AS Scotland look ahead to their Rugby World Cup quarter-final against Australia on Sunday, they have one very pertinent fact on their side. In their last three meetings with the Wallabies, they have won twice.

Underdogs can always come up with something to convince themselves they have a chance of winning a big game, but there is nothing like that tangible fact to inspire confidence. It makes the difference between believing you can do something and knowing you can do it. And such a difference can be of massive assistance to a team’s self-belief.

The Wallabies won the most recent game between the sides, claiming a 21-15 victory at Murrayfield late in 2013. But Scotland won 9-6 in Newcastle, New South Wales, on their 2012 summer tour, and back in 2009 they won 9-8 at home.

“That 9-6 win against Australia in Newcastle was my first cap,” Ryan Grant, the Scotland prop, recalled yesterday. “All I remember is that it was pissing with rain.

“Your first cap goes by so fast, but I do remember the last scrum of the game which went really well and where we won a penalty.

“I looked over at [Wallabies scrum-half] Will Genia and he was shivering – that was the first time I realised it was cold. The next minute we won the game, and then seconds after that we carted Joe Ansbro off the pitch with 30 stitches in his head.

“You can give a team the respect it deserves, and all credit to Australia because they’ve played really well so far,” Grant continued. “But we’re not looking at them like they’re unbeatable – we can beat them and have beaten them in the past. The plan is to beat them again, and that’s what we’re working towards.”

Stephen Moore, Australia’s hooker and captain who will win his 100th cap if selected for the quarter-final at Twickenham, was a member of the front row that Grant faced that day three years ago. He remembers the terrible conditions in which that game was played - and the skill with which Scotland adapted to them.

“I opened the curtains during the day and I think I saw one of the bins rolling down the middle of the street and thought, ‘Oh yeah, this is going to be good’,” he said. “It was one of the toughest conditions I’ve ever played in my career - the wind was howling, it was raining sideways - and they really played well in those conditions, controlling the game really well.

“It shows you how difficult the task is. They’re a quality team, who’ve shown that in the tournament so far. Certainly, every time I’ve played against Scotland, I’ve felt it's been a really tough test match.”

Scotland winger Tim Visser was on that 2012 tour to Australia, but unable to play in the match against the Wallabies because he had not completed his three-year residency qualification. He has good memories of both recent wins, and is confident that Scotland have come through the pool stages of the World Cup in the right condition to pull off a shock result on Sunday.

“I remember sitting in the stands and it was raining sideways,” he said. “That’s one of the times we beat them. And I remember sitting in the stands when we beat them at Murrayfield. So we’ve shown that we can beat them. We’ve just got to play some of our best rugby. In knockout rugby, at a World Cup, you’d expect that.”

Visser believes that the general improvement in playing standards among the more lowly-ranked nations at this World Cup has helped quarter-finalists such as Scotland prepare for the tougher challenges ahead. In some past tournaments, pool mismatches such as the 89-0 win over Ivory Coast in 1995 or the 48-0 win over Spain four years later were little more than chances to pick up unwanted injuries. But this year’s games against the lowest-seeded teams in Pool B, the United States and Japan, have been altogether keener contests.

“It’s going to be a different challenge again from the games we’ve played so far, but we’ve come from a tough pool,” Visser argued. “Even though on paper it wasn’t one of the toughest ones, it turned out to be a tough pool. Japan put their best foot forward, and when they beat South Africa the whole pool got thrown around.

“As you saw at the weekend, we had to go to the end to win that game [against Samoa]. That’s probably prepared us more than we thought it would for getting to these quarters, and we’re looking forward to playing Australia. They’re a good team, but we’ve played some good teams in the pool as well.

“You can’t progress to the semi-finals without playing your best rugby. We’ve improved game on game: we have to improve again to come off with a result against Australia.”

That required improvement may well need to be across every area of the game, with the defence, above all, being an area in which Scotland have to be sharper. But at least they know from personal experience that beating the Wallabies, although implausible, is not impossible.