Travis Head has been left incredulous at his latest extraordinary big match tour de force, declaring that "not in a million years" would he have imagined becoming Australia's World Cup match-winner.

In September, a fractured left hand suffered in South Africa looked set to rule Head out of the tournament in India but, backed by the selectors, he has been able to repay their faith with a series of brilliant performances, the best of which he saved until last.

It wasn't just his extraordinary 137 that broke 100-000-plus Indian fans' hearts in Ahmedabad, but one game-changing catch to get rid of Rohit Sharma and a couple of miserly overs with the ball that completed one of the great individual performances ever witnessed in global cricket's biggest showpiece.

"Not in a million years would I have believed this, what an amazing day," smiled the 29-year-old, who was not only the player of the match in the final, but also in the semi-final against South Africa and the World Test Championship final at The Oval, where he again tormented India with a wonderful 163.

Yet it had only been last month when Head still wasn't sure if he'd make it to the big show after breaking his hand.

"It's a lot better than sitting on the couch at home, I'm very lucky that everything went well and that I was able to get back here and all support the boys showed me," he said.

Coach Andrew McDonald agonised over the decision to keep Head in the squad rather than call in a fit player, likely a second front-line spinner to help brave the Indian conditions.

"The next night (after Head's injury) Ronnie (McDonald) came up to me. He's like, 'I haven't slept all last night. I think we're going to keep him'," captain Pat Cummins said.

"'We're going to take the risk. He might be right for the Netherlands (game) and then if we're going to make the finals and we want to win the World Cup, I think he needs to be there for the finals'.

"It means you probably don't have the second spinner in your squad, which is a risk, but obviously it paid off.

"I couldn't be happier for Trav."

If any moment turned the final Australia's way, it had been in the field when Head sprinted a good 15 metres from point into the deep to cling on to a magnificent catch to dismiss Sharma after he'd just smashed Glenn Maxwell for a six and a four.

"Probably the unluckiest man in the world," Head shrugged about the Indian captain.

"Couldn't imagine getting a hundred - and couldn't imagine holding on to that catch."

With the bat, he went on to join Ricky Ponting and Adam Gilchrist as the only three Australians to score a century in a World Cup final. "I'm definitely third on that list," he said with typical modesty. "It's a nice one to join."

Ponting also saluted him. "A little bit unorthodox at times, you quite often see him against that new ball and think, 'how on earth is he gonna get through this?' but he does. He not only survives, he scores quickly, and scores big runs.

"And the stage doesn't get any bigger than today. Australia three for 40, India all over him in front of 130,000 people.

"He had to change the way that he played, went from sixth gear back to second and established an amazing partnership with Marnus (Labuschagne) just when their team needed it the most."

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