Supporting the old trope that you must suffer for your art, Alice Cooper got an opus out of a toothache. On “Unfinished Sweet”, the deranged heart of the band’s sixth studio album, Billion Dollar Babies, frontman Vincent Furnier sings some lowdown dental blues, describing the pain like a “Saint Vitus dance on my molars tonight” and wincing at the paranoid hallucinations prompted by the laughing gas. The rest of the band are just as committed to the ludicrous concept, with Glen Buxton duetting with a dental drill before colliding head-on with a surf-rock/spy-theme breakdown. At no point does dentistry become a metaphor for anything else associated with rock’n’roll. It’s not about sex or VD. It’s not about drugs or ODs. It’s just candy and cavities.

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Therein lies the appeal of Alice Cooper. There was no concept so stupid that it couldn’t be parlayed into a catchy rock song, no idea so weird they couldn’t deliver it to radio with a black bow on top. Before the Ramones made dumb sound smart, Alice Cooper reveled in juvenile jokes, adolescent alienation and bludgeon-to-the-brain riffage. The band developed their love of theatre on the West Coast, where they worked briefly with Frank Zappa and gained a reputation for grotesque live shows. Around 1970, however, they moved back to Furnier’s hometown of Detroit, where The Stooges and the MC5 were bashing out a no-frills brand of heavy rock that would eventually morph into punk. That’s where Alice Cooper learned to marry their wildest notions with their heaviest riffs.

While it may not include the group’s best-known songs, it may be their best album. It’s certainly their most imaginative: a loose concept album about… well, who knows? But it does showcase their wild theatrics, their macabre imagery, their gory guitar licks and their fuck-everybody attitude that’s just about palatable thanks to the weirdo sense of humour that animates every note. With producer Bob Ezrin they recorded first at a mansion in Connecticut and later at Morgan Studios in London, where of all people Donovan added vocals to the title track.

Billion Dollar Babies is a bubbling cauldron crammed with old Mad magazines, purloined Playboys, grisly EC Comics, monster movies and vaudeville jokes. It’s a distinctly American stew – a yank interpretation of glam rock – but Alice Cooper had the songwriting skills and the instrumental chops to create and sustain such an outrageous spectacle. Furnier plays the master of ceremonies on opener “Hello Hooray”, beckoning American youth into a macabre circus tent: “Roll out with your circus freaks and hula hoops,” he commands. “I’ve been ready, ready as this audience that’s coming here to dream.” By album’s end that attention has given him almost God-like powers: “You things are heavenly when you come worship me,” he proclaims on “Sick Things”. But again, there’s no real subtext, which is impressive: rather than ponder the deleterious effects of celebrity, Furnier just likes being onstage.

That makes their sacred-cow-tipping all the more fun. On Billion Dollar Babies Alice Cooper mock everything. They attack the establishment and blow raspberries at the counterculture. “Mary Ann” sounds like they’re melting a Paul McCartney seven-inch, and “Generation Landslide” is a wry parody of Bob Dylan. On the latter Furnier mimics the folk singer’s delivery and wordplay as he describes “militant mothers hiding in the basement/Using pots and pans as their shields and their helmets/Molotov milk bottles heaved from pink highchairs.” Culminating in a cutting harmonica solo, it’s a generational anthem for a generation sick of generational anthems.

The biggest hit from Billion Dollar Babies suggests Alice Cooper’s greatest target for scorn was themselves. “No More Mr Nice Guy” has been so thoroughly absorbed into classic rock radio that you might even forget that it’s by Alice Cooper – or that it’s really savvy and really funny. It’s about rebellion, but not the romanticised counterculture of the 1960s. Furnier saw a grimmer, lonelier angst in this new decade, and he also saw the ravaging effect of adolescent hormones on America’s youth. “No More Mr Nice Guy” is a wicked coming-of-age tale, with Furnier playing the part of a kid suddenly at odds with the adult world. That title phrase may be commonly used as a threat, but any menace Furnier represents is hollow: the song ends with the former Mr Nice Guy getting clocked by Reverend Smith.

Just months after Billion Dollar Babies, Alice Cooper released the strained Muscle Of Love, a too-quick follow-up that is best known for its bulky cardboard packaging. Furnier left the group and took their identity with him, legally changing his name to Alice Cooper before releasing his solo debut. This album, then, while cementing their status as hitmakers, represents the end of an era for Alice Cooper the band and the man, neither of which would reach this peak of weirdness again. Fifty years later, it’s lost none of its morbid magnetism.

EXTRAS: The ’73 live show shows the band in their true elements, but it was already included on the 2001 reissue. The single versions are new, but largely redundant. 5/10