Are some wickets bigger than
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
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:
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:
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
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:
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
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
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:
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:
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).
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
• 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.
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:
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:
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
For those that prefer it, an expected average
(expected wickets ÷ expected runs) can be calculated and
compared to the observed average:
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.
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.