Their supporters, at least, will be attending the encounter more out of hope than expectation, thanks largely to their side's recent record at Anfield.
By chance, the last time that the Toffees actually won away from home against their neighbours was on this very day back in 1999. In true derby fashion, it was an ill-tempered affair.
The blue-touch paper was well and truly lit in just the fourth minute of the contest. Liverpool lost possession just outside their own penalty area and Nick Barmby pounced, before playing in Francis Jeffers. Instead of shooting, the youngster picked out his strike partner Kevin Campbell, who beat home goalkeeper Sander Westerveld with a confident finish into the far corner of the net.
From that point onwards, the clash turned sour. Midway through the first half Liverpool centre-forward Michael Owen launched a two-footed lunge on Everton defender David Weir. A red card looked inevitable, but referee Mike Riley, much to the disgust of the visitors, only brandished a yellow.
However, with 75 minutes played, Riley had little option but to dish out not just one, but two red cards. Following a collision between Westerveld and Jeffers, the pair traded blows inside the Liverpool penalty area and both were sent off. Liverpool boss Gerard Houllier had used all three of his permitted substitutions at that point, which meant that defender Steve Staunton had to don the goalie gloves.
With no equaliser in sight, matters got even worse for Liverpool in the 90th minute when they were reduced to nine men. As goalscorer Campbell looked to mount a counter-attack, he was caught with a challenge high on the thigh by Steven Gerrard, who was instantly dismissed by Riley.
As he headed back to the dressing room, Gerrard took with him any chance that the hosts had of claiming a share of the spoils.
Speaking after the final whistle, Houllier told reporters: "Some of my players lost the plot out there. I am not happy about that, because no matter how much provocation there is, you will pay if you lose your nerve at this level. You must have the brains to decide what is the best way of getting something out of a game like this."
Meanwhile, Everton boss Walter Smith added: "These things happen in derby games. I was especially happy with the way we competed."
LIVERPOOL: Westerveld; Staunton, Hyypia, Carragher, Heggem; Berger, Hamann (Meijer), Redknapp, Smicer (Camara); Owen, Fowler (Gerrard)
EVERTON: Gerrard; Ball, Gough, Dunne, Weir; Barmby, Collins, Hutchison, Xavier; Campbell, Jeffers