Leg Spinners – A statistical assessment

From S. Giridhar and V J Raghunath, India
Subhash Gupte and Bhagwat Chandrasekhar, Shane Warne and Abdul Qadir and all those other artists have provided individual nirvana to millions of cricket lovers. Leg spin is infinitely and uniquely fascinating. For quite some time, we have thought of sharing our love for leg spin and we decided we will begin by developing a method of statistically assessing the bowling records to see how the best of legspinners stack up.

We decided a cut off - all legspinners who have played a minimum of 5 tests and taken at least 20 wickets. We excluded from our study the left arm Chinaman bowlers and also the mystery spinners such as Sonny Ramadhin, JohnGleeson and Ajantha Mendis in this list. We thus have a list of 37 legspinners for our analysis: (Table 1)

We realized that each aspect of performance – wickets, strike rate, bowling average, five wickets in an innings and ten wickets in a match – will have a bearing on determining the overall value or effectiveness of the bowler. We decided that for the strike rate, bowling average, five wickets in an innings and ten wickets in a match, we could create a Relative Index and convert each bowler’s performance into his individual index score. To calculate the index for a particular parameter, let us demonstrate with the example of Warne’s index for strike rate: His strike rate is 57.4. The cumulative strike rate of the 37 players in our list is 2627.1. So Warne’s SR Index is 57.4/2627.1 expressed as a percentage which is 2.7. Each player’s Index for each of the four parameters is calculated. The aggregate of the index for the four parameters of each player provides us the individual players’ index scores. Thus Player’s Index Score is the sum of Index score on SR + Bowling Average + 5w/Inn + 10 W/ Match. The lowest Player Index Score reflects best in class and so ranks would progressively go down as the index scores went up.

We also need to recognize and give value to the wickets that a bowler had taken as this reflects a bowler’s longevity and sustained performance. Since the 37 bowlers in our list range from an extreme high of 708 wickets to an extreme low of 20 wickets, we decided to convert the wickets to their logarithmic value (Let us call this Log W; 100 wickets would thus have a value of 2, 200 wickets would have a value of 2.3 and 400 would be 2.6, 1000 wickets would be 3). Sticking to our convention of lowest figures indicating highest degree of effectiveness, we created an Effectiveness Index by dividing the Players Index Score by the Log value of Wickets. Thus Effectiveness Index = Player’s Index Score/ Log W. Table 2 below ranks the leg spinners by their Effectiveness Index and seemed to be a fair representation and pecking order among the leg spinners.

But having done this, one realized that we must also consider the quality of opposition and the quality of batsman whose wickets had been captured. What proportion of the wickets was against weaker teams? How many of these were either lower order batsmen or tail-enders? Should we not apply some kind of factor for taking this aspect into our calculations? Here is where Mike Holmans provided us invaluable support. Readers will be familiar with Mike’s article that appeared on 19 December 2008 in Cricinfo where he presented the “Most Efficient Bowlers” by creating an index that specifically took into account these factors. So we wrote to Mike and requested him to present us with his index for each of the 37 bowlers on our list. Mike was immensely helpful. We acknowledge Mike’s help by christening his index as the Holmans Power Index of Efficiency.

From the Holmans Power Index - it was interesting to note that while champion bowlers such as Clarrie Grimmett and Bill O’Reilly were in the top in Holmans list too, bowlers of the pre-1930 era who did not play too many tests but had stunning strike rates such as Bert Vogler, Brendon Bosanquet, Ranji Hordern and Tich Freeman surpassed players such as Anil Kumble, Richie Benaud, Chandrasekhar, Qadir on Holmans Index. We decided that we would combine (and average out) the Effectiveness Index created by us and the Holmans Power Index to arrive at a ‘Composite Effectiveness Index’. We felt that this might help smoothen out some of the sharper differences between the two methods. And so it surely did. Thus while we will find the odd bowler surprising high on the Composite Effectiveness Index List, we have a reasonably large number of players in a pecking order that intuitively also seems right. And so we have these players, each with a composite effectiveness index that ranges from the best of them all – Warne at 36.46 to Chandu Borde at 74.66. This then is the final pecking order that we have arrived at as shown in Table 3 below.

We debated quite a bit about the merits of splitting this list into two separate categories or more - for instance separate tables and rankings for bowlers with less than 100 wickets and those with more than 100 wickets. We also toyed with the idea of separating cricketing eras and have separate lists for players who were from the pre 1930 era and post 1930 era and so on. But finally we decided that we will retain all of them in one pool. The fact that Warne, Grimmett, O’ Reilly, Chandra and Kumble are in the top ten would probably be greeted with unanimous agreement and add credence to our methodology. But we wonder if are stirring up a nice royal debate by placing Vogler, Hordern and Freeman in the top ten using our methodology. Obviously, even though they took fewer wickets, they were so strong on the other parameters that they pushed the likes of Mushtaq, Benaud, Gupte and Qadir to places 10 to 14. Having done with the stats, we cannot wait to narrate anecdotes and stories on our favourite leggies. Watch this space!