Frenchman Anelka signed a one-year deal at the Hawthorns on July 4, after spending the second half of last season at Juventus.
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West Brom secured an eighth-place finish in the Premier League in 2012-13, but manager Steve Clarke has moved to improve the club's forward line after on-loan striker Romelu Lukaku's return to Chelsea.
But despite losing a player who scored 17 Premier League goals last season, Ridgewell is confident Anelka and Long can cause problems for opposition defences.
"I'm sure Shane [Long] will be looking forward to it," he told the Express & Star. "Him [Anelka] and Shane together could be frightening.
"I wouldn't want to be defending with those two running at me.
"As a pairing, I'm sure they will be very good for us."
Anelka has enjoyed a glittering career, winning Premier League titles with Arsenal and Chelsea, as well as the Uefa Champions League with Real Madrid in 2000.