If you’ve been watching the fifth and final season of the polygamists-in-suburbia series Big Love, which began airing last month on HBO and will run through March, you’ve perhaps already absorbed the disappointment: A show that once seemed so attuned to the strangest aspects of modern American life—especially in the way it riffed on the ongoing, real-life saga of Warren Jeffs, the polygamist sect leader, who was extradited from Utah to Texas in November—has by this point mostly devolved into frenzied melodrama. The shark jump first commenced in season four, when home-improvement impresario Bill Henrickson (Bill Paxton) was elected to statewide office and inexplicably decided to introduce all three of his wives to the public. Things only turned more idiotic in the first few episodes of this new season. (Did Chloë Sevigny’s Nicki really just punch a Boy Scout in the mouth?) The only quality now worth praising is the fact that, like The Wire and Deadwood before it, Big Love is at least smart enough to be bowing out before things turn too embarrassing.

But let’s not close the book on this generally terrific series, which premiered in 2006, without also acknowledging what might be its most considerable achievement: It provided the part of a lifetime for Fort Worth’s Bill Paxton, an actor who for decades seemed to float in a hazardous between-zone. Too conventionally good-looking for oddball supporting parts (though he tried) but much too bland to be a star (he tried that too), Paxton has worked for the Oscar-winning likes of James Cameron, Ron Howard, and Kathryn Bigelow and starred in two of the most successful films ever made (1996’s Twister and 1997’s Titanic). For the most part, though, audiences and critics barely seemed to notice him; the phrase “I’ve seen that guy—what’s his name?” might as well have been invented to describe him. Yet as Henrickson, a character that spent most of the show’s first four seasons trying not to be noticed by his suspicious neighbors, Paxton proved light on his (constantly moving) feet and completely comfortable as the straight man surrounded by far flashier figures. His is a curious case, and one all acting students would be wise to study: Only by fully embracing his innate anonymity did he finally become a star.

Paxton left Texas for Hollywood at eighteen, moved to New York a few years after that to study acting, and then began regularly turning up in movies in the early eighties. His Texas-boy-makes-good story sounded so appealing and old-fashioned that you hated to point out the obvious: namely, that most of his big-screen roles didn’t quite take. For a stretch, he relied on his frat-boyish features and athlete’s body to play bravado-fueled troublemakers: the constantly complaining Private Hudson in Aliens (1986), the pitiless vampire Severen in Near Dark (1987). For a stretch after that, he tamped down the swagger and gave us all-American adventure seekers: an astronaut in Apollo 13 (1995), a tornado chaser in Twister, an underwater explorer in Titanic. Not a bum performance in the bunch, but the actor mostly seemed to be cast for his ability to blend into an ensemble and not distract too much from the special effects. The kinds of leading roles that might have put him over the top all went to other actors, and for obvious reasons: Paxton lacked the impish charisma of Dennis Quaid; the imposing brawn of Liam Neeson; the sheer likability of Tom Hanks. (As lousy luck would have it, he was at his best in three movies that never caught on commercially; see “I’ve Seen That Guy.”) Taking a cue from his brother-in-bland-affability Kevin Costner, Paxton tried to direct his way to Hollywood greatness. But Frailty (2001) and The Greatest Game Ever Played (2005) were both misfires: The former is a hambone thriller, in which Paxton miscast himself as a psycho killer; the latter is a dewy underdog sports drama. Seriously, if the rap against you is that you’re too vanilla, the last thing you want to do is make an ode to the privileged-white-male glories of golfing.

Big Love came along just as Paxton was turning fifty, an age when he might easily have begun a slide into Lifetime movie oblivion. Five years later, it’s hard to imagine the show’s premise working with any other performer. Henrickson is the owner of a Lowe’s-like chain, living in the suburbs of Salt Lake City, hopping between the houses of his three wives, played by Jeanne Tripplehorn, Chloë Sevigny, and Ginnifer Goodwin. Another actor might have overplayed the bedroom farce (remember Dudley Moore in Micki & Maude?), but—as he has always done, the only thing he seems to know how to do—Paxton plays it straight. On Big Love, the actor adopts an imploring, Midwestern-accented voice and an air of carefully controlled calm. He takes what might have been an unsavory creep and makes him sweet, even universal: the ultimate overtaxed modern man. And while it’s hard to tell if he’s merely being generous to his fellow actors or if it’s just a happy accident, Paxton no longer even seems to be trying to make too much of an impression. He confidently allows the supporting players—among them Harry Dean Stanton (who plays the menacing Jeffs–inspired sect leader) and the epically weird Grace Zabriskie (who plays Henrickson’s hellcat mother)—to give Big Love its loopy idiosyncrasy.

It’s probably fitting that, in four seasons, Big Love has received only eight Emmy nominations and that Paxton himself has been ignored: You don’t win prizes by not calling attention to yourself. (He has fared better at the Golden Globes, where he has thrice been nominated for Best Actor.) But as the show comes to an end, an inevitable question emerges: Can Paxton ever again find a role so perfectly attuned to both his strengths and limitations? Already there’s an intriguing possibility: The actor recently finished production on Steven Soderbergh’s Haywire, a spy thriller due out in April, in which he plays a part that had originally gone to Dennis Quaid. But even if Big Love does turn out to be the climax of Paxton’s career, well, there are certainly worse fates than getting to shepherd a witty drama through 53 episodes, all the while delivering lines of dialogue unlike any found on television (“Like Lehi and Nephi, God has delivered us to the promised land,” he brightly announced during a camping trip in the fifth-season premiere). It’s still a Texas-boy-makes-good story, but one that feels rooted in reality instead of myth.

I’VE SEEN THAT GUY: Paxton at his most memorable

If you’re looking to create the perfect Bill Paxton triple feature, ignore the blockbusters and turn to a trio of titles that anticipates his work on Big Love and hints at the darkness behind the actor’s clean-cut countenance. In the indie noir One False Move (1992), he generates a half-perverse erotic tension opposite Cynda Williams. In the comic thriller Traveller (1997), he’s perfectly cast as a smooth-talking gypsy con man whose game is upended by a beautiful woman (Julianna Margulies) and a new protégé (Mark Wahlberg). Best of all is Sam Raimi’s somber, spooky A Simple Plan (1998), in which Paxton plays an average Joe whose life goes to rot after he and his brother (Billy Bob Thornton) find and decide to keep a bag containing more than $4 million. All three films proved a little too nervy for audiences and barely made a dent at the box office, but they remind us that Paxton’s understated, unassuming style can have unexpected range.