Appearing a mere four years after “Sugar, We’re Goin Down” turned Fall Out Boy into genuine rock stars, and covering a mere four albums, 2009’s Believers Never Die: The Greatest Hits smacks of a contractual obligation or a rush holiday treat: something to close out a contract or get a piece of product into stores during the Christmas season. Regardless of the motivation, Believers Never Die winds up as a surprisingly addictive hits record, a hyper-charged testament to Fall Out Boy’s grandiosely self-deprecating, self-aware emo-pop. Taking loud fast rules to a stylized extreme, Believers Never Die cuts away any remnants of slow songs — the acoustic guitars and lack of drums on “Yule Shoot Your Eyes Out,” one of four new songs or rarities, gives the illusion that it’s slower than it is — FOB pile up hooks and words with a smirky abandon, the sincerity of singer Patrick Stump and sarcasm of bassist/lyricist Pete Wentz tied together by a shared love of arena punk: guitars from Van Halen, melodies from Queen, outlook from the alt-rock revolution. Their Gen-Y sensibilities — not just the ceaseless snark and “I Love the ‘80s” name-drops, but their love of brick-walled production — can alienate old guys over 30, but give Believers Never Die a little time; the hooks burrow deep and Fall Out Boy seem like one of the quintessential mainstream rock singles bands of the 2000s. – Stephen Thomas Erlewine