“2nd Chance” may be the best Errol Morris movie that Errol Morris never made. It’s the first documentary feature directed by Ramin Bahrani, who has often brought a real-world edge to his dramas (“The White Tiger,” “Chop Shop”), and the figure at the film’s center could be a true-life character out of Morris land — one of those rational-on-the-surface, only-in-America compartmentalized crackpot geeks whose hidden dark depths just about scream, “Look out, I‘m a walking nonfiction metaphor!”

In “2nd Chance,” that character is one Richard Davis, who invented the bulletproof vest as we know it. He did it in the 1970s, and the way he did it was very ’70s: by putting on a prototype version of his invention, grabbing a gun with both hands, and shooting himself in the chest. He did that (and filmed it) 192 times — as a scientific demonstration, as a publicity stunt, and as a way to hawk his vests to U.S. law enforcement and the military. Each time he did it, the bullets bounced right off him, and that became the basis of the Second Chance Body Armor Company, which he set up in a small town in northern Michigan, employing most of the people in the area, until he effectively became the king of the town.

In “2nd Chance,” Davis, now in his mid-70s, with a youthful nerdish jocularity, is interviewed on a small worn leather couch, seated in front of wood paneling in what looks like a rather depressing rec room, his hands clasped as he speaks in his friendly yet detached overemphatic style. It’s very much a bug-pinned-by-the-camera Errol Morris setup; the movie lets you feel like you can study Davis.

And that’s just what you want to do, since there’s an enigma at the heart of this man, who in the home-movie shorts he directed and starred in 50 years ago comes off as an eager, balding, out-of-shape doofus who clearly had a thing about guns. The shorts, with titles like “Second Chance vs. U.A.P.” (which stands for “Unorganized Asshole Punks”), feature re-enactments of police shootings shot in a style that suggests “Cops” crossed with “Super Troopers,” though with the deliberate echo of a Dirty Harry righteous-cops-good/criminal-scum-bad executioner’s view of the world.

Before Davis came along, there were bulletproof vests, but they were bulky and heavy — flak jackets you couldn’t conceal. Davis saw the need to create a thin, light vest that could be worn invisibly and that was comfortable enough to be used on a daily basis. For a while, he owned the landscape (though he inevitably had competitors). But apart from how commercially successful he was, he had created a revolutionary product, one that could radically cut down on the odds of a police officer, during a violent confrontation, getting killed.

How do you repel a bullet without a metal plate? It’s a physics problem, and also a philosophical problem. Davis, who’d had one year at the University of Michigan College of Engineering, got a roll of nylon and designed a vest that did the trick. We see his intricate scientific sketches, though we never quite learn the logistics of how it worked. Bahrani is more interested in how the invention flowed out of Davis’s character — this man who was the definition of unthreatening and would therefore be one to obsess, more than others, over the question of armor, like a turtle inventing a new kind of shell.

Davis’s odyssey comes, as these things tend to, with an origin story. In 1969, when he owned a pair of pizza shops, one on Seven Mile Road in Detroit, he was held up in a driveway by two men during a delivery; he’d brought a .22 with him, and used it, but got shot in the leg and the right temple. This launched him, Davis says, on a mission of protection. He wanted to save lives. And he did. But later in the film, Bahrani investigates that incident; he can find no police record of it (and no sign of a bullet scar in Davis’s wedding photos). He also investigates the fact that one of Davis’s pizza shops was burned to the ground in an act of arson, which Davis says he couldn’t have had anything to do with because he had no insurance. Bahrini discovers that just one week before the fire, Davis, in fact, took out an insurance policy.

But the ultimate deception in Richard Davis’ life was one of the spirit — a mingling of compassion and cruelty. He kept a record, in the form of a mimeographed newsletter, of every police officer his vests had saved. Doing this was part of his business (he was selling safety), but it was also a way of playing God. Davis became an unabashed firearms fanatic, with cronies who made themselves into a kind of frat-house militia, blowing shit up and unleashing deafening torrents of ammo in the Michigan back country — all “harmless,” yet expressing a kind of over-the-top aggression. That Davis was such a showman is part of what made him a rambunctious businessman. But it was also unsettling. When 9/11 happened, it proved to be a bonanza for Second Chance. The U.S. armed forces stocked up on his vests — and Davis had a new-and-improved fiber technology: zylon, which was lighter, thinner, stronger. It was advertised as Kevlar on steroids.

But there was a problem. Over time, zylon degraded. Davis, who owned 51 percent of Second Chance, had the power to withdraw the vests from the market at any time, but he hesitated. And that was a weaselly decision that became a disaster. The film likens the situation to that of Ford continuing to sell the Pinto after it learned that the fuel tank located in the rear of the vehicle was, in fact, dangerously combustible. “2nd Chance” takes us into the life of a police officer who died because the bullets penetrated his vest, something that Davis lies about on camera. He had saved (by his count) a thousand lives. But now, suddenly, God had blood on his hands.

“2nd Chance” is a piece of perverse Americana, and what’s weirdly gripping about it is that it turns into a moral tale: the story of a man we think of as a goof, then a sharp inventor, then a deceiver and narcissist, then a passive-aggressive megalomaniac, culminating in the situation that defines his moral fiber — the day he learned the fibers in the vest he was promoting were, in fact, falling apart. It’s a very USA parable of someone who yearned to be a saint, in part because he was a sinner, and who flew too high, but who always looked fascinating doing it on camera.