A world away from the bumbling comic piracy of Captain Jack Sparrow, Johnny Depp plays a far deadlier real-life criminal in Black Mass, a biopic of notorious Irish-American mobster James ‘Whitey’ Bulger, the pre-eminent crime lord of 1970s and 80s Boston.

Depp’s ruthless Bulger does, however, have something in common with his Captain Jack – they both see the actor disappear beneath layers of make-up.

Here Depp is unrecognisable, totally transformed by facial prosthetics, contact lenses, and state-of-the-art bald cap and wig. Yet his performance as Bulger goes far deeper than swept-back, thinning hair and leathery, reptilian skin and delivers a soul-chilling study of sociopathic evil.

Equally chilling, however, is the fact that Bulger’s underworld dominance was enabled by a secret deal struck with the FBI. Initiated by ambitious FBI agent John Connolly (Joel Edgerton), a childhood friend of Bulger’s, this ‘unholy alliance’ gave him effective immunity in his criminal dealings in return for providing information on his Italian mafia crime rivals, the Angiulo Brothers.

In a further stranger-than-fiction twist to this saga, while Bulger was bludgeoning his way to underworld power, his politician brother Billy – played in another unusual stroke of casting by Benedict Cumberbatch – was rising to become Massachusetts state senator.

Director Scott Cooper (Crazy Heart, Out of the Furnace) doesn’t have the cinematic swagger of Martin Scorsese and no one will claim Black Mass as a crime classic in the Goodfellas league, but it is queasily riveting.

Screenwriters Mark Mallouk and Jez Butterworth, adapting the 2001 book by Boston Globe reporters Dick Lehr and Gerard O’Neill, steer us through the story’s tangled narrative, and the supporting actors deliver vivid performances, with striking turns from Jesse Plemons and Rory Cochrane as two of Bulger’s mob underlings and from Dakota Johnson, Julianne Nicholson and Juno Temple as three women unfortunately entangled in one way or another in his career.

In end, though, Depp’s dead-eyed killer simply blows us away.

Certificate 15. Runtime 123 mins. Director Scott Cooper