This late-night TV business is a tough racket. As host, you can be the toast of New York one night, and toast the next. Larry Wilmore, for example, had the audacity to talk about something as vitally important as race every night on his “Nightly Show.” Viewers yawned, now he’s gone. Stephen Colbert had the audacity to follow David Letterman, and talk about Donald Trump every night.

Where, now, does Colbert stand on his anniversary?

This is a business, so first, the business: “Late Show’s” ratings are fine, if not spectacular. “Late Show,” which launched last Sept. 8, averages about 2.8 million viewers, about a million behind leader “Tonight Show Starring Jimmy Fallon,” and a half a million ahead of “Jimmy Kimmel Live.”

While numbers don’t lie, they don’t tell the entire truth either: Colbert had a complicated first year. It was complicated by the fact that he was not Letterman — one of the greats, after all — and not even Stephen Colbert. He became the first host in late show history to assume an entirely new persona, which happened to be his own. The new Stephen turned out to be an inversion of the Old Stephen. He was still smart, funny and inventive, but a real host as opposed to a parody of one.

Meanwhile, some viewers weren’t so certain they liked the new Stephen, who could also be eccentric, obtuse, erudite or just plain odd. A post-Super Bowl shot was squandered. CBS alarm bells rang. A new executive producer was installed in April, and a turnaround of sorts began and continues. While the lingua franca of late night continues to elude “Late Show” (consistent viral content, like “Late Late Show’s” “Carpool Karaoke”), his live telecasts during the conventions were late-night standouts. Another live telecast is planned after the Sept. 26 presidential debate. Success — viral and otherwise — seems reasonably assured.

But along with ratings and viral content, late night is also a what-have-you-done-for-me-lately business, and here’s what Colbert does most nights: Trump. His opening monologue is all Trump, who also consumes the host chat segment. Trump as both fodder and punching bag sometimes even consumes up to half a “Late Show.”

Colbert’s obsession is logical and shrewd. Trump, after all, is good late-night material. Trump has long fed the late-night beast from Kimmel to Fallon. The beast is happy. But Colbert’s treatment is a step further and beyond. The logic is that no one else in late night is doing this — a nightly Trump evisceration that evokes the old glory days of Jon Stewart’s “Daily Show” and “The Colbert Report.”

The disjunction, however, is that “Late Show” has also disenfranchised a vast spread of potential audience — that right-leaning one. “Late Show” is effectively a cable niche show masquerading as a broadcast network one. That led to a flurry of rumors — which effectively began on Howard Stern’s SiriusXM show — that James Corden’s more apolitical, web-friendly 12:30 a.m. enterprise might switch places with “Late Show.”

Those have been roundly denied, but nonetheless are still part of this complicated first year.

Is Colbert a good late-night host? Without question. His show is always interesting, just never relaxing — yet another reversal of late-night broadcast tradition — and best watched over a cup of coffee in the morning. He and rival Jimmy Fallon are almost late-night antonyms. One’s verbal (Colbert has dusted off his classic “The Word,” changed to the legally palatable “Werd”), while the other is musical. One tells stemwinders about Trump. The other mimics Trump. One’s cerebral, the other’s the opposite of cerebral, whatever that is. One eschews pop culture. The other basks in it. One’s mounting a radically different late-night TV show. The other is mounting a fairly traditional one.

Will audiences learn to love and embrace both in the years to come? Or will Colbert’s politically stoked irony burn out after the elections? Big questions, and only viewers — and CBS — will determine the answers.

As noted, this late-night racket is tough, and there are no guarantees. Just ask Larry Wilmore.