Sunderland had the week off after their triumph against Newcastle United last Sunday, and Allardyce feels that this rest period could stand his side in good stead.
Everton had to play 120 minutes of football in midweek, when they knocked Norwich City out of the League Cup, and Allardyce believes that the Merseyside club could feel the effects of that in the latter stages of their weekend match.
He also thinks the mounting injuries problems that the Toffees have could work in his side's favour on Sunday.
“We’ve got advantages, Everton have got a few injury problems and they played in midweek in the Capital One Cup,” he said.
“We could take advantage of that if we’re in the game late on, their fatigue will come in the last 15 or 20 minutes.
“But we have to be in the game, and the players have to have that toughness and desire to make sure we get a result.”
Sunderland go into the match against Everton knowing that a victory could lift them out of the bottom three.
The Black Cats have been struggling to find form all season, but they won their last fixture against Newcastle United 3-0 and finally have some momentum building behind them.
Everton, meanwhile, have lost their last three Premier League matches, and need to get their season back on track.
The Toffees have shown signs of promise in the early part of the campaign, but they haven’t collected as many points as they would have liked and the pressure is on them to start climbing the table.