Last week, we identified the greatest batsmen of all time by comparing their relative superiority over peers and then factoring longevity into the equation.
Using the compare-among-peers method to judge bowlers is a tad more complex, however. For one, the average difference for elite batsmen is calculated as the difference in averages of such batsmen over every other player — including bowlers. That is because everyone has to bat (if wickets fall) in a Test innings, whereas the set of bowlers in a team and therefore in an era is limited.
Next, while the batting average (runs divided per completed innings) is a singular measure of a batsman’s quality, bowling averages (Avg: runs conceded per wicket) can’t be used alone. Strike-rates (SR: balls per wicket) are an effective measure of a bowler’s worth, too. The quicker a bowler takes wickets, the more it benefits his team.
We therefore need a derived measure that harmonises the bowling average and strike-rate to evaluate bowlers. Then there is the economy-rate — has it as significant an influence on victory as the strike-rate and average?
To sort this out, we looked at the correlation between the relative economy rates of the two opposition sides in all Tests that ended decisively, but found that there was no significant relationship between the two variables.
In order to arrive at a derived rate combining SR and Avg, we again looked at all decisive Tests and compared their relation. We found that the ideal strike-rate was 1.61 times the bowling average in such games (and this relationship explained close to 70% of all decisive Tests).
The red line denotes the strike rate-average relationship (SR=1.61*Avg) that accounts for a majority of all decisive Tests
We used this relationship to calculate the weighted harmonic mean* of the average and strike-rate — Harmonised Rate — for each Test bowler with a minimum of 100 wickets. We also calculated this for everyone who bowled during the player’s career. The difference between a bowler’s Harmonised Rate and that of all other bowlers of his era — Rate Difference — was used to compare bowlers across different eras.
For instance, the great West Indies paceman Malcolm Marshall played between 1978 and 1991. He took 376 wickets at an SR of 46.7 balls per wicket and Avg of 20.94 runs per wicket. His Harmonised Rate, the weighted mean of SR and Avg, was calculated as 31.69.
This was also calculated for all bowlers in the years from 1978 to 1991. The Rate Difference between them was found to be -16.87 — the smaller this number the more proficient a bowler is at picking up wickets.
Here are the pace and spin bowlers with the best Rate Difference:
(BS refers to India's BS Chandrasekhar)
Rate Difference is a good metric to evaluate bowlers, but this does not consider the longevity of a bowler’s career. To do this, like with batsmen, we need to see what value he offered over his career, compared to the mean bowler of his era. For this, we calculate how many wickets a bowler has taken in excess of his era’s mean bowler.
For example, Dale Steyn has picked up 419 wickets at an SR of 41.5 in 17,391 balls. How many fewer wickets would the mean bowler between 2004 and 2018 (SR: 63.27) have taken in the same number of balls? This is the measure of Steyn’s Net Value added, and is calculated thus: 419-(17,391/63.27) = 144.13.
The pace and spin bowlers with the highest Net Value are:
(Click on the links to explore the complete interactives: Pace and Spin )
Tying it together
We plot both variables (Rate Difference and Net Value) in a scatter graph and identify the highest bracket of intersection for both pacers and spinners. This bracket is set at a Net Value above 100 and Rate Difference of -13.6 for pacers, and 35 and -8.6 for spinners. The elite bowlers among them are identified in the plot.
Marshall, Steyn, Waqar, Trueman, Hadlee and McGrath were the best ever pacers based on the scatter graph. Muralitharan, Warne, Ashwin and Laker are clearly among the elite among spinners.
(Click on the links to explore the complete interactives: Pace and Spin )
We followed a similar exercise to determine the elite bowlers overseas. Among the pacers, Hadlee, McGrath, Marshall, Steyn and Ambrose slotted into the top bracket. Among spinners, Warne (by a distance), Grimmett, Richie Benaud and Muralitharan were the best performers.
(Click on the links to explore the complete interactives: Pace and Spin )
(Ashwin is yet to pick up 100 plus wickets in Tests, which is why he does not figure in the overseas elite list.)
** The harmonic mean is one of several types of averages in mathematics, and is appropriate in situations where the average of rates is desired. Weights are used when the two rates are associated, as we have determined is the case with SR and Avg.
Graphics and visualisation: Vignesh Radhakrishnan and Varun B. Krishnan
