The Baggies kicked off the Premier League season in style with victories over Bournemouth and Burnley before being held by Stoke in a 1-1 draw, and succumbing to a 3-1 defeat to Brighton last timeout.
The Hammers, meanwhile, suffered at the hands of Manchester United on the opening day of the season before losses to Southampton and Newcastle.
But they come into this match buoyed by a 2-0 win over Huddersfield.
Ahead of this match, West Brom boss Tony Pulis said: “Complacency is a word I don’t like. There’s always a little bit around after you’ve done well and that has to be eradicated.
“We’ve had a very good start to the season and we have been brought down to earth with a pretty average performance.”
Reflecting on his side’s opponents, he added: “They are a good side and I have a lot of time for Slaven (Bilic) and when you look at the squad and what they have got it’s a very strong Premier League side.”
Bilic said: “It was so important to win the game (against Huddersfield) but we have to continue like that. We were off training yesterday but we had a meeting before training today. I said, if we think that because we beat Huddersfield we have done it, then we are wrong.
“We need to build on this now. We beat them after training at our stadium and we were on fire in training.
“But we must do it in games, and that’s what we did. We have to do it again tomorrow and only then will it be a positive for us, if we get something out of the game.