The Hammers head into the game on a high after the 3-0 win over Tottenham at White Hart Lane before the international break.
Manuel Pellegrini's men won at home against Everton in their last match, but have suffered problems on the road, losing at Cardiff and Aston Villa.
Allardyce is fully aware of this frailty and hopes the Hammers can take full advantage.
"In terms of results they've been a little bit Jekyll and Hyde," he said.
"[They are] absolutely fantastic at home and unfortunately for them they've not won away from home yet - lost two and drawn one.
"We have to be encouraged by that. Last year we had a fantastic 0-0 against them."
The absence of James Collins, who suffered a hamstring injury on international duty with Wales, has left Allardyce with a defensive headache.
Winston Reid and James Tomkins are the only fit centre-backs and Allardyce admits his squad has been stretched to the limit.
"I am concerned about the fact that we only run with three centre-halves," he said.
"So James being out is a particular problem for me because I have to run with only two central defenders now, James Tomkins and Winston Reid, for however long it takes James to get fit again, that is my big concern.
"He [Collins] has been excellent and he has been very unfortunate that I decided to leave him out.
"It wasn't that he was playing badly it is just that I thought James [Tomkins] in the Cardiff game in the Capital One Cup gave a fantastic performance and that fantastic performance got him in the team."