For Australia's cricket-watching public, some series matter and others ... not so much.

Players who perform at the Adelaide Oval or the Gabba in December or January find their feats well-received and remembered.

Games in the middle of the night during winter beamed back from far-flung countries may go entirely unnoticed.

In this week's case, though, the one-day international series that wrapped up in England had more than the usual significance.

It wasn't just that Australia won at the last gasp in Manchester, thanks to a pair of brilliant centuries from Glenn Maxwell and Alex Carey, and a pair of equally vital swings of the bat from Mitchell Starc.

The first piece of context was the corresponding ODI trip to England two years ago, in the winter of 2018.

This was the first outing for any Australian men's team since the ball-tampering scandal the previous March.

It was a 5-0 whitewash, the sort of result that Australians were used to dishing out, but not receiving.

Four of the matches were competitive but the one in the middle was a new level of thrashing, as England made a world record score of 481. The rest of the series was viewed through that lens.

A year later, on the same shores in 2019, England walloped Australia in the semi-final of the World Cup.

It echoed their Champions Trophy match of 2017: another global tournament, another game at Edgbaston, another instance of England knocking out Australia.

So for four years running, Australian one-day teams had headed to England in the middle of the year, and three of those years had not been happy.

The team of 2020 had a point to prove, not so much to England as to themselves, that they could match it with the recent world champions on a consistent basis.

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The need to foster this belief became more urgent after Australia went ahead in the series and had a chance to seal it, but produced one of the more extraordinary chokes you'll see to lose the second match. Cruising at 2 for 144, Australia somehow managed to get bowled out chasing 231.

There had been a similar implosion the previous week in a Twenty20 match: needing 39 in 38 balls with nine wickets in hand, Australia's batsmen had contrived to fall short.

Confidence in Australia holding things together wasn't high. In the third and deciding ODI, the team conceded 302 despite Starc having taken wickets with the first two balls of the match, and the chase collapsed to 5 for 73.

No team has ever recovered from such a score to chase more than 300 runs.

In a year where we've overworked the word 'unprecedented', what happened next is a fair application.

While it was initially difficult for Maxwell and Carey to find singles and get momentum into the innings, they managed to stay calm enough to see that period through.

Once they could manipulate the strike, they used the short boundary on one side of the ground to great effect, making sure that either the left-handed Carey or the right-handed Maxwell could target it as his leg-side field.

Maxwell hit sixes often enough to keep them in the hunt and judiciously enough to stay relatively safe.

There was fortune for both with a no-ball and a dropped catch, but the way the partnership surged towards the end was bigger than that.

There was still the chance of a fumble when both were dismissed within 10 runs of the win, but Starc made the last over of the match as dramatic as he had made the first, swinging Adil Rashid for six down the ground before sweeping four.

Australia is still a team with a makeshift feel. So much is geared around Steve Smith, who has never dominated one-dayers as he does Tests.

After he was concussed in training before the series, his return was spoken about before each game, but he didn't end up playing any.

He was a presence in his absence.

Marcus Stoinis is still being mucked around with: he lost his mojo in 2019 during a World Cup where he couldn't be dropped because there was no reserve all-rounder, then found it in the Big Bash as an opening bat, before being popped back into Australia's T20 team as a finisher in a role that didn't suit him.

With Smith out, Stoinis batted at three but couldn't produce what we've seen in domestic cricket.

For the moment, something about playing in national colours diminishes him.

The best use of Maxwell is still unclear. There was a movement to have a player of his ability bat at number four, but then he would get scolded like a regular batsman when he got out to an attacking shot.

The first-choice top four now has a conservative build: the new-edition David Warner, Aaron Finch, Smith and Marnus Labuschagne, none of whom are whirlwind players in the 50-over format.

Maxwell remains Australia's only consistent hitter, which gives him no support in the enterprise. The inclusion of someone like Matthew Wade, who can clear the boundary on the regular, would be a boost, or Mitchell Marsh needs to grow into that job.

England meanwhile still had the side that won the World Cup. Jason Roy and Jonny Bairstow at the top, Test captain Joe Root and one-day captain Eoin Morgan to run the middle, Jos Buttler for fireworks.

Ben Stokes wasn't away but Sam Billings filled in well. Leg-spinner Rashid was there, seamer Chris Woakes, fast bowlers Mark Wood and Jofra Archer. The only permanent change is that Liam Plunkett has been pensioned off, currently replaced by Tom Curran.

So this was the team that Australia was able to best, nearly three times out of three.

England's players are probably pretty jaded after months in a bio-bubble, but it's a significant achievement nonetheless.

In March 2019, a wonder run against India in Mohali gave Australia a boost ahead of the World Cup, shifting back to contender status from something closer to a rabble.

This week's chase in Manchester could be at least as important over the next couple of years — for Maxwell, for Carey, and for the broader Australian belief that it can be done.