Woody Harrelson has played dimwits and detectives, cowboys and psychopaths, rogues you’d follow into hell, and guys you’d reverse through traffic to avoid. In 2019 alone, he’ll have played a crusty Texas Ranger, World War II hero Chester Nimitz, and even Archie Bunker. Next year, he’s set to play both a Marvel supervillain and acid guru Timothy Leary. And like many other respected actors of his caliber (and Justin Timberlake), he’s even gotten to host Saturday Night Live a few times.

Harrelson will host for the fourth time during Saturday’s 45th season premiere, rounding out a tenure that stretches all the way back to 1989—a good twelve years before musical guest Billie Eilish was born, in case you feel like dwelling on it. And while we’d dearly love to throw together a fun little listicle for you of the classic SNL sketches Harrelson has been in, turns out SNL’s “Woody Harrelson Collection” is surprisingly kind of light. How is this possible? Where is Woody’s  “Bring It on Down to Veganville”? His “The Continental?” His “Schweddy Balls”? Why has SNL had so much trouble spinning gold out of one of our most effortlessly funny actors?

You can’t blame it on Harrelson, who’s seemingly as game for surreal riffs and bad wigs as any celebrity who’s ever graced studio 8H. You can’t really blame the ever-changing cast, either. Harrelson’s run spans generations of SNL all-timers, partnering him with everyone from Dana Carvey to Chris Farley to Kate McKinnon. But he’s had a 22-year gap between appearances, absent from 1992 all the way to 2014—a pause that happens to coincide with Harrelson’s complete reinvention as an actor. It wasn’t until 1993’s Indecent Proposal and 1994’s Natural Born Killers that he even hinted he could do more than play the adorable moron. There’s no shame in that, of course: Harrelson does blissful ignorance like few others, and he has the Emmy to prove it. But unfortunately, those first two SNL episodes were taped back when no one saw Harrelson as anything but the lovable lunkhead from Cheers.

In fact, Harrelson’s first-ever SNL sketch was literally titled “Who’s Dumber?”—a game show parody that introduced Harrelson and Victoria Jackson, playing themselves, as “surely the two dumbest people in America.” It doesn’t get much subtler from there. That same episode found Harrelson mangling the word “thesaurus” in his monologue, playing a soft-spoken simpleton on the talk-show spoof “Attitudes,” then another idiot who awkwardly chats up Kevin Nealon in night school. When Harrelson returned in ’92, he was a budding movie star thanks to his role in White Men Can’t Jump. But to SNL, he was still basically Woody Boyd, which had him play a dimwit deputy to Kevin Nealon’s “Frank Gannon, Politically Incorrect Private Investigator,” plus yet another friendly moron who can’t stop putting a pregnant Jackson in harm’s way. Of course, White Men Can’t Jump had also given Harrelson a little bit of R-rated swagger, so suddenly he was a hot idiot. Harrelson’s big sketch of the night, “Take Your Shirt Off,” was basically an excuse for him to do just that (to the studio audience’s delight) while an ensemble of all-timer SNL dudes whipped out various ridiculous prosthetics.

The closest the show came to tapping into Harrelson’s hidden potential back then were his two appearances on “Sprockets,” a sketch where, in ’89, Mike Myers’s Dieter welcomed him as an East German filmmaker who’s been corrupted by the sudden flood of Mountain Dew across the newly crumbled Berlin Wall; then again in ’92 as a performance artist who, disgusted by the launch of Euro Disney, creates his own “Euro Trash” theme park. The wigs did a lot of the comedic lifting, and Harrelson doesn’t exactly nail the German accent (it’s hard to take the Midland out of the man, after all). But still, they showed glimmers of Harrelson’s untapped weirdness that the movies would later put to good use. Natural Born Killers and Wag the Dog showed us just how easily Harrelson’s laid-back stoner-isms could shift into nihilistic menace, while 2012 cranked up his loopiness to pure, acid-fried madness. It’s a shame SNL has never asked him to play full-on crazy; he’d kill it.

Meanwhile, the furthest SNL ever came to giving Harrelson a character to call his own was as part of the Singing Cowboys, a briefly recurring sketch where Phil Hartman and Dana Carvey, astride blatantly fake horses, crooned about the gross realities of cowboy life. Harrelson starred in their very first iteration, waxing romantic on the guilty pleasures of bestiality. By 2014, of course, everyone knew what Harrelson could do—and everyone knew Woody Harrelson. We all certainly knew he liked weed, for one, which the show riffed on by casting him as a stoner in a Pete Davidson video about relaxed marijuana laws, then had him sing about his pot-hazy memories to the tune of Taylor Swift’s “Blank Space.”

We also knew he was the other guy on True Detective, a role Harrelson reprised for a “Weekend Update” segment that found him mostly just sitting there, trying not to laugh, while Taran Killam ripped into every elongated vowel of his Matthew McConaughey impression. But more importantly, we knew Harrelson as an Oscar-nominated, capital-A actor who carried the weight of a long, seasoned career behind him. At long last, Harrelson had the gravitas to play the dad to a “horny as hell” bachelorette on an MTV dating show. By then he was trusted to go downright off-putting, by playing a barfly lamenting the glory days of crack in pre-gentrified New York, and as another completely different barfly sucking face with Kate McKinnon. His 2014 appearance also featured “The Dudleys,” a parody ad where Harrelson dug into all the nuances of playing a “gay 5” for a CBS sitcom that’s constantly being rewritten to keep up with social media outrage—a joke that might have proved nuclear for someone even a fraction less likable.

Still, it’s telling that Harrelson’s most well-known SNL clip, even after all this time, is probably that aforementioned Taylor Swift song. (Though to be fair, the fact that he was joined by his Hunger Games castmates definitely puts a thumb on the scale.) If there’s one thing you can count on for Saturday’s premiere—besides Harrelson probably busting out a guitar, as he typically has—it’s that there will surely be plenty more jokes where Harrelson’s the pothead goofball, the same good-and-stoned-ol’ boy he’s been playing for NBC for thirty years now. But here’s hoping Harrelson’s fourth hosting slot continues the trajectory of his last time around, and that the show’s finally figured out how to tap into Woody the actor, rather than just Woody the persona.