Manuel Pellegrini has endured a difficult start to life back in England, overseeing four defeats from four in the league and conceding 10 goals already.
Having won just once in the last 11 visits to this ground, his team are 12/5 (3.40) outsiders with William Hill to collect their first three points of the campaign.
The Toffees have won more games against this opposition than against any other in Premier League history, and are priced at 21/20 (2.05) to enhance that record even further with another victory in this one.
The hosts have drawn three of their four opening league games so far, and there are odds of 13/5 (3.60) available on them being held to yet another stalemate here.
Theo Walcott, Dominic Calvert-Lewin, and Seamus Coleman all picked up injuries during the international break, joining Yerry Mina, Michael Keane and Phil Jagielka in the treatment room.
With Richarlison suspended and Idrissa Gueye, Bernard and Andre Gomes all doubtful, Marco Silva is faced with a severely depleted squad.
Long term absentees Winston Reid, Manuel Lanzini and Andy Carroll remain the only players missing for the Hammers.
Even without their numerous absentees, Silva’s team should feel confident of hitting the net against a team that has conceded 10 goals so far in the league – the worst record in the division.
However, the Everton are also struggling for solidity at the back, having failed to keep a clean sheet in any of their five competitive fixtures this season.
Having served up four goals in both of their league encounters last season, odds of 4/5 (1.80) are not to be missed on at least three going in when they clash this time out.