Unlike former prime ministers, the rugby teams performing before the British establishment in Sunday's Anzac World Cup final will refuse to play to colonial type.

Cliches of Australia as New Zealand's bullying big brother, cocky and uncouth, bear no relation to reality on the rugby field. Contrasting portrayals of New Zealanders as dour protestant free settlers and Australians as thrusting convict-bred larrikins are also wide of the mark. Rugby, as Kiwis will affirm, is a world of its own, in which they are the black-clad overlords and Australia the perennial underdogs.

Since belting Australia 22-3 in their first rugby Test in Sydney 112 years ago, New Zealand have won 105 of the nations' 154 contests and have held the Bledisloe Cup for 69 of its 83 years.

This proportion is more or less the inverse of what has occurred in cricket, rugby league, soccer, basketball, netball, Olympic sports and immigration. Just this year, in the centenary of Anzac, Australians have shown no sibling solidarity, dispatching New Zealand in World Cup finals in cricket and netball.

This rivalry has become central to the trans-Tasman relationship and if taken across all sports, has superseded Australia's competition with England. Its history is characterised by Australian dominance and New Zealand pluck – except in rugby, where, if the natural order persists, the All Blacks will give their country joy enough to balance out all those other defeats.

If there is pizzazz at Twickenham, it is expected to come from the team that were once described as "all backs". Australia, against type, have found their strength in their forwards, from a rejuvenated scrum and lineout combination to the dark arts practised by the back-row trio of David Pocock, Michael Hooper and Scott Fardy. Just as Jemaine Clement, of New Zealand's comic duo Flight of the Conchords, described the Australian accent as 'kind of like an evil version of our accent', Australians play an evil version of New Zealand rugby.

Which is why the thought of losing the final at Twickenham on Sunday would cast a long black cloud over New Zealand. A losing All Blacks dressing room, said their one-time captain Anton Oliver, smelt like death.

That was after his team was knocked out of a World Cup, an event in which Australia has asserted a peculiar knack for over-achievement. As has been pointed out often in the lead-up to this final, Australia and New Zealand have won two Rugby World Cups each, even if the All Blacks have been favourites in all eight stagings of the event and, according to former Australian player Phil Kearns, will remain favourites in every World Cup until the end of time.

Australia's wins in the 1991 and 1999 World Cups still haunt New Zealand's idea of itself, and the prospect of another is unbearable.

As Oliver also said, "If history repeats itself, I should think we can expect the same thing again."