It Figures

The table below lists the records of all teams after winning tosses in home games, and none is as imposing as the Sri Lankans. In 19 matches before the ongoing one in Colombo, they'd won 15 and drawn four. Their preferred method has been, as you'd expect, bat first and knock the stuffing out of the opposition - they've done that 11 times. And on six of the seven occasions when they've fielded, the opponents have been Bangladesh - so the move was probably to ensure an early finish to the match. None of the other sides have a record which is as dominant, though Pakistan haven't lost any of ten Tests either. (To see how these teams perform when they lose the toss, click here.)

The last team to achieve the near-impossible feat of losing the toss and winning the match against Sri Lanka in Sri Lanka was England, in that acrimonious series in 2001, when they edged past the home team by four wickets at the SSC. On the basis of what has been witnessed in the first two sessions of the current match at the SSC, it can safely be said that MS Dhoni's team won't repeat that feat over the next four days.

In my first column for It Figures, I took a look at innings-to-innings consistency among batsmen, and reached the conclusion that, on balance, it appears to be a good thing. This time around, I've performed an analysis looking at bowlers. My methods are identical, with particular reliance on the coefficient of variation (CoV) as an estimator of consistency; please see my previous post for full details.

At the outset, it should be noted that bowling stats present a small problem. Whereas our primary concern about batsmen is how many runs they score, we tend to be interested in two things with bowlers: how many wickets they take and how many runs they concede (and, of course, the standard measure by which we judge them – the bowling average – is a quotient of the two). The problem is that it is only straightforward to observe the innings-to-innings variability of one or other of these measures at a time. For the purposes of this analysis, then, I have just relied on wickets taken.

In a way, this is helpful: although it's not a stat on which we tend to focus much attention, wickets-per-innings (WPI) is the direct equivalent of runs-per-innings (or, give or take a little adjustment for not-outs, the batting average). It is also a good, sensible measure to use to think about bowling consistency: I hope most readers would agree that a bowler who takes 5/95, 5/176, and 5/23 in consecutive innings conforms more closely to our intuitive sense of bowling consistency than one who takes 1/30, 6/180, and 2/60, even though the latter took his wickets at an identical cost in each innings.

There are some fairly good reasons why WPI is a seldom-seen stat, however. The biggest problem is that it might be heavily influenced by factors over which the bowler has no control. You might be the finest bowler in your team but, unless your captain believes that, he won't ask you to bowl much and you won't take many wickets. Moreover, if the teammates with whom you share the ball are good bowlers, they are liable to take plenty of wickets, themselves, thereby depleting the finite number of scalps left for you to claim. (Pelham Barton has made the excellent point that batting in a team of good batsmen increases your opportunity to score runs, whereas bowling in a team of good bowlers reduces your opportunity to take wickets.) For these reasons, it might be argued that WPI tells us as much about the other players in a team as it reveals about the one in whom we're interested. This is fair enough: I have to acknowledge that a bowler might have a more or less consistent record for reasons for which he cannot, himself, take all the credit or blame, but that's a way to explain differences, rather than a rationale for assuming they don't exist.

Test consistency

There's a familiar name at the top of the most consistent bowlers list (Table 1). Unless something remarkable happens in his final game, Muttiah Muralitharan will retire not only as Test cricket's most prolific wicket-taker, but also as its most consistent. He has taken between 2 and 5 wickets in over two-thirds of the Test innings in which he has bowled, and his remaining analyses are fairly evenly divided between more and less successful returns. It is predictable that these characteristics would be reflected in an exceptionally low CoV.

Joel Garner may be an example of the type of bowler whose WPI is constrained by formidable competition for the scarce resource of opposition wickets. Seeing as he took at least 4 wickets in an innings 25 times, it's hard to imagine that he wouldn't have managed more than 7 fiver-fers if wickets hadn't invariably been tumbling at the other end, too.

In the upper reaches of a list that is dominated by some very high-class bowlers, Darren Gough's name may look a tiny bit out of place, but his low CoV is testament to his dependability at a time when his country's attack sorely needed it.

S Rajesh comes close to answering the first of my questions in this It Figures avant la lettre column from 2006. He proposed a consistency index that is derived by dividing a batsman's average by the standard deviation (SD) of runs scored in each of his innings. I think he's on exactly the right lines, here, but I think the index can be improved in two ways. Firstly, I'm twitchy about combining one measure - the batting average - that makes an adjustment for not-out innings with another - the SD of the same dataset - that does not. For this reason, I'd rather rely on simple runs-per-innings (RPI), in this context. This way, both halves of the sum are quantifying the same thing and, although both may be affected by not-out innings, they are both affected equally. The second modification I have made is to turn the sum upside-down, so we have SD divided by RPI. Mathematically, this makes no difference to the ranking of results (although it means that low numbers, rather than high ones, indicate greater consistency).

The advantage of doing these two things is that the number you end up with has a solid interpretation: it is the percentage of deviation around the mean that is observed, on average, throughout the dataset. Dividing the SD by the mean is a trick statisticians use quite often; they call the result the coefficient of variation (CoV). As Rajesh pointed out, it's important to perform this scaling, rather than concentrating on SDs on their own, otherwise the batsmen who score most runs will always appear to have more variability in their records. A batsman with scores of 5, 30, and 100 has the same CoV as one with scores of 10, 60, and 200, though they have very different SDs.

So much for the theory; what about the results? Table 1 shows the batsmen who have been most and least consistent on an innings-to-innings basis throughout Test history, with a few notable figures picked out from the middle of the table.

Top of the lot is Kiwi opener Mark Richardson. He may not have set the world alight compared to some of his dashing contemporaries, but his solidity as an opening batsman can easily be overlooked: he reached double figures in 80% of his Test innings (a very high proportion, as noted in another Numbers Game a few years ago), and only ever registered one duck. What stopped him from threatening the real top rank of the game was that, though he'd seldom get out cheaply, he was also pretty unlikely to score very heavily, as a total of four centuries from 65 innings and a top score of 145 attests. These characteristics are perfect for a low CoV, because they imply that a large majority of his innings fell in a relatively tight range in the middle of possible scores. Cricket will always find a way of surprising you but, to a greater extent than with any other batsman, you knew what you were going to get from Richardson.