When an opening pair starts breaking records held by the likes of Greenidge and Haynes, Sachin and Sourav, Hayden and Gilchrist you know they are in territory reserved for the very special.

So perhaps it is time to start thinking of Bairstow and Roy - Jonny and Jason, as they may well come to be remembered - in such a category. It's not just that, in this match, they recorded their third successive century opening stand - no opening pair has made more in a single World Cup campaign - or that they have the best average partnership of any pair with more than 1,000 ODI runs between them in history.

No, perhaps the most remarkable aspect of their partnership is that they have achieved all those things while setting a record for the highest strike-rates of any opening batsmen with more than 1,000 runs to their name. "Incredible" was Eoin Morgan's description; "awesome," Kane Williamson's. "I don't know if there's an answer to them," the New Zealand captain added.

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So let us acknowledge a slightly uncomfortable truth: England enjoyed some significant luck both in this game and in the defeat over India. It wasn't just the run-out of Williamson - nobody is pretending that was part of any plan - or the injury that ruled Lockie Ferguson out of the New Zealand side. It wasn't just the leg before decision won by Chris Woakes against Henry Nicholls or the first ball of the match that defeated Roy but somehow missed the stumps on its way to four byes, either. Roy's reprieve in the previous game - he would have been out for 21 if India had called for a review - was crucial, too.

No, the most significant slice of fortune in this game was winning the toss. As Morgan said after the game "I don't think I've played on a wicket that has changed as dramatically as that" and there is no doubt batting first was a substantial advantage. As Williamson explained, England's openers were "able to hit through the line nicely" but doing so "became a lot harder to do" as the wicket started to offer purchase to cutters and slower balls. Those deliveries "were a lot less responsive" in the early stages of the England innings, he said.

But we cannot keep explaining away the success of the Jonny-Jason partnership as luck. We cannot dismiss their 10 century opening stands in 31 outings as nothing but flat-track gorging and then ignore the fact that everybody else in some of these games struggles to hit the ball off the square. We cannot keep suggesting, as we did on Sunday and again on Wednesday, that the pitch changed suddenly the moment they were out. We cannot dismiss Bairstow's three successive ODI centuries against New Zealand or Jason Roy's seven 50-plus scores in eight ODI innings (or three centuries in 10) as luck. It fails to appreciate there is something pretty special developing here.

Instead we must acknowledge that they have the audacity and skill to seize the moment. They have the power to intimidate bowling attacks and the ability to rush games away from their opposition before they have had the chance to take stock and adapt. Look at the figures here: they brought up their 100 stand in the 15th over (New Zealand took until the 21st) and, having built a platform whereby England might have been looking at a score of 400 at the 30-over mark (they were 194 for 1), they saw their colleagues add just 111 for the loss of seven wickets in the final 20 overs. It's an overused expression, but it really did look as if they were playing on a different pitch to everyone else.

Did New Zealand bowl poorly or were they forced to bowl poorly in that first half-hour or so? Certainly Tim Southee looked understandably rusty in playing his first ODI since February and Bairstow, who at one stage took him for five fours in nine balls, was merciless. There was a full toss in the first over, bowled by Mitchell Santner, that pretty much every professional player in the world would have hit for four, too.

But some of the bowling, from Trent Boult in particular, was pretty much blameless. So fearless was the batting, however, and so well executed, that perfectly reasonable deliveries were hit through or, very often, over the field. Some of the shots looked relatively high risk but, as Baristow kept finding the gap between fielders with precision, it became impossible to believe he was simply in luck. "They put us under a lot of pressure," Williamson said. "And when they do have momentum, it can be a big challenge, regardless of the surface, to stop them."

"Ridiculous" was how Morgan described the stand. "It is incredible, really, the talent they possess and what they can achieve on a consistent basis," he said. "If their average wasn't as high, the manner in which they play would still be the most important thing as we bat all the way down.

"The two of them are outstanding. One of the things that stands out for me in that it doesn't happen in normal partnerships, it happens in great partnerships, is that they ebb and flow. So, Jonny got off to a flyer and Jason was quite slow, but then he caught up and Jonny slowed down. It was really brilliant to watch because normally you have two guys competing with each other the whole time, trying to get the strike, trying to be more dominant, whereas as a partnership they are extremely dominant.

"The guys in the dressing room are buzzing, laughing, smiling at how ridiculous some of the shots the two guys are playing are. Good balls being hit for four or six. You have to laugh at how difficult to bowl at they are."

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England are a team offering far more than a strong opening pair, though. Already Jofra Archer has taken more wickets than any man to have played in any previous World Cup campaign for England. And Mark Wood is only one wicket behind.

Meanwhile England's batsmen have already scored seven centuries in this campaign; the most they have managed in any previous World Cups is two. They had only scored 11 in the previous 11 tournaments. So whereas New Zealand's batting looked overly reliant on Williamson and New Zealand's bowling looked overly reliant on Boult, England have the depth of batting to empower their openers to keep attacking and the variation in bowling to exploit most surfaces. In this tournament, however, it has been noticeable that they have prospered, on the whole, by hitting the pitch as hard as they can and using their variations. At the pace they have - and four England bowlers have registered 90 mph in the this World Cup - and on the pitches we are witnessing, it is proving an effective tactic.

Wait there, you may be saying. This time last week England were on the verge of going out of this tournament. They've still lost three games. Aren't they a bit overrated?

Maybe. It's certainly true they have taken the scenic route to the semi-finals. They have lost to two of the sides ranked in the lowest five in the tournament, after all.

But they have also beaten three in the top five. And they have now won two high-pressure games, against two high-class teams within the space of a week. And while that may sound run-of-the mill to the supporters of teams from some nations, it is worth remembering that England hadn't beaten New Zealand in a World Cup match since 1983 or India since 1992. They are now ranked the top side in the world again.

If the remainder of the group stage results go to form - notably Australia defeating South Africa on Saturday - England will play India in a semi-final on July 11 at Edgbaston. Whether it's relevant that England have won their last 10 internationals at that ground - and their last three ODIs against India in England - is debatable. The pitch, two across from the surface on which they met on Sunday (so with a slightly longer boundary to the shorter side), will be new. "If we had a choice of where we play our group games it would be Edgbaston, The Oval and Trent Bridge," Morgan said. "It's a place we really like playing."

Perhaps the winner of that game, given just two days to recover before the final, will be at a disadvantage. The winners of the other semi-final will have an extra two days, after all. But there are a few in this England side - not least Chris Woakes, who came through a fitness test ahead of this game, and Archer, who came through one ahead of the last - who will benefit from an extra few days off now. "Our bowlers need a rest," Morgan admitted.

Such issues can wait. For the first time in nearly 30 years, England are in a World Cup semi-final. And for perhaps the first time ever, they have the most destructive opening batsmen and the quickest fast bowlers. They've come a long way since the debacle of 2015. And you sense they're not ready to go home just yet.