That is despite a wretched run of luck in the last month with refereeing decisions going against them which has arguably cost them as much as six points.
Bilic and the club's co-owners David Sullivan and David Gold have all spoken out about the fact the Hammers have been hard done by this season.
Manuel Lanzini had a perfectly good goal ruled out when two yards onside while Mesut Ozil was a yard offside when giving the Gunners the lead.
Dimitri Payet also had a goal chalked off in the second half while Lanzini had legitimate claims for a penalty turned down.
'It's quite obvious'
Now former Liverpool star Danny Murphy has spoken out on the issue in his role as a pundit on BBC's Match of the Day, where it was even put to him that the Hammers might have been 'lucky' to keep striker Andy Carroll on the pitch.
"I think that (sending off Carroll) would have been really harsh," Murphy told MOTD in defence of the Hammers.
"It's (Lanzini offside goal) quite an obvious one that the assistants have got wrong.
"West Ham are having no luck at the moment that's for sure.
"If you look down the line it shouldn't be a difficult one.
"Bellerin's moving out as Lanzini is moving in but it's the wrong decision."
Hammers paying the penalty
West Ham fans will be grateful to see the issue highlighted by respected pundits such as Murphy.
Indeed a more detailed look at the statistics suggests West Ham haven't had much luck for the last four years.
The club has only been awarded one penalty this season, the lowest in the Premier League by some distance.
And they have not had a penalty away from home in four years.
The club will be hoping that changes this weekend when they travel to the King Power to face the champions-elect who have had eight penalties this season.