That led Cotter to try to play down the expectations surrounding his own improving side by saying of Ireland: “It’s a huge task to try to break down a team that doesn’t have any weaknesses at all.

“They (Ireland) only have strengths, with a very control-focused game plan. Teams beat the All Blacks rarely but beating them with 40 points ... that’s something.”

Cotter added: “It’s a tough start for us. We’d love to be able to beat them but it’s going to take a huge effort.”

Ireland, who clinched the 2015 championship with a 44-10 win against the Scots at Murrayfield, made history with their five-try win against New Zealand in November but Scotland underlined their own progress with victories over Argentina and Georgia and a near miss against Australia.

Former Ireland wing Shane Horgan believes that Cotter, who will join Montpellier in the French Top 14 after making way for Glasgow coach Gregor Townsend in June, has “the best group of Scottish players in 25 years”.

Meanwhile former Scotland centre Alan Tait said the current side stood comparison with the 1999 team of which he was a member that won the last Five Nations title in 1999.

Saturday’s match will be a momentous contest in at least one respect as it will mark the arrival of the trial bonus-point system (extra points will be awarded to sides who score four tries and also who lose by seven points or less) in the Six Nations Championship.

The Scots do not have history on their side, however. They have not won an opening Championship match since 2006 and have also lost their last four encounters with Ireland.

But Ireland will be without the guiding light of Johnny Sexton as the Leinster fly half has a calf injury and will be replaced by Ulster’s Paddy Jackson.

A concerned Schmidt was wary of Scotland’s ability to upset his superbly-drilled unit.

“Scotland away first up is really tough,” said Schmidt. “They’ve been going really well.

“We expect a torrid time. They are in super shape at the moment.”

The positive mood created by Scotland’s encouraging November performances had been enhanced with Glasgow’s progress to the quarter-finals of the European Champions Cup, which included a remarkable 43-0 win away to two-time champions Leicester.

Cotter’s starting XV features nine Glasgow players – including the dazzling fullback Stuart Hogg, who was voted Player of the 2016 Six Nations.

Scotland also have Huw Jones returning in midfield. The Stormers centre made a huge impact on his first international start in November, scoring two first half tries in the 23-22 defeat by Australia.

Ireland will doubtless miss the tactical kicking of Sexton but they have ten of the starting XV who secured victory over the All Blacks three months ago.

Not that Schmidt is dwelling on that historic success.

“I think we’ve got to get that absolutely out of our mind,” he said. “It’s a fantastic memory but we’ve got to really work hard to try to build a few new memories and that is going to be tough.”