Stories about ships often train their spyglasses on the frontiers of human nature. Mr. Grann, whose books include “Killers of the Flower Moon,” a true-crime story about racial injustice, and the archaeological adventure “The Lost City of Z,” writes historical narratives focused on such extremes. “The Wager” draws from an unusually rich trove of firsthand documents—including logbooks, correspondence, diaries, muster books, court-martial testimony and Admiralty reports. Many of the accounts are at war with each other—a circumstance Mr. Grann uses to illustrate his larger point about national narratives.

“Just as people tailor their stories to serve their interests—revising, erasing, embroidering—so do nations.” Stories swirled around the Wager disaster—both first-hand accounts of survivors as well as retellings by the growing press, derided by the old literary establishment as the “Grub Street hacks.” Despite the official silences that followed the apparent mutiny of its crew and a savage breakdown of naval authority, these stories became a maritime epic that would resonate for centuries.

Mr. Grann starts his tale by leading us on a tour of what he calls “the wooden world” of the fearsome navy of warships that helped Britain build and rule its expanding empire. This was a hierarchical realm of rigid regulations and harsh punishment for infractions. Mr. Grann describes these armed ships as “buoyant wooden castles . . . in a lethal, floating chess game, these pieces deployed around the globe.”

While some of the ships in the British fleet elicited awe—the Centurion, with its 16-foot wooden carving of a lion, was painted bright red—the Wager did not. It was a 123-foot “eyesore” of a merchant ship refurbished for war, hardly the kind of fighting vessel that inspired dread among Britain’s enemies. Both ships set off as part of a squadron, led by Commodore George Anson, whose goal was “outright thievery.” The Admiralty deployed the squadron during a disastrous and relatively short-lived conflict between Britain and Spain in the 1740s, which was later comically dubbed the “War of Jenkins’ Ear”—triggered by a British captain’s claim that a Spanish officer had sliced off his left ear.

British authorities had devised a plan to launch an attack on the Caribbean port of Cartagena, a hub of Spain’s colonial wealth. Anson’s squadron, made up of the Wager, four other warships and a scouting sloop, was charged with a secret mission: to snatch a Spanish galleon loaded with silver. The officers and crew were lured by the prospect of sharing in the plunder. It was a blatant (if conventional) scheme of state-sponsored piracy.

The squadron’s plan unraveled in the most horrific way possible, a tale of woe replete with gory twists and turns that Dickens himself would have enjoyed, including delicious cliffhangers: “No longer were they prowling the sea in secret. They were themselves being hunted.” Part One ends with a captain’s deathbed prophecy that the expedition “would end in poverty, vermin, famine, death and destruction.”

The sea itself is an ever-present antagonist. Mr. Grann renders vividly the furies of the waters around Cape Horn, “where winds routinely blow at gale force, waves can climb to nearly a hundred feet, and icebergs lurk in the hollows.” Plus a few other surprises from the natural world, including lightning, tempests, even an earthquake. Human nature is just as violent, with Lord-of-the-Flies behavior among the castaways and at least two murders. Mr. Grann has a finely tuned ear for details that reveal character—the Wager’s rigid and increasingly isolated Capt. David Cheap wields a silver-headed cane “which clacked like a pirate’s wooden leg.”

Mr. Grann delights in the arcane expression of the nautical lexicon. When ordered to pull sheets, a sailor had “better seize the ropes instead of his bedding. He must not speak of the privy but, rather, the head” and the boys who delivered explosives from below deck to the guns were known as “powder monkeys.” Who knew that so many common expressions come from shipboard life? For example, “under the weather” comes from the practice of putting ailing seamen belowdecks.

The story of the Wager’s disastrous fate leads into an equally riveting story of what happened to the castaways when they straggled back to England in ragged groups, armed with often conflicting stories of who was to blame for the series of epic catastrophes and reversals of fortune. Mr. Grann unspools their narratives against the backdrop of the Admiralty’s high-stakes court-martial, in which surviving crewmembers and officers faced possible execution. “No matter which story prevailed, the trial would surely expose how the officers and seamen—as part of the vanguard of the British empire—had descended into anarchy and savagery.”

Mr. Grann relies heavily on the perspective of the ship’s gunner, John Bulkeley, who kept a contemporaneous, if somewhat skewed, record of events. Many stories, such as those of the free black seaman John Duck and the indigenous people the castaways encountered, were not recorded in surviving diaries or letters. “Empires preserve their power with the stories that they tell, but just as critical are the stories they don’t—the dark silences they impose, the pages they tear out,” writes Mr. Grann.

The various tellings of the Wager disaster reverberated far beyond the Admiralty courtroom. Commodore Anson’s account, for instance, became a bestseller that offered Rousseau examples of men in a state of nature, acting only in the interest of self-preservation. Capt. James Cook carried a copy of Anson’s book on his ship Endeavour during its first expedition around the world, as did Charles Darwin aboard the Beagle.

Two decades after the court-martial, John Byron published his own account. By then, he’d gained the nickname “Foul-Weather Jack” for his bad luck in encountering nasty meteorological conditions over his long career as a ship’s officer. While his book never gained a wide readership, Mr. Grann notes that “it cast a spell on Byron’s grandson, whom he never met”—the poet wrote that his hero Don Juan’s “hardships were comparative / To those related in my grand-dad’s ‘Narrative.’ ” “The Wager” is likely to cast a powerful spell on modern readers as well.

Ms. Siler is a former WSJ staff reporter who recently returned from an expedition aboard a wooden barquentine sailing ship above the Arctic Circle.