The atmosphere at Chelsea home games has been hostile since former Liverpool boss Rafael Benitez replaced Roberto Di Matteo as interim manager until the end of the current season.
The Hammers inflicted a 3-1 defeat on Chelsea just three games into Benitez's tenure when the fans' wrath was still at its strongest.
Now Allardyce takes his team to Stamford Bridge looking for a famous league double over their London rivals and he reckons the animosity towards Benitez can work in his side's favour.
"You can see the importance of your fans being behind you rather than not," he said.
"I think Chelsea's team has suffered at Stamford Bridge because the fans have not been fully supportive of what has happened. That is nothing to do with Rafa, he can't help that.
"He is a manager trying to do a job the best he possibly can and he's obviously got a great CV at the jobs he has done at his other clubs.
"But it shows the importance of a volatile fan base that turned the other way, what effect it can have on a team.
"In the reverse of that we all know the extra man that fans can create. You see the opposite of that at Chelsea and certainly in the early stages when Rafa took over and Chelsea suffered some poor results because of that. That's the effect the fans have on the team that plays on the field."