The Black Caps have won just once in their 15 visits to the home of cricket and are currently six places below England in the world rankings.
And, as McCullum weighs up whether to include seamer Doug Bracewell or spinner Bruce Martin in the bowling attack, the 31-year-old acknowledges he may have to go against the grain to have the chance of toppling England.
“I would hope they’re educated gambles,” said the New Zealand right-hander.
“Just because you run past the principal’s office doesn’t mean you’re not doing your homework.”
England were held to a 0-0 draw when the two teams met in a three-Test series in March.
But captain Alastair Cook, who is preparing to lead England in a home Test series for the first time, refuted suggestions that his team had been complacent overseas and insisted they are fully focused for the start of the summer.
“I don’t think there was complacency around, but we didn’t play as well as we could have done; that’s the bottom line,” said the Essex opener.
“Every Test series you play for England is a hugely important series, it doesn’t matter what has gone before. We are fully focused on these two weeks of Test cricket. We have to be at our best to win.”
■ A Cook (c), N Compton, J Trott, I Bell, J Root, J Bairstow, M Prior, S Broad, G Swann, J Anderson, S Finn
■ P Fulton, H Rutherford, K Williamson, R Taylor, D Brownlie, B McCullum (c), B Watling, T Southee, D Bracewell, N Wagner, T Boult