All of England knows one thing about the Ashes this winter. They can be won all right, but it will need Kevin Pietersen to bat like the prince he once was and not the pauper to which he has been reduced in the past year.
It is the rider to every knowing prediction, the asterisk against all those forecast scorelines, the essential component. Perhaps it forgets that England have learned to cope without Pietersen (they even regained the Ashes in 2009 largely in his absence) but crucially it also remembers how he can shape and govern innings and matches.
The thinking is that in Australia, of all places, if Pietersen does not do it, nobody can. England have skilful if frequently underperforming batsmen, but none can take the game by the scruff like he can. There have been occasions these past few months when this commanding maverick seemed a phenomenon from the past, but there was enough in his 58 yesterday, his first innings of the Australian tour, to cling on to the hope yet that the old KP may one day be with us again.
He got out when he should not have done (but hey, he has done that before and yesterday everybody else did it too). There was an intermittent fluency about his performance which was as heartening as the mood which matched it. Unless he is striving hard to conceal the demons, Pietersen seems to be gloriously at ease with himself.
"I really enjoyed it," he said after his innings. "I've been working a hell of a lot over the last six weeks to get to the place where I'm at at the moment. After coming back from South Africa for a couple of weeks, I feel top drawer and hopefully there's plenty more to come."
It was hardly vintage Pietersen. He messed up a couple of shots against Michael Beer, a purveyor of left-arm spin, the type of bowling which has come to pierce his defences, disturb his attack and intrude on his soul. He was dropped once, an edged drive to slip. But there was plenty of thumping, no-nonsense stuff in between, drives down the ground, ferocious flicks through mid-wicket.
Pietersen has not made a Test hundred since March 2009, 20 months and 27 innings ago, and his average in that time barely scraped 40. But he has not truly looked the player of yore since he lost the captaincy in January of last year. Something has gone. The debate is whether it has gone forever.
Pietersen himself must have wondered at times. But his fortnight back in South Africa, land of his birth and maybe still of his dreams, seems to have had a dramatic effect. He barely made a run there but it seems the conversations he had with the coach Graham Ford, a long-time confidant, might have been vastly significant. "It was amazing to work with Graham," said Pietersen. "I have worked with him since I was six or seven years old, he is a close family friend, and I feel great at the moment.
"They were mental advances. I have never really been a technical player, you have seen me play for six years and I play like a clown. It is just my mental approach that I needed to change, I needed to get a lot of confidence back and I am on fire at the moment, so I am happy. I felt really good. Graham just knows me, he has known me since I was a little nipper."
While it is not necessarily true that Pietersen has played like a clown for the last six years, it is obvious that he does not observe conventional batting methods. Therefore it follows that these have the potential for exposing him. This is probably what happened first. The mental weaknesses followed, as they tend to do when runs dry up.
If Ford has worked his way into Pietersen's psyche and found the key to rediscovering his ego, he may require English cricket's everlasting thanks. Pietersen is adamant that he is not thinking of the failures that have piled one on the other. "I have talked about it but I am looking forward now," he said. "I am not interested in what has gone, I am very happy with what is happening at the moment.
"It's always nice to get time in the middle. South Africa was tricky because we played in some horrible weather, with the lights on and in drizzle. For the sun to be out and to play on a really good wicket was great. I love playing in Australia, I have had some really good success here and personally last time went well for me. So it was good to get out here and get another 50 at the Waca."
He smiled at the thought of coming out at the Waca again next month. Pietersen scored 490 runs at an average of almost 55 in England's lamentable Ashes series four years ago. He was England's best performer by far. "It was just a case of batting well," he said. "That's probably the second-highest score I have got in a warm-up game going into a Test match so I'm not too fussed by it, it's nice to get the runs but if they come in the warm-up games, they come; if they don't, they don't, it only counts at the Gabba."
It counts all right and England are counting on it.