The punch of the air and broad smile told the story: Joe Root needed this century.

He had certainly been made to work hard for it. No hundred had taken him longer - 259 balls - and at one stage, he went more than 30 overs without a boundary. More than that, though, it had been eight months since his previous Test century. In the time since, his membership of the 'big four' had lapsed and questions about his future as captain had started to crop up with increasing and uncomfortable persistence.

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Let's be clear: had Root been dismissed for a pair in this match, he would still have led England in South Africa. If there were a viable alternative that might not be the case, but there isn't. Not really. And he retains the confidence of his team.

Joe Root drives through the covers AFP / Getty Images

But there had been a creeping suspicion that the cost of retaining Root as captain was compromising his ability to perform his day job: scoring runs. And England, a team who have not scored 400 this year (and did so only once in 2018), cannot afford their best batsman to endure such a fallow spell. They are going to end a year without a Test series victory for the first time this century, after all (the last time they did so was in 1999)

If you had any doubt about the importance of Root's runs to England consider these statistics. Before this match, England had won 13 - and lost none - of the 16 matches in which Root has scored a century. And in a side in which only five men have scored a Test century - one of them bats at No. 9 and another at No. 11 - his contributions are magnified.

So England needed this innings from Root. And this innings from Rory Burns. Not just to give them an outside chance to square this series against New Zealand, but to show they could adapt to conditions where patience and discipline are as important qualities as flair and aggression. To show they were making progress.

But most of all they needed it to give Root some breathing space. This hundred, albeit one made on a docile surface, will quieten - at least for a while - the voices calling for change and, probably more importantly, quieten the doubts within Root's own head. It was his first century in his team's first innings since August 2017 while the partnership between Root and Burns (177) was England's highest since Alastair Cook was in the side in September 2018. Clearly in some discomfort at times - he received treatment on his long-standing back injury at various intervals - it was, in its way, a brave and determined innings, too. Root is, once again, a captain leading from the front.

Joe Root celebrates reaching his century Getty Images

This innings was, in many ways, a model of denial. It was a reminder of the adage that batting is as much about the shots you don't play as those you do. So the drive was, largely, put away - he has scored only 14 of his 114 to date in front of square on the off side, with his only boundary in the area taking him into the 90s - and, in waiting for the ball to come to him, picked off 69 runs from his legs and hips between fine leg to midwicket. 75 of his runs have come behind square on either side of the wicket and he hasn't given a chance. It was probably fitting the century was achieved with an under-edge which scudded to the boundary. This wasn't anywhere near his prettiest innings, but it has been important.

Might it be compared to Andrew Strauss' career-saving century at Napier in 2008? Michael Vaughan was still captain but Strauss was highly regarded for his character as much as his cricket. He was struggling to command a place in the side though and, when he came into bat on a pair in the second innings, there was a sense that he was out of chances. And we all know what he went on to achieve.

Maybe there is nothing as dramatic at stake here. This innings doesn't resolve anything, after all. It hasn't even given England the upper hand in the game. But it has kept them in it and it has boosted Root's authority as player and leader. It may yet prove to be a fresh start, too. In a game played as much in the mind as on the pitch, it will certainly help him travel to South Africa without some of the excess baggage that might have accompanied him.

Regardless, England will struggle to win this game. Rain that curtailed the day by 16.2 overs may also have denied England of any realistic chances they may have had. With the pace of run-scoring so slow - a reflection of the pitch more than England's caution - they cannot expect to reach parity until lunch at the earliest. And there's some work ahead to achieve even that.

That means they will have to bat on into the final session of day four, at least, to be able to consider the sort of declaration that could pressure on New Zealand. And, bearing in mind they took only nine wickets in the whole of the first Test, they will be asking a lot of themselves to claim 10 within three or so sessions. There is the prospect of more poor weather, too, though maybe the hints of irregular bounce that crept into play late in the day will prove some encouragement.

Most of all, though, England will be encouraged by Root's return to productivity. It doesn't solve all their problems, by any means, but it does represent a significant step in the right direction.