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BLOG: Are some wickets bigger than others?

Are some wickets bigger than others?

The 1st Test of the 2011 English Summer produced one of the more incredible results in the history of the game, with Sri Lanka collapsing for 82 all out in fewer than 25 overs.

It is the first, rather than the third, innings of that match to which we wish to turn our attention to here however. Specifically, the summary of England's bowling:

OPB-Bowler-Study-1

This was in the middle of Broad's lean spell as the supposed 'enforcer', which elicited - somewhat remarkably now - calls for him to be dropped. The statistical stars of the show are clearly Swann and Anderson, accounting for more than half of the tourists' wickets.

On the face of it there is not much to split the two, with Anderson edging it in economy (2.35 to 3.16) and average (22.0 v 26.0) but Swann holding the advantage in strike rate (49.3 to 56.0). The advantage probably goes to the quick but there's not much in it.

At least until you look at the batting card:

OPB-Bowler-Study-2

Anderson accounted for the heart of Sri Lanka's middle order, including the scalps of two of the finest batsmen of their generation. While Swann did pick up Dilshan, the first wicket of the innings, his numbers are padded by cleaning up the tail of Herath and Lakmal.

So, given the disparity in ability of the batsmen dismissed, should we really count Anderson's three wickets on a par with Swann's and, if not, how do we settle the difference?

Accounting

To state the obvious, a bowler wants to take wickets and prevent runs, while a batsman wishes to score runs whilst preserving his wicket. So, a logical place to start is to look at which players have best achieved these aims. The tables below show the top and bottom five batsmen for each discipline over the last five years in Test cricket:

OPB-Bowler-Study-3

Interestingly, two of Anderson's wickets in that Test appear amongst the five most difficult to take, while Swann accounted for the game's third quickest scorer as well.

Using these measures we can attribute an expected performance for each bowler against the given batsmen. So, bowling 10 overs against Chanderpaul, we would expect an average bowler to take 60 ÷ 154 ≈ 0.4 wickets. Against Test cricket's greatest rabbit Chris Martin however, we would expect 60 ÷ 12 = five wickets.

We cannot necessarily just use the players' five year average, however. How would this work for players with little or no experience? Or those that suffer large changes in form?

To - attempt - to tackle this problem, we used an (up to) three-year average, taking in to account past, current and (where available) future performance. So, in the case of a game played in 2012, we would have the last 18 months as the sample for the player but for one in 2009 we would use both the 18 months prior to and after the game in question. This, to some extent, deals with the issue of debutants, as well as the varied nature of opponents played over the cricket calendar.

Specifically, we weight a players' data according to how much they have played, combining it with an average for their batting position. So, were England to improbably hand a Test debut to Jos Buttler in their next Test, he would be assigned Test-average figures appropriate to the position he bats at. Then, as he played more games, his actual performance data would be weighted more and more heavily, to the point where an Alastair Cook uses about 99% of his data and 1% of the Test average.

Returning to our Sri Lanka v England example, Kumar Sangakkara was dismissed 32 times in 3,893 balls in the period encompassing the 18 months preceding the 1st Test in England and to date (less than 18 months since), or 122 balls per dismissal. Given the volume of deliveries faced, we use 97% of this figure and the remaining 3% of the average, to give an expected figure of 119 balls per dismissal for this match.

We can do the same for all batsmen, for expected wicket and run-scoring rates for the 1st  innings example from before:

OPB-Bowler-Study-4

For the Anderson v Paranavitana head-to-head, Anderson bowled 47 balls, allowing 15 runs and taking 0 wickets. Per the xBpD and xRpO, we would expect an average bowler to take 0.5 wickets and allow 19 runs. So Anderson is credited with -0.5 wickets but also -4 runs (in this case a negative number is a good thing).

Summing this up for all the England bowlers versus all the Sri Lanka batsmen, we get these adjusted figures:

OPB-Bowler-Study-5

Anderson now grades out as the best bowler of the innings both in terms of wickets taken (picking up 0.7 more in his 28 overs than we would expect an average bowler to do) and runs prevented (allowing nearly a run per over less than expected, given the batsmen faced).

Updated Rankings

Listed below are the top and bottom five bowlers in Tests since the start of the 2010 English summer for:

•  Traditional strike rate (adjusted to exclude wides).

•  Expected strike rate (i.e. the rate of wicket-taking an average bowler should achieve given the quality of batsmen faced).

•  The difference in achieved wicket taking against the players' expected total.

OPB-Bowler-Study-6

There are not significant differences between the 1st and third tables, with Steve Finn's easy opposition dropping him out of the top five, while the quality of batsmen faced by Dwayne Bravo and Mahmudullah somewhat offsets their disappointing strike rates.

We can instead look at the biggest changes in relative ranking to see who has most been penalised and rewarded for their strength of opposition:

OPB-Bowler-Study-7

Johan Botha's streike rate of 61.2 is more than acceptable for a Test spinner but, taking into account who he as bowled against, his +0.24 dW60 places him in the top 20 bowlers of the last two years. This is on a par with Chris Tremlett (+0.23 dW60), despite Tremlett's strike rate being 10 balls better (51.6) per wicket.

At the other end of the scale, England's two tormentors-in-chief in the UAE, Abdur Rehman and Saeed Ajmal, appear to have benefited from relatively straightforward competition (fourth- and fifth-lowest xBpD), with both ranking around average over the two-year sample. It should be noted that they were anything but in the England series, scoring +0.54 and +0.64 dW60, respectively.

Repeating the process for runs allowed:

OPB-Bowler-Study-8

OPB-Bowler-Study-9

Interestingly, Botha is on the receiving end of the largest negative change this time around, dropping from average economy to near the bottom, once quality of opposition is factored in. This suggests he faced a large quantity of Dravid-esque batsmen, that were hard to dismiss but he should have remained economical against. Indeed, the four batsmen he faced the most often (Azhar Ali, Misbah-ul-Haq, Younis Khan and Shivnarine Chanderpaul) all broadly fit into this category.

For those that prefer it, an expected average (expected wickets ÷ expected runs) can be calculated and compared to the observed average:

OPB-Bowler-Study-10

Mohammad Amir's involvement in the spot-fixing scandal becomes all the more regrettable, with his performance topping even the recent sensational starts to Test cricket made by Vernon Philander, James Pattinson and Doug Bracewell.

As an aside, the use of average as the defining stat has always baffled me, as I am yet to be convinced that the worth of limiting runs and taking wickets are exactly equal (as implied by the 1:1 ratio of wickets:runs in the average calculation). Certainly - ceteris paribus - given the option of Simon Jones (28.23 average, 3.54 economy, 47.8 strike rate) or Ryan Sidebottom (28.24, 2.78, 60.9) I'd take the wicket taker. Regrettably for Jones and England, all was not paribus.

Summary

This study hopefully demonstrates some of the limitations of the traditional statistics used in cricket and of their uses, although is by no means conclusive. Indeed, it looked at only one factor - the quality of batsmen faced by bowlers -- to attempt to better quantify bowling success.

For example, this does not take into account the location of the match and how difficult it is to score runs and take wickets there (and how much that is impacted by the teams playing). It also assumes that batsmen lose their wickets at a constant rate (i.e. they are as likely to get out first ball as when 150 not out), a subject looked at in more depth here.

Posted by Sam Green at 10:08

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