.04 26.08 6.04 0 16
Ambrose 8.27 0 21.19 20.78 0.41 6 22
Lillee 5.78 2 23.73 24.28 0.55 6 23

Thus, the final rankings are:
  1. Muralitharan-51
  2. Hadlee-33
  3. Grimmett-33
  4. Warne-29
  5. Kumble-28
  6. McGrath-26
  7. Marshall-26
  8. Lillee-23
  9. Donald-23
  10. Ambrose-22
  11. Younis-19
The point criteria has not been chosen arbitrarily and here we shall attempt to provide a justification for the choice. In the first round, we wanted to analyze three broad skills of a bowler to obtain our first shortlist. All three skills were deemed to be equally important to the impact a bowler has in the game. 8 points was chosen as the toughest benchmark to obtain. For example, in the number of five wicket hauls criteria, Muralitharan has 44 such hauls and gets 6 points. With just one more such haul, he would have got 7 and with 6 more he would have got the maximum 8 points at 50, a very conceivable option for the future. In the averages category, there have been bowlers who have taken between 100-200 wickets at an average of less than 20. That is why Garner, Marshall, and Ambrose get 7 points instead of a perfect 8 for their superb averages. Also, such a choice does not disturb the relative point slab, which is all that is relevant for this study. Similar thought process went into conceiving the point system for strike rates where there have been bowlers in the 100-200 wicket range with strike rates better than Waqar, who comes out at the top with a strike rate of 43.4.

The point system for the number of 10 wicket hauls in a career is pretty simple and straightforward. While the point system surely rewards great performances, one of its strength is the maximum points in any criteria. For example, Muralitharan takes 3.33 W/I and the median is 2.3. If there were no cap on the maximum points, Murali would end up getting 11 points in this discipline. In the end, he gets the maximum of 8. This prevents the final statistics from being skewed towards a particular player’s exceptional strength in a certain area.

The point system for exceptional innings and/or match performance has been crafted to give the correct balance. While these performances are very important, they cannot outweigh the merits of a consistently good strike rate, average etc. which are basic parameters defining a good bowler. Each subsection thus carries 5 points maximum rather than the 8 for all other sections till now.

The final part on consistency was rather easy to define. We wanted it to be equally important to brilliant innings/match performances and again not more important than the basic definition of a great bowler i.e. average, strike rate etc. While the number of innings for a five wicket haul is important, consistency in bowling in all conditions slightly outweighs it. Hence we chose the 4:6 split of the 10 points in this section. For a note on the robustness of the study see [5].

No statistical study can be complete without looking at its limitations. No matter how hard we try it is not possible to have a final say on the best bowler purely based on numbers. While it is true a large number of older test cricketers have missed out because they did not play a lot of matches, this study was never about finding the best bowler but the most successful one. It is very likely that even if they had been included initially, none would have been able to make the top ten. The idea to separate the averages and strike rates of spinners and pacers might not appeal to a few and it is maybe not the ideal solution. What is undeniable is that historically spinners considered equal to their fast bowling contemporaries have averaged more and had a lower strike rate. We had a correspondence with PwC when they still ran cricket rankings. They informed us that in devising the rankings they do take into account this fact. Conspicuous by their absence in the top 10 are members of the WI 4 prong of the 70s-80s barring Marshall and the Indian spin quartet. Again, the study focuses on individual success as a bowler. The WI 4 prong and the Indian spin quartet were extremely successful as a unit, but individually their records are not as great as far as longevity and averages are concerned. Marshall, Warne, Lillee, Ambrose, and McGrath make it in the top 10 despite being part of excellent bowling attacks where the spoils were being shared.

[1] http://plus.cricinfo.com/db/STATS/TESTS/BOWLING/TEST_BOWL_MOST_WKTS.html

[2] The mean bowling average of 13 spinners in the top 50 bowlers was 28.28 and that of the 37 fast bowlers was 25.79. After making the first cut, based on total number of wickets, bowling average, and five wicket hauls, 11 spinners with an average of 27.4 and 22 pacers with an average of 24.01 remained. It is a clear and obvious trend that spinners average higher than pacers. The trend indicates the different methods of the two categories to take wickets. Spinners have the ability to bowl longer spells, while pacers are generally used in short bursts.

[3] Harbhajan and McGrath were assigned an extra point because they are on 199 and 499 wickets respectively and surely expected to cross the barrier in their next match.

[4] 2.3 wickets per innings is the median for the bowlers remaining in the analysis. Any bowler performing better than the median was awarded points. We chose the median and not the mean as the comparison benchmark because of the skewed data set.

[5] It is also important to note that changing the weights associated with different parameters does alter the ranking a little bit, but more importantly the general trends are preserved. As an example, Muralitharan’s position at the head of the table can be changed only by a serious change of the parameters used to study the bowlers. On the other hand, the remaining bowlers in the top 10 are sufficiently close together that a few changes do cause some shuffle in the order. But more importantly, these shuffles are not drastic unless the parameter changes are drastic. This robustness of the study is important in ascertaining a group, which has performed well and although the ranking among the group may change on the choice of parameters, the top 10 bowlers obtained in this analysis would come out to be the same if the parameters were tweaked moderately.

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