Consistency — one of the most important and desirable traits in a batsman, yet, one of the most vague and misunderstood ones. Unlike the objective metrics like average, strike rate, runs per innings, etcetera, which are well defined and only divide the public in how much importance to give to each, consistency divides the public in its definition itself. In this article, we’ll try to define some objective metrics to evaluate consistency, and look at who were the most consistent batsmen in the inaugural World Test Championship.

The inspiration for this article has been taken from Himanish Ganjoo’s article on ESPNCricinfo, where he tried to evaluate consistency based on how often and how regularly batsmen crossed 50. We’ll use the same metrics defined there, in the context of the inaugural cycle of the World Test Championship.

#### Mean Gap

The first and simplest of the three metrics we’re going to need, is the mean gap. Mean gap, as the name suggests, is the average gap between two innings of a certain pre-defined score.

Marnus Labuschagne scored 5 centuries in the World Test Championship in 23 innings. **A simple division of the number of innings by the number of centuries, subtracted by one, gives us the mean gap between scores of 100+.** For Labuschagne, this stands at 3.6.

Mean gap gives a fair idea as to how frequently a batsman crossed a certain score on average. Lower mean gaps imply a higher frequency of scores above the pre-defined threshold. The problem with this metric though, is the fact that it doesn’t give you an idea of the regularity with which the batsman crossed the threshold.

Labuschagne’s mean gap between 100+ scores was 3.6, but he had two stretches of 7 innings each where he didn’t score a 100, and one stretch of 3 innings where he scored 3 consecutive 100s. To take this fluctuation into account, we’ll need our next metric, the Spread.

#### Spread

Continuing with the Labuschagne example, let’s look at his gaps between hundreds in the World Test Championship. These gaps are calculated between his first and last hundreds. The innings before the first hundred and after the last hundred are not considered because they aren’t ‘gaps’ technically. So in the case of Labuschagne, since he had 5 hundreds, he’ll have 4 gaps — between the 1st and 2nd, 2nd and 3rd, 3rd and 4th, and 4th and 5th hundreds respectively. And they are [0, 0, 3, 7].

Now, the spread is calculated by finding the standard deviation of this list of gaps. The formula goes like this.

**Spread = Square Root(Summation[(Gap — Mean Gap)²]/Number of gaps).**

Spread in case of Labuschagne = Square Root([(0–3.6)² + (0–3.6)² + (3–3.6)² + (7–3.6)²]/4) = Square Root(37.84/4) = 3.08.

What this tells us is quite literally, how spread out the batsman’s scores were. **If the mean gap between 100+ scores of a batsman is say, 3, and he scores his hundreds in exact intervals of 3 innings each, then the spread of his 100+ scores will turn out to be 0.** This means that the more regularly a batsman crosses the pre-defined threshold, the lower will be the spread, indicating that the batsman was consistently good instead of being poor in some patches, and brilliant in others.

There’s one small issue with the spread though. It is highly correlated with the mean gap, which is pretty intuitive. Because if the mean gap is high, it means the batsman scores less frequently. And there’s generally a greater chance of a batsman who crosses a threshold less frequently, to cross it less regularly as well, as compared to a batsman who crosses the threshold more frequently.

Hence, to meaningfully compare batsmen on regularity, we need a third metric, the Spread Index.

#### Spread Index

**The spread index is simply calculated by dividing the spread by the mean gap.** In our Labuschagne example, the spread index for his 100+ scores would turn out to be :

Spread of 100+ scores / Mean Gap between 100+ scores = 3.08/3.6 = 0.85.

As with all our metrics so far, this also come with its caveats. A batsman with a high spread and high mean gap, will also have a low spread index, just like a batsman with a low spread and a low mean gap. To put it simply, 10/10 will also equal 1, and 2/2 will also equal 1. To overcome this, we simply plot the spread index with respect to the mean gap, and with that, we have all our ingredients for evaluating consistency of batsmen, ready.

We’ll look at data for 4 thresholds:

- 20+ runs — Consistency of getting starts
- 35+ runs — Consistency of an above average innings (The average score of top 6 batsmen in the World Test Championship was 34.5)
- 50+ runs — Consistency of crossing 50s
- 100+ runs — Consistency of crossing 100s

#### Consistency with which batsmen got starts in the WTC

Let’s move in ascending order of scores and start with looking at the consistency with which batsmen got starts in the WTC.

Marnus Labuschagne is the leftmost name on the plot, having the lowest mean gap. He crossed 20 in a whopping 19 out of a total of 23 innings, never going more than 1 inning without crossing 20. Talk about consistency. If you’re wondering why is he so high on the spread index axis and why not more towards the origin, it’s because his mean gap is so low(~0.2), that even a gap of 1 innings will contribute significantly towards the spread value, and thus, the spread index. In short, he was too consistent for his own good!

Rassie van der Dussen is the lowest name on the plot, indicating he was the most regular in getting starts. He had a mean gap of 0.89 innings between each 20+ score on average, while his actual gaps were [0, 1,2,1,1,1,0,1]. This reinforces the importance of plotting both the spread index and the mean gap together. While Dussen got starts in regular intervals, his frequency of getting starts was nowhere near that of Labuschagne.

Mominul Haque had a strange progression of 20+ scores. He played 14 innings in the WTC, got a start in his first innings, then didn’t get one for 3 consecutive innings, and then got starts for each of his remaining 10 innings! Perfect example of poor in one patch, and brilliant in another. Hence he occupies the top most position in the chart, despite being the guy with the second least mean gap between starts.

Mayank Agarwal meanwhile, had the worst mean gap between innings of 20+ among all batsmen who scored 500 or more runs in the WTC. For every innings in which he scored more than 20, he played almost 2 innings where didn’t reach 20. His numbers weren’t this bad in the first half of the WTC. In his first 12 innings, he got starts in 6 of them at very regular intervals. But in his last 8 innings, he managed to cross 20 only once.

Rohit Sharma, Steve Smith, and Babar Azam expectedly appear in the left half of the plot. While Rohit and Smith were slightly irregular in getting starts, Babar got both frequent and regular starts. There are some unexpected names too though in that area. Niroshan Dickwella, sitting right beside Marnus, had the 3rd best mean gap between starts, crossing 20 in 15 of his 20 innings in the WTC. Ajinkya Rahane, contrary to popular belief, was among the more consistent batsmen, at least in terms of getting starts, having got 20 starts out of 30 innings.

Two more interesting observations to take away from this. Rory Burns, Dom Sibley, Zak Crawley, and Ollie Pope, the four young, rather inexperienced batsmen on whom England have invested and are pinning their hopes heavily, all lie on the right half of the plot with the exception of Burns who lies just to left of the midway mark. All four have unquestionable quality, but all four are highly inconsistent. This perfectly illustrates England’s batting woes. Meanwhile for India, Virat Kohli and Cheteshwar Pujara were the two most inconsistent batsmen after Mayank in terms of getting starts.

#### Consistency with which batsmen played above average innings

The threshold for this chart is 35 runs or more. Since the average of the top 6 batsmen from all teams in the WTC was 34.5, we’ll consider any innings of 35 or more to be an above average innings. Here too, Labuschagne turns out the clear winner. Out of the 19 innings in which he got starts (crossed 20), he also crossed 35 seventeen times. No one played above average innings more frequently than him. Next comes his compatriot, Steve Smith, who had the 2nd best mean gap for crossing 35 runs, but had the worst spread index.

Batsmen who have such low mean gaps have a greater chance of having a high spread index because even one bad patch of 3–4 innings where they don’t cross the designated threshold will result in a significant deviation from the mean and will increase the spread index value. Same happened with Smith. He had one stretch of four innings where he didn’t cross 35, in fact, he didn’t even cross 20 — against India in the first two tests of the BGT. And that pushed his Spread Index so high.

Dickwella stands out here as well, having the lowest spread index among all batsmen who scored more than 500 runs in the WTC. He crossed 35 eight times out of 20, and did so in intervals of [1, 2, 0, 2, 2, 2, 2]. Not extremely frequent. But extremely regular. Ollie Pope meanwhile, had the worst mean gap. 17 of his 22 innings in the WTC were below average. Those are numbers you’d not like to see from one of your young, premier batsmen on whom you’re investing heavily.

Babar Azam and Mohammad Rizwan were brilliant for Pakistan, having the 3rd and 5th best mean gaps between 35+ scores respectively, while Lahiru Thirimanne finally came good in Test cricket, scoring more than 700 runs in the WTC at an average of 43.23, while being the most consistent Sri Lankan batsman in terms of frequency of above average innings.

Ajinkya Rahane took over from Rohit Sharma in being the batsman with the best mean gap for India, as the threshold increased from 20 to 35. But a look at his actual gaps tells the story of his perceived inconsistency. [0, 1, 2, 0, 0, 0, 0, 3, 1, 3, 3, 3] — He started the WTC in the West Indies with two consecutive above average scores, then had another stretch of five consecutive above average scores in between, and then finished the tournament with only five more scores of 35+ in his last 19 innings. Consistent, yet inconsistent.

#### Consistency with which batsmen crossed 50s

The previous two thresholds were rather arbitrary thresholds I chose. Let’s now look at the consistency with which batsmen crossed the threshold of 50, a score which can safely be assumed to be a mark of a successful innings. And you’ll get no prizes for guessing who tops this list (at least in terms of mean gap between 50+scores).

Marnus Labuschagne crossed 50 fourteen times in the WTC in 23 innings. Next best were Smith and Joe Root, who crossed 50 eleven times each, in 22 and 37 innings respectively. Hence he rightly occupies the leftmost slot in this chart as well. But this time, apart from occupying the leftmost spot, he’s also occupying the topmost spot, signifying that he crossed 50 most irregularly. Once again, the same principle comes to fore.

His mean gap was so low (0.64), that even one stretch of 3–4 innings where he didn’t cross 50 would have had a major impact on his spread index. And he had 2 such stretches — one of 3 innings in his last 3 innings in the Ashes, where he scored 11, 48, and 14, and another of 4 innings in the first two tests against India, where he scored 47, 6, 48, 28. Apart from that, he had separate stretches of 2, 3, 4, and 5 consecutive innings where he scored more than 50 runs. Labuschagne had activated God mode.

The next five names after Labuschagne, in order of increasing mean gaps between 50+ scores, are Babar Azam, Steve Smith, Dimuth Karunaratne, Lahiru Thirimanne, and Mohammad Rizwan. While you’d expect Babar, Smith, and to an extent, Karunaratne to be up there, Thirimanne and Rizwan are the surprises. Thirimanne crossed 50 seven times in 17 innings, five of which came in his last seven, while Rizwan crossed 50 seven times in 18 innings, five of which came in one consecutive stretch in England and New Zealand combined. That is also why he’s so high in the spread index axis.

Dhananjaya de Silva was the most regular in crossing 50. He made five 50+ scores with intervals of [1,2,1,1] between them. This shows that he was consistently among the runs and didn’t have bad patches and extraordinary patches. Matthew Wade meanwhile, had the worst mean gap between 50+ scores(7.33), having crossed 50 only thrice in 25 innings. And he played as a specialist batsman, not as a wicket keeper.

Among Indian batsmen, Ravindra Jadeja had the lowest mean gap(2 innings between every 50+ score), Virat Kohli was the most regular in getting 50+ scores with a mean gap of 2.43 innings and actual gaps of [0, 3, 2, 4, 2, 1], while Rahane was the least regular, with a mean gap of 2.33 and actual gaps of [0, 1, 2, 0, 0, 0, 6, 7]. Typical Rahane.

#### Consistency with which batsmen scored 100s

Although Labuschagne scored the most hundreds in the tournament, this is one threshold where he doesn’t appear at the top in terms of mean gaps. Babar Azam and Dimuth Karunaratne had the two best mean gaps of 3.25 and 3.5 respectively, while Labuschagne was third with a mean gap of 3.6.

Crossed 100

The most regular century maker in the WTC according to the above chart was Lahiru Thirimanne. But his position can be considered as more of an outlier than a true representation. He scored 2 hundreds in 17 innings, with a mean gap of 7.5, and scored the two hundreds 7 innings apart. While his only gap was very close to his mean gap, it doesn’t necessarily mean that he was the most regular in scoring hundreds. Among the five bottom most names on the plot, only Rahane and Ben Stokes had more than 2 centuries (3 and 4 each respectively).

Shan Masood scored 3 hundreds in 17 innings which puts him among the best in terms of mean gap, but he had the second worst spread index because all three of those hundreds came in consecutive innings. Steve Smith meanwhile, had the worst spread index. Three of his four hundreds came in his first four innings of the WTC in the memorable 2019 Ashes, but that was followed by a 14 innings gap which ended with his hundred against India at the SCG.

#### Conclusion

The key takeaways from all the analysis done above are :

- Labuschagne was too consistent for his own good.
- Rahane was India’s most consistent batsman. Rahane was India’s most inconsistent batsman.
- Thirimanne finally cracked Test cricket.
- Rishabh Pant was good. Mohammad Rizwan was better.
- New Zealand’s batsmen, staying true to their image, were so unassuming that they didn’t get a mention in the entire piece.
- Steve Smith was Steve Smith, except against India, when he wasn’t Steve Smith.
- England’s batsmen are due for a consistent period of scoring.