Are Kohli and Pujara in slumps? Let's look at what the control data says

ESPNcricinfo defines control as a measure that records whether or not a batter was in control of any given delivery, and whether or not the delivery went where the batter intended. The control measurement is binary. For each delivery, the batter is either in control of the delivery or not in control.

Not being in control does not automatically result in a dismissal. For example, the batter could play and miss, or a leading edge could land safely, or the batter could be defending and the edge may not carry, or the batter may be beaten, but it might not result in an lbw dismissal. There are a range of not-in-control scenarios that cricket fans can (and do) imagine.

A batter who has a low control percentage of, say, 70% (three of ten balls are not in the batter's control) has been luckier than one who has a higher control percentage - of, say, 88% (12 out of 100 balls faced are not in the batter's control) if they survive for the same number of deliveries in their innings.

A batter who is dismissed on the third or fourth false shot (which is a shot where the batter is not in control), is less lucky than one who is dismissed on the 23rd or 24th false shot. There are between ten and 11 false shots per dismissal for a batter in Test cricket, on average. So the former batter in the example above is less lucky than the average batter, while the latter is luckier than the average batter. Luck, here, is not the opposite of skill. Luck represents merely the gap between the average outcome for a given set of actions, and the outcome in any specific case.

This idea vexes some fans because it suggests that a batter did not play better to score 130 than they did to score 30. They often suggest that not all false shots are created equal. They say that a batter who plays with soft hands so that the edge is less likely to carry to the slip cordon is not playing a false shot in the same way that a batter who edges an attempted cover drive towards the slips.

This is true. Still, in both cases the batter has played a false shot. In the first, it is a failed attempt at a defensive shot. In the second, it is a failed attempt at a cover drive. The defensive shot is not inherently better than the cover drive. It is a choice. The objective of batting is to score runs. The defensive shot trades the possibility of scoring runs for survival, while the cover drive risks dismissal in the pursuit of runs.

Another type of common false shot is comparatively less spectacular than being beaten outside off stump: a batter can miss a flick and be beaten on the inside edge and get hit on the pad or the thigh guard. Usually, but not always, when the inside edge is beaten in this way, the ball is drifting down the leg side. Sometimes a "strangle" dismissal down the leg side might result, or a bat-pad chance into the infield or to the cordon or a short leg.

A defensive batter can be expected to have a higher false-shot-to-dismissal ratio ("NIC per dismissal" in the tables below) than an attacking batter. But a defensive batter will not necessarily have a better runs-per-false-shot ratio ("Runs per NIC" in the tables below) than an attacking batter. (Runs per false shot is a ratio of the total runs scored to the total number of false shots played. It does not give, as the name might suggest to some, the average number of runs scored from one false shot.)

Control is an elegant descriptive measure precisely because it is binary and can capture trade-offs inherent in the choices batters make. Control records the singular essential fact about the batter's action in the encounter between bat and ball.

The table below gives the control record by batting position in Test cricket from January 2015. Note that only dismissals that accrue to the bowler are included in this record, so the batting averages in the tables below do not correspond perfectly with the players' actual batting averages.

Some false shots (about 10%) result in dismissal, a few result in runs. About 88-91% of runs scored by specialist batters are off balls where they are in control. The scoring rate from false shots (2.1 runs per over) is lower than the scoring rates when in control (3.2 runs per over).

The frequency of false shots increases as the quality of the batting declines as you go down a typical batting order. So does the rate at which false shots produce dismissals. Batting coaches and ex-players often talk about "holes in technique". One way to think about this pattern of the production of false shots and dismissals in the batting order is to say that the better a batter, the narrower the range of deliveries on which they are likely to play a false shot.

It is in this sense that luck is not the opposite of skill. The skill is evident in the rate at which different players survive false shots, and the rate at which different players score. The skill involves choices about risks that individual players make. Some players prefer to take chances and risk dismissal in the pursuit of runs. Others prefer to wait until they get a delivery to which they can play their shots. We have often heard commentators recommend that on bowler-friendly pitches, it is better for a batter to "play his shots", since the unplayable delivery "with his name on it" is just around the corner. The essential word in that first phrase is "his". These shots are different for different batters. Some don't sweep or hook. Others have a comparatively weak back-foot game. It is always worth watching when a batter starts attempting uncharacteristic strokes.

Rishabh Pant has played a false shot on 18.6% of the deliveries he has faced, at the time of writing - one every 5.4 balls. He takes more chances than the average top-order batter, for whom the rate of false shots lies somewhere between one every 6.4 and one every 7.2 balls. Pant scores 3.8 runs per false shot. Below is the control record of five outstanding batters of the past decade, summarised according to the three measures described above.

Note that the averages listed in the table consider only dismissals that accrue to bowlers, or that occur when the batter is on strike for the delivery. Consequently, the averages reported here (until the end of the Trent Bridge Test in August) are slightly higher than the players' actual averages. Also, there is the rare dismissal, such as Cheteshwar Pujara's on 73 in Chennai earlier this year, where the batter is dismissed despite not playing a false shot.

Compared to Pant's 18.6% false-shot rate, the five batters in the table above play false shots at rates from 10.4% (Kane Williamson) to 14% (Joe Root). In other words, where Pant plays a false shot every 5.4 balls, Williamson plays one every 9.6 balls, Root one every 7.2 balls, and the figures for the other three lie between those for Root and Williamson.

A good picture of how players' run-scoring is shaped by, and shapes, these figures is given by the example of Virat Kohli's Test career. The graph below shows a 1000-ball rolling average for runs per not-in-control delivery, and not-in-control deliveries per dismissal. Each point on each line represents the average figure over the previous 1000 balls faced by Kohli at that point in his career. A red circle represents a false shot; a black cross represents a dismissal.

Over the course of his career, Kohli has on average survived 11 false shots per dismissal. Over his last 15 innings (since the start of 2020), this has dropped to 7.1. Over the course of his career until the start of 2020, Kohli was dismissed from his first five false shots 61 times in 141 innings (or in roughly 43% of them). Since the start of 2020, until the end of the Trent Bridge Test, this has happened to Kohli nine times in 15 innings (or 60%). At some point in the very near future, there will be a reversion to his mean. This suggests that he is very likely to get a century during this England tour.

Consider the three portions of Kohli's Test career in the table above. The first two are successful series against England. The third spans his current run of low scores. Kohli has been dismissed inside his first seven false shots in 12 out of his 15 innings since the start of 2020. By contrast, he survived at least eight false shots in nine out of ten innings in England in 2018, and at least 14 false shots in eight out of ten. His brilliant 149 in 225 balls at Edgbaston involved 56 false shots.

False shots were significantly less frequent (one every 10.7 balls) for him against England in India in the 2016-17 season. But even in that series, in six of his eight innings, he survived at least eight false shots. His 235 in 340 balls in Mumbai featured 37 false shots.

When a batter goes through a lean patch, they are usually getting out to early false shots more often than not.

One of the most striking things in the data set, which includes 781 innings by these five batters, is that there is no indication that bigger scores involve easier starts to innings. One would expect that if a batter scores 80, they play fewer false shots at the start of their innings than if they scored 20. This is not the case. The average number of false shots in the first 15, 30 or 45 balls of innings in which the batter scores 80 is not lower than the corresponding figures for innings in which the batter scores 20s or 30s.

This suggests that for players of this elite quality, a low score does not imply a poorer quality of actions or decision-making. On average, Kohli or Smith or any of the others do not play with greater control in the innings where they get big scores than they do in the innings where they don't.

While there is no evidence to suggest that these batters start with greater assurance when they score 80s than when they are dismissed cheaply, there is evidence to suggest that as a batter survives more deliveries, the probability of a false shot declines. The first ball in the innings is a false shot 16.8% of the time (one in six first balls tends to produce a false shot). By the 101st ball, this reduces to 11% (one in 9.1 101st balls tends to be a false shot). By the 201st ball, it reduces further to 10% (one in ten 201st balls tends to be a false shot). This can be understood in conventional batting terms as evidence of the batter "getting set" or "being in".

When is a player in a slump? And when is a player in decline? There is no obvious flag in the data that helps the reader pinpoint the match or innings where the decline began (if at all there is a decline). But the data does point to some interesting things.

Pujara's last prolonged slump in Tests was in 2014. He made 70 and 32 at the MCG in 2013, after which his next big score came in August 2015 at the SSC in Colombo, where he carried his bat for 145 not out in an Indian total of 312 all out. In 21 Test innings between those two Tests, he crossed 50 twice, and made only 483 runs in all. For these 21 innings he played a false shot once every 6.7 balls, was dismissed once every 8.6 false shots, and produced 2.8 runs per false shot. In his recent slump, which began after the Sydney Test of 2019 (in which he made 193), Pujara has played a false shot once every 7.4 balls, has been dismissed once every 10.7 false shots, and has scored 2.67 runs per false shot.

Pujara is scoring slower in his current slump (41.5 runs per 100 balls faced in the first slump; 34.8 runs per 100 balls faced in the second). This could simply be because the attacks he has faced since 2019 have offered fewer scoring opportunities than the ones in 2014. But it could also be that Pujara has become more conservative in his assessment of scoring opportunities. This could be because he's not picking the length up as quickly today as he was in his 20s. It could also be due to team instructions. The evidence on the question of decline is weak, and the jury is still out on whether there has been a decline. There have been examples of batters getting a second wind in their mid-30s after a mid-career slump, and those of such slumps ending careers. But there is a definite shift in Pujara's scoring patterns over the last two years compared to in his 20s.

How often a batter makes a false shot depends on their skill and how much risk they are prepared to accept. The more defensive players like Pujara make the conservative choice of playing a limited number of scoring shots and attempting these to a specific narrow range of lines and lengths. The more aggressive players, like Kohli, and in extremis, Pant, play a wider range of attacking shots to a wider range of deliveries. They risk dismissal more often, but they also score more quickly.

James Anderson made the observation in 2016-17 in India that a number of things that were in play for him when bowling in England were simply not available in India. When Anderson has bowled at four out of the five batters who feature in this article in Tests in England, he has forced a false shot once every 6.2 balls. When he bowls at them outside England, this figure rises to 10.6 balls. These batters score 2.3 runs per false shot against Anderson in England (compare this to their overall figures), while they score 4.1 runs per false shot against him outside England. The conditions determine how much jeopardy there is for a batter.

Williamson makes false shots less frequently than Pujara, but he also survives them less often than Pujara. Of the five batters considered here, Steven Smith has evidently made the best technical and tactical choices. His method of shuffling across in the crease enables him to take the stumps out of the equation against seam. Smith also does not commit to the front foot when he shuffles. This helps him defend his outside edge better than, say, Kohli. It helps him to both survive false shots and find good positions to score from deliveries. Smith is an uniquely excellent batter.

All batters can be dismissed early. Being dismissed early does not mean a batter has played badly. A batter's skill is evident in the long-term figures, which reveal the efficacy of the trade-offs made between chasing runs and risking dismissal, and the technical prowess of the batter in avoiding and/or surviving false shots.