The Australians left yesterday for the three-match one-day series which begins in Auckland on Saturday, with matches to follow in Wellington next Wednesday and Christchurch on December 10.
Long-time Kiwi tormentor McGrath is not part of the 13-man squad after accepting an offer to rest from the series, an offer also given to Adam Gilchrist but later withdrawn after Cricket Australia overruled selectors.
In comments sure to rile Ricky Ponting's tourists, Richardson, who retired after last summer's Test series in Australia, has again taken aim at the world champions.
"In 2001 New Zealand played on the arrogance of their Australian opponents and nearly pulled off a couple of Test victories," he said.
"Australia were on a crusade to speed up Test cricket and force results.
"They set New Zealand a very makeable target at Brisbane and then nearly lost at Perth when they chased a huge target low into their batting order.
"The resting of Glenn McGrath for the Chappell-Hadlee series smacks of arrogance once again and just might be the opening the Black Caps need."
McGrath's absence will buoy Black Caps spirits after they were humbled at home 5-0 in the one-day series and 2-0 in Tests by the Australians earlier this year.
But this has been tempered by the loss of skipper Stephen Fleming for the first two matches as he recovers from a cancer scare.
The Caps have endured a largely miserable year, having recently been thumped 4-0 in the one-day series in South Africa.
McGrath's absence has enabled Australia to promote Michael Lewis, 31, who has taken more than 30 wickets for Victoria in three successive seasons.
The national selectors want to look at as many fringe candidates as possible before the 2007 World Cup and are also keen to ensure their best senior players remain fresh.
"While McGrath is only one man and Australia have many match-winners capable of single-handedly taking a game, he is a shining star," Richardson told The New Zealand Herald.
"Without him the gloss is taken off the Australian bowling unit somewhat.
"Brett Lee is more impressive in one-day cricket than Test cricket. He attacks the batsman and, with that, coughs up runs.
"A few runs as trade-off for wickets is tolerable if the other end is sewn up - McGrath's end.
"With McGrath not there, the tandem effect is not present and an opportunity is presented.
"Andrew Symonds, Brad Hogg and Cam White are handy bowlers but New Zealand's middle order should be capable of knocking them round and picking up singles through the middle of the innings.
"If the Kiwis get away to a good start, then these singles and safer play in the middle provide substance for a big score."
The Australians were furious at Richardson when they toured in February after he accused them of gamesmanship.
Richardson branded Shane Warne a master manipulator of umpires and Adam Gilchrist "a burglar".
The story spotlighted Gilchrist's record of the time at never being given out lbw in 37 home Tests and only twice in 77 one-day games in Australia, claiming the statistics were "astonishing".
"You see the way Gilly throws the ball in the air. He tends to play on his walking, his honesty, but he still tries to burgle anyone and everyone," Richardson said.
Herald Sun