And the odds are in their favour. In the 60 Heineken Cup quarter-finals to date, the home team has won 46 times — that’s a 77% success rate.
So it’s rather unusual for the travelling team to start as favourites, but with four European titles under their belts, the French champions are the natural choice to set up a semi-final against either Munster or Ulster in Dublin.
Edinburgh head coach Michael Bradley makes one change from last weekend’s 26-23 win over Scarlets, with Netani Talei returning to replace Stuart McInally at number eight.
“The ability of both teams to play an open and free running brand of rugby is a very exciting prospect for fans,” said Bradley.
“Toulouse will travel with a strong, powerful and competent team, confident they can win at Murrayfield. It is a contest that will demand a complete performance from Edinburgh.
“However, we can rival the top sides in Europe when we play at our best. We have genuine and justifiable belief that we can progress from this match but it’s a massive challenge and one which the club, the supporters and the city are relishing.”
In the absence of a specialist full-back (Maxime Medard and Clement Poitrenaud are injured), Toulouse have been forced to name veteran centre Yannick Jauzion in the number 15 jersey.
The visitors will also be without former All Black pivot Luke McAlister, who has failed to recover from the calf injury that ruled him out of last week’s clash in Paris. Lionel Beauxis starts at fly-half outside former Wallaby Luke Burgess, who is back from injury.
EDINBURGH: T Brown; L Jones, N De Luca, M Scott, T Visser; G Laidlaw [capt], M Blair; A Jacobsen, R Ford, G Cross, G Gilchrist, S Cox, D Denton, R Rennie, N Talei.
Replacements: A Kelly, K Traynor, J Gilding, S McInally, R Grant, C Leck, P Godman, J Thompson.
TOULOUSE: Y Jauzion; T Matanavou, F Fritz, Y David, Y Donguy; L Beauxis, L Burgess; J Poux, W Servat, C Johnston, Y Maestri, P Albacete, J Bouilhou, T Dusautoir [capt], L Picamoles.
Replacements: C Tolofua, D Human, Y Montes, G Lamboley, J Doussain, C Poitrenaud, Y Nyanga, G Galan.