This weekend, thinking about David Letterman’s pending retirement—last Thursday, he announced that he will retire in 2015—I came up with a theory: Letterman is for cat people. Dog people, who seek out affability and enthusiasm in their late-night hosts, gravitate toward Jay Leno and Jimmy Fallon, hosts who tumble down the driveway, eager to please. Cat people, by contrast, like Letterman, because he’s prickly, indifferent, and mysterious. Staring down at his blue index cards, chuckling ominously to himself, Letterman doesn’t seem to care about being funny. Instead, he seems frustrated, distracted, and maybe even a little bored.

Nonfans find this off-putting. But Letterman’s boredom—his reticence or, on a good day, his guarded enthusiasm—is the secret to his comedy. In fact, it’s been his main theme for more than thirty years. When Bill Murray appeared on the première episode of “Late Night,” in 1982, Letterman prefaced his first question by saying, “This may not be of interest to anybody, and it’s barely interesting to me.” In 1995, when Drew Barrymore, who’d just celebrated her twentieth birthday, claimed to find birthdays depressing, Letterman was all too ready to ask, “Why? Because it signifies the passing of time? Some kind of pointless existence?” In the eighties, Letterman staged elevator races at 30 Rock, where “Late Night” was filmed. The runners, charged with “racing” in their elevators from the sixth floor to the lobby, gathered at the starting line, dashed out of the studio to jab at the buttons, and then waited, while Bob Costas filled the time with play-by-play (“David, the atmosphere down here is incredibly tense”). Sometimes, the races would go on for so long that Letterman would move right into a guest interview. If the guest was boring, it was hard to miss the parallelism.

Casual viewers are often perplexed by Letterman’s recurring gags—the Top Ten list, “Will it Float?,” “Stupid Pet Tricks,” throwing stuff off a five-story tower—because they’re so often both boring and anti-climactic. But anti-climax is the whole point. Letterman’s Top Ten list was originally devised as a way of mocking the self-important lists in magazines like People; that’s why he takes such joy in throwing away the blue index card on which the list is printed. (The first list was “top ten words that almost rhyme with ‘peas.’ ” No. 5 was “lens.”) Letterman even optimizes the interstitial moments for maximum boredom. One of the mainstays of the show is the interlude, after each monologue, when Letterman, sitting at his desk, aimlessly chit-chats with Paul Shaffer, drifting into this or that conversational eddy, resolutely not getting to the point, hunching and shifting in his chair, flashing a fake, pained Nixonian grin, shuffling his papers, and cackling. The audience, confronted by a sort of play-within-the-play representing late-night television’s fundamental tedium, fidgets and laughs. It’s almost Beckettian: boredom as drama, boredom with an edge.

To some extent, Letterman’s bored affect is simply an accurate response to—and subversive comment on—the nature of late-night TV, where stars beg for attention while viewers fall asleep. That’s not why his show is interesting to watch, though. Letterman’s boredom is fun because it flows from something like a sense of Midwestern decency (Letterman is originally from Indianapolis). Late-night TV is all about suspending the rules of everyday life; the premise is that every night, even a weeknight, can be special. Letterman’s humor centers on the opposite idea, that every day is just a day like any other. It acknowledges that the rules of adulthood can never really be suspended. That’s why, while other hosts turn their studios into glamorous fantasy lands, Letterman treats his like an office. On Thursday night, for example, when he announced his plan to retire, Letterman calculated that he’d spent half of his sixty-six years “behind this desk,” filming five thousand four hundred and nineteen shows. (He admitted only grudgingly that much of that time had been spent interviewing beautiful actresses.) Even his most absurd stunts, like being lowered into a tank of water wearing an Alka-Seltzer suit, have a workaday, let’s-not-kid-ourselves-and-get-carried-away-with-laughter-here quality. It’s not that Letterman isn’t funny. It’s that every joke is delivered with a little wince, as if to say, “We’re still adults, unfortunately!” (Fittingly, much of Letterman’s humor revolves around workplaces; he loves to take the cameras backstage, where the workers are.)

Perhaps because it never leaves the real world behind, Letterman’s show isn’t always inventive enough to be truly side-splittingly funny. The upside, though, is that the show is often surprisingly real. Letterman is the best interviewer on late-night TV, for example, because he seems not to believe in the idea of celebrity (his own or anyone else’s). When he interviews famous people he doesn’t respect, he’s openly judgmental and censorious (he refused, for example, to talk to Paris Hilton about anything other than her time in prison); by the same token, when he interviews people he admires, like Tina Fey, his respect is palpable. (“Our first guest is an exceptionally talented and funny woman,” he said, introducing Fey, with great seriousness, earlier this year. “You can’t overstate this.”) Sometimes he lapses into respectful silence. On the other hand, when he’s angry, annoyed, impatient, or exasperated, he can’t hide it. Today’s comedy is fascinated by awkwardness, and comedians like Zach Galifianakis and Ricky Gervais excel at creating elaborate spectacles of squirm, but the awkwardness is almost always staged, and therefore toothless. Letterman’s interviews with Lindsay Lohan, Madonna, and Bill O’Reilly are actually awkward, because Letterman’s real personality is engaged. His sense of decency prevents him from keeping it light. Faced with Lindsey Lohan, he can’t bring himself to talk about “Scary Movie 5”—only about rehab. Faced with Bill O’Reilly, he can’t feign respect, or put on the airs of a serious political commentator; he can only be honest, telling O’Reilly, “I have no idea what I’m talking about, but I don’t think you do, either.”

Having been a Letterman fan for many years, there are a lot of funny moments I remember: The “top ten things that sound creepy when John Malkovich says them.” Letterman working the McDonald’s drive-through (when a man orders “two number threes,” Letterman perplexes him by suggesting he try one number six instead; later, he reversed the trick, driving through the same drive-through over and over). Elaine Stritch pretending that Letterman was her pool boy. But, in their own way, the unstaged moments are closer to the real spirit of the show: his humble monologue after 9/11; his tale about a bear invading his cabin; welcoming his heart-surgery team onstage; his story about being blackmailed; and, of course, the extraordinary show he did with the musician Warren Zevon, after Zevon had been diagnosed with terminal lung cancer, which has to be one of the best talk-show hours in the history of television. (Zevon was the only guest that night; cancer, he said, had taught him to “enjoy every sandwich”—a very Letterman-esque sentiment.) Being a late-night host is one of the most extroverted jobs in the world, and yet Letterman has brought to it a resolute inwardness—a sense that he is separate from his circumstances. Over time, those glimpses of his inner self have added up to a vivid picture.

I’m sure a great comedian will be found to replace Letterman (I’m rooting for Tina Fey, or Grumpy Cat), but I suspect that it will be hard for that person to do a show like Letterman’s. It’s not just that Letterman himself is irreplaceable; it’s that his audience is, too. Today, the main purpose of late-night television seems to be creating the batch of YouTube clips we watch the next morning. That’s not a bad thing: Jimmy Fallon’s “Tonight Show,” designed for excerpting and sharing on social media, features segments that are immediate, inventive, and hilarious. Fallon’s water fight with Lindsay Lohan, for example, is great fun to watch over lunch. But, in these tightly edited, sharing-ready clips, there’s no time for boredom to set in—and, therefore, no time for reality to show through. Letterman played a long game; I’m not sure today’s hosts can. In the meantime, as a fan, I’ll take comfort in the fact that we have about a year of Letterman’s low-key, real-life late-night before, in 2015, the valedictory celebrations begin.

Photograph: Jeffrey R. Staab/CBS