During a tense passage of play, when a bowling attack appears to have a batsman pinned down at the striker's end, we often hear commentators wonder why the batsman doesn't try to score a single to ease the pressure. This is especially the case when a left-right pair are at the wicket. Otherwise, it is only a matter of time before a wicket falls, we hear.

I've often wondered about this. If batsmen were able to hit the ball into a gap for one or more runs, why would they choose not to do so? Batsmen, it seems to me, get pinned down on strike only when the bowling is too good to give them a chance to hit something for runs. At the elite international level, it is not unusual for a combination of bowling quality, field setting and bowling conditions to create such a scenario. Nevertheless, the idea that "batsmen should look for the single" against difficult bowling, or that "the best place to survive a great spell is at the non-striker's end" has wide currency. Are batsmen missing a trick? Or are the commentators misreading the situation?

A few years ago, I showed from partnership level records that there's no advantage to having a left-right batting pair at the crease over a left-left or right-right pair if all the batsmen involved are equally good. In this article, I will consider the record at the ball-by-ball level first to measure the effect of a single on a stand, and then to measure the effect of a left-right pair if the single is taken. Ball-by-ball data for the 841 Tests and 2452 ODIs from the 21st century for which such records are available is used here. The earliest Test in this data set is the 2001 Lord's Test between England and Pakistan. The most recent one is the 2020 Christchurch Test between New Zealand and India. The earliest ODI is the 1999 Lord's ODI between England and Sri Lanka. The most recent ODI is the 2020 Potchefstroom ODI between South Africa and Australia.

During this period in Tests, 60% of deliveries faced by opening batsmen have been faced by left-handers. Twelve of the 15 most prolific Test openers (and 11 of the top 12, Virender Sehwag being the sole exception) in this period have been left-handers. Left-hand openers average 39.8 while right-hand openers average 34.4. This basic record does not reveal an advantage to being lefty or righty; it reflects the quality of the average left- and right-hand Test opener in this period. This difference in quality does not extend to the rest of the top six. In the top six, the average right-hander averages 40.3, while the average left-hander averages 40.1.

In ODI cricket left-handers don't dominate quite as much as they do in Tests. Nevertheless, even in ODIs, left-handers tend to be openers more often than middle-order players. While 12 of the 20 top-scoring ODI openers in the matches under consideration are left-handers, only four of the top 20 ODI middle-order bats are left-handers. All told, there is no evidence in the record to suggest that the overall quality of left-hand bats is superior to that of right-hand bats. The only indication is that left-handers make up a higher share of the batting in the top half of the order than they do in the bottom.

(The data below considers the full batting order and not just the upper half of it.)

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To study the consequences of a bowler having to bowl at a different batsman from the one who faced up to the previous delivery, the batting average on the (n+1)th delivery in an over when the strike changes on the nth delivery is compared below to the batting average on the (n+1)th delivery when the strike does not change. This comparison ignores whether the batting pair are both left-handers, right-handers, or one of each. By definition this comparison also ignores the first ball of each over. Strike changes that might occur due to dismissals are also ignored. The chart shows a 20-over rolling average over the first 100 overs of the innings.

The evidence does not suggest that it is harder for a bowler to effect a dismissal after a strike change than otherwise, especially when the ball is new. When the ball is older, it becomes marginally harder to dismiss the batsman when the strike does not change. The scoring rate on the ball after a strike change during an over is about a tenth of a run faster than in cases where the same player is on strike.

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In cases where the strike has changed, the evidence shows no advantage to having a left-right pair, except against the older ball. As can be seen from the graphs above and below, against the new ball there is no benefit to having a left-right pair over a pair where both batsmen are either left or right-hand in cases where the strike changes. (If anything, there is a marginal advantage to having a left-left or right-right pair over a left-right pair.)

There's nothing that suggests having a left-right pair adds to the security of a partnership when compared to a left-left or right-right pair.

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There is some evidence elsewhere for the proposition that batsmen who are prepared to bide their time are often harder to dismiss than ones who prefer to assert themselves. Cheteshwar Pujara is dismissed once every 86 balls in Tests outside Asia compared to 82 balls for Virat Kohli at the same venues, even though Kohli averages ten runs more. Pujara's game is based on defence, and he makes bowlers bowl longer to get his wicket. Scoring becomes easier against the older ball (and perhaps against the change bowlers, who tend to be less challenging than the new-ball bowlers).

Sachin Tendulkar would often start slowly in Test innings in the 2000s. In the 27 innings where he had scored fewer than 20 by the time he faced his 50th delivery, Tendulkar averaged 70. Rahul Dravid averaged 68 in the 71 innings where he played his 50th ball without reaching 20. When batsmen make a quick start to a Test innings it indicates either that the field is attacking or that the bowling is inconsistent.

Singles are the most common way to rotate the strike during an over in cricket. The number of singles scored in the first 50 balls of a Test innings is proportionate to the number of runs scored overall during those first 50 balls.

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There are 10,765 individual innings that lasted at least 50 balls in the 841 Tests under consideration. These are summarised in the table below by the number of singles scored in those balls. The most singles scored in the first 50 balls of a Test innings is 28. (There are only 12 innings out of 10,765 where more than 20 singles were scored in the first 50 balls, and these have been ignored below.) Ninety percent of innings involve ten singles or fewer. Ninety-nine percent of innings involve 15 singles or less. The table does show that a batsman's average score goes up when he takes more singles - from 48 when he takes no singles, to 70 when he takes 16 - even though the length of the innings in terms of balls faced does not improve.

The examples of Tendulkar and Dravid thus illustrate a larger point, which is shown in the summary above. The ability to score a single is not a weapon available to a batsman in Test cricket. It is better seen as a symptom of the quality of the bowling. In Test cricket at least, the answer to the dilemma that forms the basis of this article is that the batsman doesn't take a single because he can't, and not because he chooses not to. The better batsmen are superior not because they are better at getting off strike against top-class bowling, but because they are technically better equipped to keep facing it at the striker's end. The frequency of singles might appear to be down to the batsman, but it is, in fact, a function of what the bowler's line of attack may or may not allow.

In the limited-overs game, the conditions change. Field settings are designed to restrict runs and especially boundaries. Singles are often available uncontested in large sections of the outfield. The fielding restrictions influence the effect of strike changes on batting. In the early overs against the new ball, there is no advantage to stealing quick singles. Against the spread-out fields of the middle overs, preventing singles is in the interests of the fielding side according to the graphs below. This could be read simply as a question of how many singles the fielding side is really contesting. If the fielding side is in a position to contest more singles and prevent them more frequently, then not only are fewer runs conceded, but dismissals occur more frequently as well.

At the beginning and at the end, when the boundaries form the lion's share of the scoring in limited-overs innings, there is no added benefit to rotating the strike, the numbers show.

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When the strike is rotated in the first half of the innings, there is a definite advantage to having a left-right pair at the crease. This includes the early overs against the new ball. Given that there isn't a significant difference between the quality of left- and right-hand top order ODI players in the 21st century, this evidence suggests that it is probably a good idea for batting sides to try and get left-right pairs to the crease in the first half of ODI innings. In the middle overs, this advantage disappears. The significant difference between the middle overs and early overs is the field setting. Against the well-spread fields that are commonly found in the middle overs, the advantage of the left-right pair over the left-left and right-right pair disappears, because fielding sides essentially cease to contest singles since they can post four fielders on the boundary.

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Overall there seems to be no evidence to support the idea that the pursuit of the single to get off strike against top class-bowling in Test cricket is a viable tactic for the batting side. And there's no evidence that single-taking has any relationship to how long an individual innings will last. Whenever you see a lot of singles being taken in a Test match, it is a sign that the bowling is not good enough or that the field setting is not suited to the bowling. The presence of the left-right pair does not make things easier for the bowling side. On the whole, Test attacks are far too good to fail to cope with having to bowl to a left-right pair as well as they cope with a left-left or right-right pair.

In ODI cricket, the fielding side can earn a definite advantage by keeping the singles down in the middle-overs of an ODI innings, and batting sides benefit from having left-right combinations on in the first half of an ODI innings. Here the conditions and field restrictions create more opportunities for tactical jousting, because pure quality is not as much of an advantage in the limited-overs game as it is in Test cricket.

It is understandable why some commentators are keen on the quick single. However, Test cricket is a bowler's game, as I have learnt increasingly from my observations over the years. As we wait for the 842nd Test or 2453rd ODI to be added to the available record, this is perhaps something to reflect on.