Well before this tour began, the firm contention was that while New Zealand would be highly competitive in the two short forms of the game, once it came to the ANZ international test series, the gulf in quality between the No 2 and No 8-ranked teams would stretch.
No wonder, then, New Zealand are backing themselves to, at least, be right in the contest over the next five days at the Basin Reserve.
"We gave ourselves a great opportunity [in Dunedin]. We dictated terms from day one and the progress we made in a short space of time from the South African lessons was encouraging," McCullum said.
"The challenge now is to back that up, and consistently. We've got the bowlers to take 20 wickets and put pressure on their batting lineup. If we execute well, we give ourselves a good opportunity."
Bowling first is his preference on a Basin Reserve pitch expected to be good for batting most of the time, McCullum's thinking that the first day is likely to offer seamers their best opportunity.
He acknowledged England's premier swing bowler Jimmy Anderson and Stuart Broad bowled well on the ground on the previous England tour five years ago, before asserting he'd seen New Zealand's leading seamer Tim Southee perform strongly on the ground too.
McCullum talked of the pitch having "a little bit of sting taken out of it", but New Zealand will expect more shorter-pitched bowling from, in particular, tall speedster Steven Finn and Broad as they seek to utilise the bouncier conditions.
Equally, Southee, Trent Boult and Neil Wagner represent New Zealand's best chance of chasing 20 wickets.
McCullum followed his team news with the insistence that bowling first is his probable course of action if he gets the choice at the toss today. He doesn't expect the pitch to break up to any degree, meaning day one and making early inroads will be crucial.
For what it's worth, New Zealand's last six test wins - in places as diverse as Bulawayo, Hobart and Colombo - have come when batting first.
The TAB doesn't rate New Zealand's chances, Dunedin notwithstanding.
It has England warm favourites at $1.67 to win, the draw at $2.80 and New Zealand at $7 to win a 15th test on the Basin, its most successful test venue.
New Zealand v England
Second test
Basin Reserve, from 10.30am today
New Zealand: Brendon McCullum (c), Peter Fulton, Hamish Rutherford, Kane Williamson, Ross Taylor, Dean Brownlie, BJ Watling, Tim Southee, Bruce Martin, Neil Wagner, Trent Boult.
England (probable): Alastair Cook (c), Nick Compton, Jonathan Trott, Kevin Pietersen, Ian Bell, Joe Root, Matt Prior, Stuart Broad, Steven Finn, James Anderson, Monty Panesar.
At the Toss
* New Zealand have got 38 of their 72 test victories bowling first.
* Eleven of New Zealand's 14 wins at the Basin Reserve have come when bowling first.
* Their last six test wins, however, going back to late 2009, have been achieved when batting first.