Does strike rotation matter in cricket? Yes, but not in the ways you might think

It is a truism in Test cricket that strike rotation is a virtue, and that bowlers typically prefer to keep a batter at the striker's end, since this improves the likelihood of dismissal. Strike rotation is also considered a virtue for batters in shorter formats. Even though scoring rates exceed a run a ball comfortably in T20 matches, and the value of boundary-hitting is now widely recognised, scoring one from a delivery is still considered better than scoring zero.

What are the consequences of keeping a batter on strike in each format? Using ball-by-ball records, I analysed all sequences of consecutive deliveries over which the same batter has been on strike by the length of the sequence. Batters in positions one to eight have been considered. Sequences of lengths that occur less often than once in every 1000 sequences are ignored. The ball-by-ball record is available for some matches from 1999 to 2003, and for all matches since.

The strike changes in cricket for three reasons - dismissal, runs, and the end of the over. As one might expect, in Test cricket the most common sequences are those that last up to one over in length. For the current purpose, a sequence is considered a set of consecutive deliveries in a team's innings in which a batter stays at the striker's end. The sequences of more than six balls in length are those where the batter has taken a single off the sixth ball of an over; and for the few sequences of more than 12 balls, the batter has also taken a single off the sixth ball of a second consecutive over.

A batter in a Test match is about three times less likely to face five consecutive deliveries (one in 11.9 sequences) than he is to be on strike for one delivery (one in 4.1). Staying on strike improves the batter's chance of accumulating runs - five-ball sequences produce 46.8 runs per wicket, while two-ball sequences produce 22.0 runs per wicket. They scoring rate does not improve, however. A two-ball sequence on strike is about equally likely to involve a boundary as to involve a dismissal. As sequences get longer, the likelihood of the sequence ending in dismissal does not increase. The likelihood of the sequence involving a boundary improves marginally.

The table below gives the data for the same sequences in Test cricket for batters in the top eight batting positions facing James Anderson or Stuart Broad. These two bowlers have stellar career records and ball-by-ball records are available for their entire careers. These great bowlers are harder to score against than the average bowler, but the pattern holds even for them: playing three, four or five consecutive balls against them is less likely to result in dismissal than playing out two balls against them. The record is noisier (since the number of sequences is smaller), but the pattern is nevertheless discernible.

When batters face bowlers of the quality of Broad and Anderson, the received wisdom is that it is best to rotate the strike. This is reinforced when a batter is dismissed against them following a prolonged scoreless period. However, the record suggests that surviving sequences of deliveries against them is the norm, and being dismissed after facing most of an over against them is an exception. What are commonly seen as set-ups are anomalies.

In ODI cricket, fields are spread out for the most part and catching fielders are a rarity. Scoring rates tend to be lower than a run a ball as a rule, and even in high-scoring contemporary matches are usually below seven runs per over. Keeping a batter on strike improves batting averages, but it also slows the scoring rate. The longer the batter is kept on strike, the slower the scoring rate, by varying degrees - a single is, on average, the best result for the batting side, given the infrequent occurrence of boundaries. This is a feature of ODIs that separates the format from T20. Slowing down the scoring rate is beneficial to the fielding side even if it makes wickets less likely to come by.

In T20, scoring rates are higher than a run a ball. This makes both the dot ball and the single valuable to the bowling side. The sequence record in T20 shows that unlike in ODI cricket, the scoring rate improves as the length of the sequence increases. This is because of the increase in boundary percentage: staying on strike for a bigger sequence of deliveries makes it more likely that a boundary will be scored in T20 than in ODIs. It also appreciably increases the probability that an illegal delivery will be bowled. One way to think about this is that a batter who hasn't scored a single is likely to face a dot, score two, four or six, or receive an illegal delivery. In ODIs the dot is the most frequent of these outcomes by some distance, while in T20s it is not.

For bowlers, keeping the batter on strike has some advantage in ODI cricket, but doing this is a disadvantage in T20 matches. The tables above do not show whether this is because the batter is likely to play the second, third or fourth ball better than they play the first ball after a change of strike. So I looked at a batter's record on the nth ball of a sequence of consecutive deliveries on strike. This data is given below for the three formats for the first, second, third, fourth, fifth and sixth balls of a sequence on strike. As with the other records in this essay, here too, only batters in the top-eight batting positions are considered.

In Test cricket, boundaries are equally likely to be hit off each ball of the sequence. The cost of a wicket that might fall on each ball of a sequence is also more or less the same - around 38 runs. There's a small effect in favour of batters in terms of survival. A batter who survives three consecutive deliveries on strike is likely to be dismissed once every 75 balls, compared to roughly 71 balls for the first, second or third delivery of the sequence.

In T20, the advantage to the batter lies in an improved frequency of boundary-hitting - from one every seven balls off the first delivery after a change of strike, to one every 5.5 balls from the fifth or sixth delivery. It is worth noting though, that it is significantly more rare for the same batter to be on strike for four balls (15% of sequences) in T20 than it is in ODIs (24%).

In all three forms, as a batter stays on strike for a longer sequence, the probability that the batter faces a dot ball increases. So also with boundary percentage (though this increase is fractional in Test cricket). The magnitude of the increase in the frequency of boundaries or dots varies. In Test cricket it rises from 79% to 84%, in ODIs, from 61% to 69%, and in T20s from 51% to 57%. The distinction is that in T20, the majority of that increase is in boundaries, while in the other two forms the majority of that increase is in dots. The magnitude of the effect (in terms of runs or dismissals) is greatest in T20 and smallest in Test cricket.

The central insight from this record is that the consequences of strike rotation are not as clearly in favour of the bat in any format as might be generally thought to be the case. In the shortest format, staying on strike inspires greater adventurousness from the batter, while in Tests, it is a sign of greater security. Conceding a single is a win for the bowling side in a T20 game, and it is not necessarily a defeat for the bowler in a Test match either.

How the strike changes (or stays the same) does matter. To briefly consider this, I consider the Test and T20 forms in the concluding part of this article. These figures are also restricted to the top-eight batting positions.

In T20 the ball immediately following a six produces 10.2 runs per over, but it also produces a wicket every 14.9 balls. By contrast, the ball immediately following a dot ball (row two in table above) brings 7.5 runs per over and a wicket every 19.0 balls. The frequency of each outcome is also worth noting. A no-ball has been hit for six (penultimate row) 213 times in the record - once every 31 T20 team innings. In five of those instances, a wicket has fallen on the next ball (there can be run-outs on free hits, and free hits became available for all types of no-balls only in 2015). A wide or a no-ball is also overall more likely to be followed by another illegal delivery when compared to a legal delivery.

This record suggests that in T20 the relationship between one delivery and the next reflects the ambition of the batter rather than the balance of power between bat and ball. Hitting a six does not mean that the next ball is likely to go for more runs with impunity. It means that the next ball is likely to involve greater than average risk-taking (producing a higher scoring and dismissal rate), but not that hitting a six from the next ball is likely to be safer or more certain.

The idea that a score off a delivery reflects the ambition of the batter is evident in the Test record as well. For instance, the delivery immediately following a six in a Test match produces 40 runs per wicket and a wicket every 47 balls, on average, while the ball immediately following a single produces about 39 runs per wicket, and a wicket every 68 balls. The dot ball is overwhelmingly the most common delivery in a Test match. The jeopardy facing a new batter first ball is relatively much greater in Test cricket than it is in T20. While a dismissal does mute the average and the scoring rate in T20s as well, in Tests, the new batter is likely to be dismissed significantly more frequently compared to later in the innings. This corroborates evidence from the control figures.

The range of the cost of a wicket from the eight most common outcomes in a Test (dot to six) is from 20.1 to 41.0 runs. Excluding dismissals, since they bring a new batter to the wicket, it is 37.5 to 41.0, or 8.5%. The corresponding range from strike rates is 34%. Excluding sixes and dismissals, it is 11.1%.

In T20, the corresponding figures for the eight most common outcomes are, for cost of a wicket, 29% (15% excluding dismissals). And 24% for frequency of dismissal (21% excluding dismissals).

The figures in the tables above provide the cumulative effects of these conditional outcomes. While it can be tempting to think that the consequences of this conditionality are significant, and that a lot depends on small sequences of deliveries in games, the effects of conditionality are relatively minor. Outcomes on individual deliveries reflect the amount of risk the batter is prepared to undertake in T20. In Test cricket they reflect the amount of jeopardy imposed on the batter. Individual deliveries are basically standalone events. Scoring runs does not make scoring runs from the next ball easier. Rather, it reflects the propensity to take a risk from the next ball. All cricket, it seems, is overwhelmingly contested one ball at the time.