Making of a Test bowler: Time it takes to find your feet

Interesting times are back in Cricket. Debutant bowlers since September 2011 have surprised the batmen and as many as six new entrants (four of those are fast bowlers) have started their careers with a five fours. In fact the 12 debutant bowlers of in 2011 have shared as many as 18 five fors. Although data is not sufficient, but this new breed of bowlers seem to bring a hope that finally balance between the ball and the bat will be restored (see Number Game). What is really encouraging is that six of these new bowlers are less than 22 years of age. So I think there are interesting times ahead for Test Cricket where runs will not be easy, or at least that what I would like to happen.


To appreciate the importance these superb performances by the debutant bowlers we (together with Ajit Padmanabhan) looked at the probability to take a certain number of wickets in first four innings. To this end we looked at the bowlers who took at least 200 wickets and bowled at least 71 inning (otherwise the great Clarrie Grimmett would be left out and we dont want that). This way we have 57 bowlers for this analysis.


So we asked how these obviously successful bowlers performed early on in their career. In the figure below we have the probability of taking a certain number of wickets in first four innings of a bowler who finished his career with at least 200 wickets (left panel). The probability to take a certain number of wickets decreases as we increase the wickets count. This decrease is almost linear. But more data may change the picture. The figure also shows that for some of the very successful bowlers the probability to take five wickets or more is only 7% (right panel). This really reveals how amazing  the success of the class of 2011 has been.

Figure 1. Left: Probability of taking a certain number of wickets in the first, second, third and forth career inning of a bowler. The linear decay of the probability traces shows how difficult it is to take more wickets in a test innings.
Right: Probability of taking 'n' or more wickets in the first four career innings. The dark line in both panels is average of the four innings. It turns out that there is only 7% chance to take five of more wickets in your first four outings as a Test bowler. Data taken from cricinfo. 

How much time you want to invest in a new bowler
In cricket early success or failure is no predictors of long term success. So how much time a team should invest in a bowler if he is not responding. We turned to the  numbers of the bowlers who took at least 200 wickets and extended our previous analysis. This time we averaged the innings by innings wickets of these bowler in the 200+ club. It turns out that, when averaged over 57 bowlers, it takes about 10 innings before the bowlers reach their steady state of taking on average 1.5 wickets per inning. 

Figure 2. Evolution of a Test bowler. The probability distribution shown in the figure 1 is color coded and shown for first 71 innings of 57 bowlers who have taken at least 200 wickets. Dark colors mean less probability and other way around for bright colors. The thick blue line is the mean of the probability distributions. The slow rise of the blue line indicates that test bowlers take some time to find their feet at the highest level of Cricket. After about 10 innings the line hovers around 1.5 indicating that after that bowlers stats dont vary much. It also shows that even the very successful bowlers on average take only about 2 wickets per innings. This consistent with the fact that most teams field 4-5 bowler who fight to take 10 wickets.

So we argue that the teams should look into their bowlers at least for 5 test matches before giving up on them. By the same token if a bowlers has not reached his steady state of 1.5 wickets by the fifth match, there is a little chance for him, statistically speaking.


right arm over
Arvind

PS: I was helped by Ajith Padmanabhan in collection and analysis of the data.