You have to go back to their run to the final of the same competition in season 2014-15 for their last success in a one-off tie.
Since then, they have lost one last-16 match, five quarter-finals and one semi.
It’s a wretched record but there has been plenty of evidence this season to suggest it can be consigned to the dustbin of history by this group of players.
As well as a new coach and a new style of rugby, Edinburgh have a new stadium which has yet to be breached in a competitive match.
Such has been their dominance in the DAM Health that they have won their last three home games 66-3 (Brive), 56-8 (Connacht) and 54-5 (Pau).
Blair expects Saturday’s match to be a lot closer despite Bath’s lowly standing in the English Premiership and is especially wary of stand-off Orlando Bailey and the opposition back row, which comprises international trio Josh Bayliss, Sam Underhill and Taulupe Faletau.
“He’s really talented,” Blair said of Bailey. “He seems to have to have the ability to pick out the right runner but he’s also a runner himself and a threat.
“You look at their team selection, it is an impressive side. Back-row in particular, but they’ve got internationals throughout their team, speed and power on the wing, so this is going to be a proper test for us.
“Bath are a quality squad with world class players - Faletau is one example. They’ll be targeting this competition. Their results and performances have improved week on week. So it’s a massive test for us against a top quality Premiership team.”
Edinburgh fared well against English opposition in the group stage, defeating Saracens away before being edged out by a single point by London Irish in Brentford.
They will face Bath without Darcy Graham, who picked up a quad muscle injury in training, and the suspended WP Nel. Emiliano Boffelli returns on the wing to replace Graham while Lee-Roy Atalifo steps in at tighthead where Edinburgh are also without the services of Luan de Bruin who was injured against Pau.
Blair said he was “disappointed” with the decision to suspend Nel for three weeks after the prop was adjudged to have struck the head of Pau’s Téo Bordenave. The ban will be reduced to two weeks if the player completes a “World Rugby Coaching Intervention” but Blair describes the disciplinary hearing as “probably one of the most stressful things I’ve done”.
In the end, Edinburgh opted not to challenge the citing commissioner’s decision and accepted the verdict but losing Nel at the same time as de Bruin is unfortunate.
Elsewhere, Blair has brought back his big guns, with Mark Bennett, James Lang, Blair Kinghorn, Ben Vellacott and Hamish Watson all returning to the side.
Unsurprisingly, the coach was reluctant to dwell on the club’s poor record in knockout games.
“It’s not something I’ve discussed with the players,” said Blair. “Focusing on what we are trying to bring to the game is more likely to win the game than bringing facts like that out.”