Is it time to rethink cricket's stereotypes? The gutsy "Aussie battlers" are getting knocked over like ninepins. "Mercurial Pakistan", notwithstanding letting a first-innings lead dissipate at Edgbaston, have played determined cricket with a sense of collective purpose. And England are talented and exciting but flighty. After the second day of the Edgbaston Test, the former England captain Mike Atherton wrote that he felt a sense of role reversal: Pakistan had come dressed as England, England as Pakistan.

In this third Test, I certainly did watch some classic "English" cricket. A burly and strongly built right-arm seamer, sturdy but prone to stiffening up after a long spell, banged away at a length outside off stump. He didn't swing the ball much or create an aura of artistry, but he bent his back willingly, and five wickets in the first innings were due reward for his virtuous toil. From first impressions, he seemed reassuringly "old school", just the kind of county pro I played against in the 1990s. Indeed, if he is drinking protein shakes and taking pilates classes, he is hiding it well. The bowler, of course, was not an Englishman, but Sohail Khan.

A question for you: could you, if players' shirts, helmets and sweaters were swapped over, tell those of one country from another? Would you, from the shape of the shot and the bowling action alone, feel confident that you could still identify players' country of origin? If the stripes on his jumper were a different colour, would you attribute a rearguard innings as the inevitable toughness of a never-say-die Aussie battler? Without an Indian star on his jumper to guide your assumptions, would you race to describe a routine flick to leg as evidence of wristy Indian genius?

I am not so sure. After all, when Joe Root hits his trademark, a back-foot drive, as though he grew up on bouncy wickets on which he could trust the bounce, it would be easy to assume he grew up in New South Wales rather than playing for Sheffield Collegiates. As a child I was lucky to hear Colin Cowdrey explain the theory of "soft hands" and how to place the ball on the off side by varying the point of contact. But among today's players, it is Kane Williamson, more than any Englishman, who has mastered Cowdrey's manifesto for controlled batsmanship. Give him a different accent and Graeme Swann - who bowled an attacking line outside off stump, caught unfussily at second slip, chanced his arm in the lower middle order, and made the most of his extrovert self-belief - could easily slot in as an Australian game changer.

I am not arguing that teams do not have a culture, or even sometimes a personality. But it is often overstated as a permanent quality. In fact, a team's identity is constantly in flux. Stereotypes endure in our minds, but beneath the surface, national "styles" are being significantly redrawn by two major trends in modern sport.

"Choosing a coach is now a question of fitting together complementary attributes. Instead of "Is he a good coach?" we might ask if he is the right coach for the circumstances"

First, in the age of satellite television, aspiring cricketers can pick from the full range of international stars when it comes to choosing their role models. Before television captured such a wide variety of matches, aspiring players were more likely to copy stars closer to home. Geoffrey Boycott cherished the bloodline of English master batsmen (Hobbs, Hammond, Hutton); for my generation, in contrast, it was Richards, Lara and Tendulkar. Your choice of hero is now global. It is a mistake to think that globalisation inevitably leads to complete homogeneity - globalisation is more like a conversation, bouncing back and forth - but it certainly reduces the likelihood of parochial tastes.

Secondly, globalisation has a similar effect on coaching. Mickey Arthur, a South African, coaches Pakistan; Trevor Bayliss, an Australian, coaches England; India won the World Cup under Gary Kirsten, a South African; England's finest hour, the 2005 Ashes, was planned by a Zimbabwean, Duncan Fletcher. The tactical conversation, especially at the IPL, brings all cricket's ideas and accents around the same table. The market for coaching talent is fluid and global, with ideas following employees around the world. Besides, with modern cricketers floating between T20 franchises, players coach each other. AB de Villiers taught himself to sweep after lengthy consultation with Younis Khan: don't get beaten on the underside of the bat, better to top-edge than get out bowled or lbw.

As a consequence we should be more vigilant about calling time on sporting labels that are no longer fit for purpose. During the 2015 rugby World Cup, on the eve of the New Zealand v France quarter-final, I admired the prediction of former England fly-half Stuart Barnes. Forget the cliché that France are mercurial and unpredictable, wrote Barnes, they're predictably bad and will get smashed (and they were). As a Wales fan, I grew up on the stereotype that Wales were rugby's true romantics, driven by Celtic flair and instinctive imagination. Now they are brutally powerful, but predictably so.

It is the suddenness of change, not the stubbornness of continuity, that should surprise us. Australia's recent disasters against the turning ball, though gathering momentum, are not - from a historical perspective - part of their default cricketing character. Darren Lehmann (now head coach), Mark Waugh and Michael Bevan were three of the most technically accomplished players of spin that I played against. For my generation of batsmen, it was to Australians (especially New South Welshmen) - not just Indians - that we turned to learn how to play spin.

Finally, a conjecture about how teams might harness the forces I've described. Choosing a coach is now a question of fitting together complementary attributes. Instead of "Is he a good coach?" we might ask if he is the right coach for the circumstances. Arthur, Pakistan's avuncular coach, has helped them be competitive in this England series. He has connected with the culture, while subtly improving it - especially in terms of fitness and preparation. Even if they do not reach No. 1 in the rankings - and what an achievement that would have been for a nomadic Test team - this Pakistan team has warmed the English summer. During his stint as Australia's coach, Arthur became a lightning rod for wider frustrations within the Australian game. With Pakistan, he may do the opposite. Yet he is the same coach. Stereotypes may be misleading, but all teams have unique needs.