The Baggies take on Southampton tonight on the back of thrashing Chelsea in their previous outing.
Every year teams battling the drop pull off surprise results against the division’s heavyweights.
And Allardyce – who has previously defied the odds to keep the likes of Crystal Palace, Sunderland and Blackburn in the Premier League – believes that is down to reality starting to bite for the players.
“There are many things I have experienced in relegation battles,” the 66-year-old said.
“When it gets to this stage it’s all about producing performances on a consistent basis.
“At Crystal Palace that was something like winning six out of eight at some stage.
“At Sunderland, it was the same – maybe five out of seven.
“Blackburn we went on a roll just after Easter where we were getting more wins than losses.
“That is accumulated by the fact time is running out and also the fears the players are facing makes them play better.
“They are facing being relegated, losing their status as a Premier League player, seeing a massive reduction in their wages and or getting sold off to a club that may not be as good as this one.
“If you accumulate all that together, from my experience, that explains why teams produce performances that shock everybody.
“I hope our players can continue to shock everybody around the Premier League.”
Allardyce says all Albion’s players have a duty to give everything they can to stay in the Premier League – with the boss suggesting there could be redundancies if they go down.
“Cut-backs are devastating for a club that is relegated,” he added.
“I experienced it when I went to West Ham.
“I had to overcome all that devastation of relegation.
“People who had been at the club for years, losing their job through no fault of their own because the players failed to stay in the Premier League.
“That is not what I want to happen here.
“Players have that responsibility as well as the responsibility for themselves and their families.”