It has been the conceding of 10 goals at the other end which has foiled their early-season progress and the Spaniard has admitted that he is surprised that his back line has been so leaky.
The Champions League chasers more than played their part in the nine-goal thriller with Chelsea a fortnight ago, but have thrown away points in conceding late on in draws with Leicester City and Arsenal.
New Baggies boss Alan Irvine will be desperate to get a first win under his belt ahead of upcoming games against Tottenham Hotspur, Liverpool and Manchester United.
Martinez may give England international John Stones a chance at centre-back as he looks to solidify his defence. The highly-rated 20-year-old played 171 minutes for the Three Lions this week.
Aiden McGeady was another to impress on international duty, scoring twice, including a skilful last-minute winner, to secure the Republic of Ireland a 2-1 success in Georgia, and will probably keep Chelsea loanee Christian Atsu, who is available again after being ineligible to face his parent club, out of the side.
Ross Barkley is apparently ahead of schedule in his rehabilitation from a knee injury, but he, Leon Osman and Steven Pienaar are all out as Martinez is forced to manage without several of his midfield regulars.
His striking ranks are looking stronger following the arrival of Samuel Eto'o, who scored on his debut against his former team at Stamford Bridge, and Arouna Kone is nearing fitness after a long-term layoff.
West Brom have only won one of their last 10 Premier League home matches, although both of the ties between these sides last season ended in draws.
West Brom: LDD
Possible starting lineups
West Brom: Foster; Wisdom, McAuley, Olsson, Davidson; Brunt, Mulumbu, Gardner, Berahino; Sessegnon; Ideye
Everton: Howard; Coleman, Jagielka, Distin, Baines; McCarthy, Barry; Mirallas, Naismith, McGeady; Lukaku
Sports Mole says: 0-2