It was the most stirring image of England's 2010-11 Ashes mirabilis. Not Tim Bresnan taking the final wicket in Melbourne or Chris Tremlett in Sydney; not the sprinkler; not the scoreboards which read "England 1/517" or "Australia 3/2". When the Ashes were retained, Andrew Strauss left the MCG field triumphantly. He was walking down the tunnel when he met Andy Flower halfway; the pair enjoyed a brief, proud embrace.

It was a rare example of public affection between two men whose bond was usually implied. Never mind Jimmy Anderson and Graeme Swann; Flower and Strauss was the real bromance of the 2009-12 England team. All evidence and understanding points to their relationship being abnormally strong, and it was clearly one of the key factors in England's golden period. The bond between Alastair Cook and Flower may not yet be as strong, but it is of a similar nature - as captain, Cook is essentially a mini-Strauss - and will be a key strength in the attempt to win a fourth consecutive Ashes series. Some feel it will also be a weakness.

A team can win without a good relationship between captain and coach but it is not an advisable business model. The recent history of the England team confirms as much. The best periods have come during strong coach/captain relationships: Flower-Strauss, Flower-Cook, Duncan Fletcher-Nasser Hussain, Fletcher-Michael Vaughan. The darkest times came between 2006 and 2009, when Fletcher's relationship with Andrew Flintoff broke down and both Vaughan and Kevin Pietersen struggled to work with Peter Moores' workaholism.

The success of Flower's relationship with Cook and particularly Strauss stems inevitably from shared values, most of which are alien to modern society: organisation, discipline, responsibility, integrity, a belief in doing things properly and privately. Yet if their values are of an old-school nature, their tactics are entirely modern. They believe in a passive-aggressive approach that involves bowling dry and starving impatient modern batsmen of their oxygen: runs. There are occasional exceptions - such as Strauss successfully placing Cook at backward silly point against Yuvraj Singh at Trent Bridge in 2011 - but essentially England do things by the book.

Or rather the MacBook. They have an intractable belief in statistics. Never mind betting; in the England dressing room all kinds of gambling are unofficially outlawed. Decisions are taken because of logic and hard evidence, not instinct. As a result England find themselves in the unusual position of being derided for being too modern, such is their perceived defensiveness. Interestingly, such an approach was introduced by Vaughan, who was generally hailed rather than criticised for revolutionising the perceived orthodoxy of field settings.

Eight years on, England's fields are not sexy enough. Or, rather, not funky enough. That became the unlikely word of the Ashes in the summer, with various commentators contrasting the "funky" fields of Michael Clarke with those of Cook. Even Strauss used the word, albeit with the fair degree of contempt you would expect for a man whose belief in his former team's methodology in unshakeable. Cook might privately acknowledge a degree of puppetry in his field settings; not because he is weak, but because he concurs with the ideas imposed by Flower. As a former choirboy, he knows plenty about singing from the same hymn sheet.

He is keen to point out that tactics are only a small part of cricket. "I've always said I'm trying to learn on the job," he said recently after Shane Warne's 708th public critique of him. "And, yes, there will be times when I could be a bit more imaginative and think slightly differently. There are two sides to the job and the unseen one is the man management in the dressing room and how you handle certain individuals. But I will be judged on results."

Cook was justly praised for his Vaughan-like calmness in the excruciating denouement at Trent Bridge last summer; he leads by run-laden example and seems to have easily found the delicate balance of being captain while still retaining strong, jokey friendships. He did not get the credit he deserves for his fearless and seamless reintegration of Pietersen. And he might point out that world cricket's most celebrated captains, Clarke and Brendon McCullum, have a combined Test record of P20 W1 D7 L12 in 2013. That record is funky only in the malodorous sense. Statsguru does not have a filter for eye-catching fields.

Cook might privately acknowledge a degree of puppetry in his field settings; not because he is weak, but because he concurs with the ideas imposed by Flower

Cook seems entirely happy to go along with Flower's approach, although it is legitimate to wonder how much of that approach comes naturally to him and how much he has unconsciously absorbed from the Strauss/Flower years. The same is true of the players. Flower is a deceptively charismatic man whose hold over the England dressing room, not just Cook, is enormous. You suspect they would crawl to the ends of the earth for him - or, more painful still, go to a pre-Ashes boot camp in Germany. In his autobiography, Matt Prior says, "I never argue with Andy!" If a soft exclamation mark existed, Prior might have used that; he was surely only half-joking. Graeme Swann, in his 2011 book, said "You just don't mess about with Andy; you get the feeling he used to be an assassin or something like that."

Nobody messes with Andy. His stare could make hell volunteer to freeze itself. This is not an entirely good thing. The evangelism of the England dressing room, which surely stems from Flower, has rubbed plenty up the wrong way, and there is legitimate concern that they are sometimes too intractable. Some would blame that lack of flexibility for the failure to come even close to maximising the terrifying potential of Steven Finn, for example. There is also an argument that the limitations of England's methodical approach were exposed in South Africa in 2012; that the only times they troubled South Africa were through sheer dramatic bursts of ability from Pietersen at Headingley and Finn at Lord's. Against that, this is evidently a very happy dressing room, in which all the players buy into Flower's doctrine. He created a strength and unity that rapidly propelled an excellent but not great team to unimaginable heights.

It would nonetheless be interesting to see how he would work funkier captains like Clarke and McCullum - or even Vaughan, who liked to run with instinct. Vaughan's most famous dismissal as captain, Matthew Hayden's first-baller at Edgbaston in 2005, came about because he had a hunch as he went onto the field and decided to add a short extra cover to the pre-planned man just off the cut strip. Hayden drove straight to Strauss at short extra.

When England won in Adelaide in 2010-11, Flower described it as "the perfect Test", almost as if it had been programmed on computer. Yet England are not just automatons: they are capable of exhilarating, almost vigilante demolitions of opponents, as they showed at Trent Bridge in 2011 and Durham last summer in particular. We rarely see such performances; but when we do, they evoke the most off-the-cuff team of all, Pakistan.

It might be tempting to conclude, such is the influence of Flower, that English cricket has started to follow the cult of the manager evident in English football. Far more likely is that Flower is a coach with an unusually strong personality, capable of inspiring rare levels of loyalty. To some extent his players are also his disciples. This creates a formidable environment. But it also means that England - and Cook in particular - could be a little lost when he decides to move on.