The Grand Slam winners have twice been World Cup semi-finalists – at the inaugural tournament 31 years ago, and in 2011, when they lost by a point to France after skipper Sam Warburton was sent off.
If Anscombe and company win their pool – one that includes Australia and Fiji – France or Argentina are potential quarter-final opponents, then a possible last-four clash against Ireland or South Africa, should they progress.
“The thing with World Cups is that you need an ounce of luck,” said Wales fly-half Anscombe, whose 20-point haul underpinned a Grand Slam-clinching victory over Ireland last weekend.
“You can be a good team and still get a bad call here or there, a bounce of the ball and a few injuries, and you don’t quite make it.
“We are fairly confident in what we can do, I think we have reason to believe we can go there and ruffle a few feathers.
“With the World Cup, it is about getting out of the pool, and then in knockout rugby anything can happen.
“Like ‘Gats’ (Wales head coach Warren Gatland) has said, we have a habit of winning at the moment. Hopefully, that holds us in good stead, come Japan.”
Wales have won their last 14 Tests – an ongoing national record – leaving them just four more victories short of equalling the Tier One world-best run that is jointly held by England and New Zealand.
Their next game is a World Cup warm-up clash against England at Twickenham on August 11, by which time, tournament preparations will be well advanced.
“I guess it (winning Six Nations) might come with a bit of added pressure,” Anscombe added.
“For some reason, I think we have always been able to slip under the radar and I guess maybe for some reason there is a consensus among the rugby public that they don’t rate us.
“That probably suits us down to the ground. We just try to keep our heads down, we work extremely hard for each other and we are a tight group. We know what we are capable of.
“There will be some added pressure no doubt, but we have every right to go to Japan with a hell of a lot of confidence and see what happens.
“We’ve got so much competition for places. Our squad depth has grown tremendously, and we’ve got three or four guys who can really do a job in every position.
“We are building well, we’ve had a good period, and it has been nice to have this run of 14 wins. More so, when we finish our careers we can look back and say we were part of something pretty special.
“Come Japan, it all counts for nothing, and we are a pretty level-headed group. We will enjoy this, and then come back together in June or July and start focusing for a big six months.”
Watch: Alun Wyn Jones and Warren Gatland reflect on Wales Grand Slam glory
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