What is Luck?

This is a short note on what luck is in cricket.

Let’s start with what it is not. Luck is not the opposite of skill. Luck is the accumulation of favorable outcomes for a set of actions to an extent that is significantly beyond the expected outcomes for this set of actions.

Skill is evident in a player’s actions. Luck characterizes the outcomes.

On Day 1 at Trent Bridge Bumrah induced 41 false shots in 122 balls. Mohammed Shami induced 27 in 99 balls. Between them induced 68 false shots in 221 balls and ended up with 7/74. In the WTC final, Bumrah induced 54 false shots in 220 balls and ended up with 0/92. 7 dismissals from 68 false shots is marginally better than the average expectation for false shots per dismissal. 0 dismissals from 54 is well below the expectation. From this, one can conclude that Bumrah was unlucky in the WTC Final, while on Day 1 at Trent Bridge, his luck held (4 wickets for 41 false shots is about the average expected return).

In 2014 in England, Kohli was dismissed 4 times for 19 runs in 50 balls by Anderson. He played 11 false shots against Anderson in those 60 balls. In 2018, he made 0/114 in 270 balls against Anderson and played 58 false shots. He was dropped a few times off Anderson’s bowling in 2018.

Kohli hasn’t made a Test hundred in nearly two years. During this period he has played four terrific innings - 74 in 180 balls at Adelaide, 72 in 104 balls, and then 62 in 149 balls at Chepauk, and 44 in 132 balls in the WTC final. At Southampton, he survived 23 false shots. In Adelaide, 16. On Day 1 at Trent Bridge, Joe Root also survived 16 false shots in his 64.

Kohli has made 27 Test hundreds. His average century score is 151(231) balls. On average, he survives 24 false shots per innings. That’s 24 false shots out of 231 balls, or one every 9.6 balls. For his hundreds in SA, ENG, NZ or AUS (there are 11), Kohli’s average score is 131(208). He survives 25 false shots per innings, or 8.3 deliveries per false shot.

Some conditions are more batting friendly - the pitches are easier, and bowling is not as difficult to play. The likelihood of a batter playing a false shot increases. Other conditions are easier.

But the point of the false shot figures is that to reach a century, a batter has to survive more false shots than average. In other words, the batter has to be lucky. How lucky? That depends on how often the conditions (bowling + pitch) induce false shots.

Some batters are more defensive than others. They don’t play many attacking shots. Consequently they are likely to survive more false shots than their more attacking counterparts. But they are also likely to score fewer runs per false shot than their more attacking counterparts. This is the essence of a batter approach to risk. Some batters take more chances than others.

For example, over the course of their careers, Kohli scores 2.4 runs per over of false shots, while Cheteshwar Pujara scores 1.67 runs per over of false shots. Pujara played false shots to 11% of deliveries he faces, while Kohli plays false shots to 11.6% of deliveries he faces. Kohli is dismissed once every 91 balls in Test cricket. Pujara is dismissed once every 103 balls. Their records can be summarized as follows:

Kohli’s average Test innings is 52(91) with 10.6 false shots (4.9 runs per false shot). Pujara’s average Test innings is 46(103) with 11.3 false shots (or 4.1 runs per false shot).

So when does a player’s decline or improvement become evident? It becomes evident when the averages shift over a period of times. Pujara, for example, hasn’t scored a Test hundred since January 2019, and his scoring rate has declined during this period as well. So its possible that bowling attacks are bowling differently against him than they used to. Its also possible that his method has either changed or become less incisive.

Batters keep trying to evaluate how they can score against a given type of bowling. This is what produces different patterns of facing up to, say right arm seam bowling. The basic fact is that batters cannot determine the outcome of a delivery in cricket. Their skill helps them move the probability of a favorable outcome in their favor. But Kohli’s still going to get out to his 3rd, 5th, 9th or 1st false shot from time to time. At other times, he’s likely to survive longer, and will probably score a century.

Its the same with bowlers. A bowler’s skill lies in making it difficult for the batter to score and in increasingly the likelihood of the batter playing a false shot. On some days, the false shots are not converted to dismissals. On others, they are. But the bowler’s skill - the quality of the bowler’s action - lies in how relentlessly the bowler puts the batter in situations with low-probability of success.

This is also why cricket is not a symmetrical contest between ball and bat. Only the bowler gets to begin each play. The batter can only face up to whatever is delivered. And so, if a bowler keeps bowling good balls, there’s nothing much the batter can do about it. Good bowling lies in offering the batter few good options. Good batting lies in having to skill to survive until easier bowling comes along. But neither of these outcomes can be determined by one contestant.

It is easy to imagine the relationship between luck and skill. The more skillful bowler will bowl few bad balls as a rule, and so, in the long run will force significantly larger numbers of errors than the less skillful bowler. A skillful action improves the probability of a favorable outcome. Bowlers and batters work on their skills all the time. They learn new deliveries, modify their footwork, make choices about trying new variations, or adding or subtracting different shots. They work out which shots are on against which type of bowler, and which aren’t. These things constitute the skillful labour of the cricketer.

What we often see as “bad form” is a run of play in which the bowler or the batter has below average luck. If this bad form becomes the norm, then the bowler or batter is probably not (or no longer) good enough to compete at that level of opposition.

This is also why the idea that when Kohli is dismissed cheaply he has played worse than when he’s dismissed for a bigger score, is not tenable. Kohli’s actions in both innings are almost certainly equally skillful. But his returns are not. That is where luck plays its part.

Note: The false shot figures are drawn from Cricinfo’s control figures. Thanks to Sidharth Monga for supplying some of these.