The Baggies are currently sixth in the Premier League table ahead of Saturday's trip to Old Trafford.
And Downing, the assistant manager, believes it is all down to hard work: "I think we've surprised a few people. I don't think we've surprised ourselves.
"It's been a work in progress the last two or three years. The club has worked exceptionally hard behind the scenes.
"The players have been collected and there has been a real strengthening of the squad. It's been built up over the years.
"I don't think it has surprised us from within. Thirty-three points at the half-way stage is a fantastic return for a club like us.
"We have to reset the goals. We are still looking at 40 points and people will raise eyebrows at that, but that's our prime objective, to stay up for another season.
"Then we can assess things again once we get to 40 points but we are not jumping ahead of ourselves and we've got a lot of people with their feet on the ground."