Of all personality traits, charisma is the hardest to appreciate at second hand. We read Cicero’s letters and can instantly tell that he was vain, insecure and ferociously clever; we read scraps of Samuel Johnson’s conversation in Boswell’s biography and know at once that he was magnificent, lovable and desperately unhappy. But as to what it was like to have Lord Byron turn the full force of his attention onto you – well, we have no conceivable way of knowing. We just have to trust his contemporaries that it felt like ‘the opening of the gate of heaven’.

This causes problems for a biographer of Alcibiades. On the face of it, the man was utterly insufferable. Born in around 450 BC into one of the oldest and richest families of ancient Athens, Alcibiades was the only Old Etonian (as it were) to play a leading role in the late-fifth-century radical democracy. The account of his childhood in Plutarch’s Life of Alcibiades suggests a bad case of antisocial personality disorder: biting during wrestling, mutilating dogs, punching his future father-in-law in the face for a dare. His later political career makes Boris Johnson seem like a man of firm and unbending principle. Exiled from Athens in 415 BC over some particularly odious Bullingdon Club antics, Alcibiades promptly sold his services to Sparta (where he seduced the king’s wife) before double-crossing both sides and wheedling his way into the court of a Persian satrap.

But Alcibiades, like Byron, clearly had that indefinable something. One catches a glimpse of it in the unforgettable last scene of Plato’s Symposium, when he crashes into the room, blind drunk, flirting with everything on legs, shouting about his love for Socrates. Thucydides captures it in his report of Alcibiades’s speech whipping up the Athenian assembly to vote for the disastrous Sicilian expedition of 415 BC – an extraordinary stew of egotistic bragging (about how successful his racehorses are), mendacious demagoguery and brilliantly acute strategic thinking. The unwashed Athenian masses, not usually prone to atavistic toff-grovelling, absolutely adored him: when Alcibiades finally returned to Athens in 407 BC after eight years of exile, sailing coolly into Piraeus on a ship with purple sails, they welcomed him back with paroxysms of joy.

Behind the Peloponnese-sized ego, Alcibiades was a general of spectacular genius – when he could be bothered. In 410 BC, shortly after his controversial reinstatement as admiral of the Athenian navy (on the back of a bogus promise of Persian support), he wiped out the entire Spartan fleet at the Battle of Cyzicus; two years later, through sheer chutzpah, he captured the city of Selymbria near Byzantium with only fifty soldiers, and without striking a blow. When things went wrong – as in 406 BC, after a disastrous campaigning season in the eastern Aegean – he showed an infuriating ability to wriggle out of trouble. His final years (406–404 BC) were spent once again in exile from Athens, holed up in a private castle on the Gallipoli peninsula. The circumstances of his death are still shrouded in mystery. One story tells that he died in the remote mountains of central Turkey at the hands of the brothers of a Phrygian noblewoman whom he had decided to seduce. This is, I fear, all too believable.

A genuine biography of Alcibiades, of course, cannot be written. He left behind no diaries or private letters and no contemporary visual portraits of him survive, though he was, we are plausibly told, stunningly good-looking, with an affected aristocratic lisp. All we have to go on are the mountains of gossip and scurrilous anecdotes left behind by his contemporaries, which – even when affectionately intended – have an unfortunate tendency to make him seem like an obnoxious lout. Somehow or other, the biographer has to try to conjure up the blazing charisma that must have underpinned his disreputable career, which is no easy task at twenty-five centuries’ distance.

David Stuttard’s new life of Alcibiades is a lively, fast-paced and eminently readable attempt to bring the insolent young monster back to life. Over the past twenty-five years, no one has done more than Stuttard to keep classical Greek drama alive on the English stage. The Actors of Dionysus, founded by him in 1993, are still turning out thrilling modern adaptations of Greek tragedies and comedies, and Stuttard’s translations of Medea, The Bacchae and Lysistrata are among the best contemporary performance texts of Greek plays. It is easy enough to see why Alcibiades’s life, with its tragic ironies and dramatic reversals of fortune, might appeal to him. Indeed, much of Stuttard’s book could serve as stage directions to a non-existent Tragicall Historie of Alcibiades, Captain of Athens.

Nemesis rips along in a hurricane of adjectives. Alcibiades is ‘enviably well-connected, strikingly handsome, immensely rich, intensely charismatic, unashamedly louche’. No buckle is left unswashed, and Stuttard never uses one metaphor when three would do. The Parthenon’s ‘forest of columns’ serves as ‘the exoskeleton of the exquisite jewel-box of a temple’, and in the space of two paragraphs, the Spartan admiral Lysander sweeps west through the Aegean ‘like a firestorm’, shoots northeast ‘like a comet’ and descends on the city of Lampsacus ‘like an inferno’.

When he turns to Achaemenid Persian culture, Stuttard really lets himself go. Alcibiades’s tame Persian satrap Tissaphernes enjoyed ‘banquets held in dining rooms hung with close-woven tapestries and strewn with the softest carpets, while, in the torchlight, concubines plucked harps and sang soft, soothing songs in eastern cadences as, languidly, still others danced’. Misunderstanding a phrase in Thucydides, Stuttard concocts an imaginary meeting between Alcibiades and the Persian king Darius II: ‘dark-eyed, hook-nosed, long-bearded, his soft-shod feet resting on his golden footstool, he wore robes shimmering with gold thread and picked out with jewels’. Languid concubines, hooked noses, softness and more softness – it is enough to give Edward Said an aneurysm (and I assure you, we have no accurate idea what shape Darius’s nose was.)

Still, Stuttard does succeed in giving some sense of what it must have been like to know this appalling man. Right now, somewhere above Mount Olympus, in the great symposium in the sky, he, Dionysus and Lord Byron are having a whale of a time.