The England captain remained in Hamilton while Stuart Broad's Twenty20 team flew to Wellington to complete a 2-1 series victory over New Zealand with a crushing 10-wicket success there. Cook senses such an impressive win can only give England extra confidence as they begin the second leg of their tour.
"Clearly any win against pretty much the same opposition you're going to be playing is helpful," he said. "It's obviously a different format, so not that relevant. But it's great for the guys' confidence."
Two of the architects of that win, openers Alex Hales and Michael Lumb whose unbroken stand of 143 finished the decider more than seven overs early, are not part of the ODI squad. Similarly, there are a couple of changes to personnel for the hosts as they move from one limited-overs format to another.
Cook, who has also confirmed Jos Buttler will retain the wicketkeeper's gloves in 50-over cricket after being preferred to Jonny Bairstow in that role in the sprint format, has just minor concerns about the readiness of some of his rested team-mates to immediately hit top form.
Graeme Swann, James Anderson and Jonathan Trott will be playing for the first time since December.
"It's great to have those guys coming back," said their captain. "In one way, they're a little bit undercooked - because the last time they played a game for England was 10 days before Christmas.
"(Ian Bell) Belly and I played a couple of weeks ago, so the other guys are probably a little bit underdone.
"They've had a bit of time off - which they needed.
"They haven't had a game to practise here. But they're world-class players who've played here before. So it shouldn't be too much of a problem ... and I expect them to be able to adapt well."
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