Black Caps captain Stephen Fleming, who has a poor record when it comes to winning the toss, called correctly and batted against Sri Lanka here Thursday only to be out lbw fifth ball to Chaminda Vaas as his side collapsed to four for two in a game they lost by six wickets.
The Kiwis were facing South Africa on Saturday with the Proteas able to draw level with Bracewell's men on eight points if they won.
Graeme Smith's side are renowned for a strong batting line-up - they scored 356 for four against the West Indies - and a disciplined pace attack.
But they lack a quality specialist spinner, whereas New Zealand have the experienced Daniel Vettori.
And, as their shock 67-run defeat against Bangladesh showed, South Africa are vulnerable against slow bowling.
"We've got the flexibility within our side to cope with winning and losing the toss," said Bracewell. "Some other teams haven't.
"With a balance between spinners (Vettori and off-break bowler Jeetan Patel), medium-pacers (James Franklin and Jacob Oram), cutters (Scott Styris) and genuine pace (Shane Bond) and our depth of batting, we have more flexibility to lessen the odds on the toss.
"And a captain who doesn't win it that often, so we're pretty used to it."
Bracewell said defeat against 1996 champions Sri Lanka hadn't come as a complete surprise.
"We were never under the illusion any team was going to have a safe journey right the way through. There are a lot of teams that are fairly close."
And the former New Zealand off-spinner said the sight of seeing his top order collapse - the Black Caps were four for two when Styris, who scored an unbeaten 111 came in - was something he'd taken into account as well.
"It is a trend (teams losing early wickets). That shifts as the mini-competitions at each venue progress because the wickets change their character as they are being used.
"Over 12 days they are only using three wickets here and they are going to get slower and slower.
"We were all surprised at how slow that one was on Thursday and how little it did for such a short period of time. It only swung, and that was only shape, for an over and a half."
That was still enough time for left-arm quick Vaas, who dismissed all the New Zealand top three, to have Fleming lbw for nought for the fourth successive time as the 1996 World Cup-winner took three for 33.
New Zealand had to reshape their order after Lou Vincent's tournament ended last month when the opener had his wrist broken batting in the nets by Bond.
Peter Fulton has moved up to partner Fleming at the top of the innings while Thursday's match was number three Ross Taylor's first after four games out with a hamstring injury.
"Stephen Fleming is still in very good form, a little unfortunate on Thursday," said Bracewell.
"Peter Fulton is becoming very comfortable with the role, Scott Styris is having a great tournament and Ross Taylor, it was his first game back for quite some time. I've got no concerns at all."