Joe Root doesn’t like batting at number three. Joe Root prefers to bat at four. Joe Root will bat at number three next month, but it is clear he’s taking one for the team.

We’ve been here before. In 2019, with the Ashes imminent, England’s captain announced that he would start the series coming in at one wicket down. “It was completely my decision,” he said. “It’s something I’ve been thinking about for a long time.” So far, so positive.

“I’ve always thought the best thing for the team is for me to score runs. And for a long time my record at No.4 would suggest that would be the best thing. But, where we are as a team currently and where I’m at as a captain, I’m a good enough player to be able to make the same returns at No.3….There are a number of different ways you can lead. This is just another opportunity to take my leadership forward and sort of show the rest of the group that it is something I’m more than prepared to do. I’m not expecting anyone to do something that I wouldn’t.”

And there you have it: “where we are as a team…. not expecting anyone to do something that I wouldn’t.” The skipper takes the poisoned chalice because no one else has the ability to. Taking one for the team. The experiment would be abandoned by the start of the next series.

Now the same scenario is playing out ahead of the three-Test series in the West Indies: interim supremo Andrew Strauss claiming that it is the Captain’s idea because he feels he should “take that responsibility on.” But why should it make any great difference for a player like Root whether he goes in at three or four?

It clearly seems to. In the 106 innings that Root has batted at four, he averages 51.27 with 27 fifties and 14 hundreds. In 53 innings at three, it is 38.66 with 14 fifties and two tonnes. It’s no calamity – nobody else in the tour party can boast a Test batting average of 38 or above – but you can’t deny there is an effect.

The obvious explanation is, well, the obvious: at number three you come in earlier and take guard against fresher bowlers with a harder ball. Suggest that to anyone who has watched England’s Men’s Test side over the last decade and the natural response will be that such an advantage for the number four has proved negligible to none given that two batsmen are usually back into the pavilion before the opening bowlers have worked up a sweat.

Yet, such an impression is misleading. In Joe Root’s Test career, when operating at number three he has come to the crease, on average, with the game 70 balls old. At four, the average, is 116. Looking at recent times – since he assumed the captaincy in 2017 – the difference is greater: 46 to 118. That’s the difference between facing the opening bowlers mid-spell and coming in with an hour and some of play gone. Of course, that is an average and Root has made his entrance at number four during the first over of the innings (2020/21 vs. India) and at number three with the ball over 40 overs old (2020 vs. West Indies).

More to the point, surely for a player of Root’s exceptional quality it shouldn’t make a whole heap of difference at what stage the game is at. For anyone the new ball is a challenge, but to suggest that there is an element of the flat-track bully to his record would be outrageous. Surely?

Surely so. Because a bit of number crunching shows that there is little connection between how old the game is and how many runs Root goes on to score. First, let’s look at every Root Test innings (I’ve removed his few not outs to prevent the argument that very late entrances would inevitably mean lower scores and also his times opening):

Immediately, what jumps out is that Root’s three highest scores came when he arrived at the crease with fewer than 60 balls bowled, as did five of his top seven. Of his six innings where he needed to wait for over 400 deliveries before making an appearance, only one made much of an impact. The correlation between balls bowled and score, should you be interested, is -0.02; i.e. barely worth mentioning.* Furthermore, no pattern is evident if you focus in on his innings at three or four separately:

Looking at the captaincy era alone, the picture remains – mostly – the same:

The only time the correlation gets anywhere above 0.0something is both times the innings at number three are isolated but at -0.12 (all number three innings) and 0.27 (captaincy number threes), the case is hardly convincing.

Finally, let’s separate out the successes and failures. There’s no agreed definition, so I’ll go with 50+ and lower than 20. It’s only worth looking at all career Test innings as there are too few captaincy number threes to make for a decent sample size.

The upshot remains no discernable pattern with the strongest correlation being -0.2 (50+ at number four).

So, if it makes no difference to Root’s scoring prowess how early or late in the innings he is called to the crease, then why the discrepancy in averages between batting positions and why the sense of doing-my-duty whenever the switch to number three?

It may be a case of number of appearances in each position and a confusion over causation. Had Root batted 106 times at three – as he has at four – then a batsman of his quality may likely have pushed his average much higher; especially if he’d been there during his annus mirabilis of 2021. Or it could be that the times he has been required to make the sacrifice of his preferred position in the line-up have happened when the team and their results were in the doldrums, which can’t have helped with his state of mind about the situation he found himself in.

And perhaps that’s it. It’s all in the mind. Perhaps Root bats worse at number three because he believes he bats better at number four. Can someone please show him these graphs?

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* For non-stats people: 1 or -1 is a perfect correlation, 0 is completely random. You’d start to get slightly interested around 0.3 positive or negative, and very interested around 0.7 or -0.7. Positive and negative numbers indicate the direction of effect of set of numbers one on set of numbers two; in this analysis a strong positive correlation would show a pattern that suggested the later Root came in the higher his score, a strong negative correlation would show scores getting lower the later he batted.