More than 400 scripted, primetime shows aired in 2015, so how can anyone winnow that array down to the 10 best programs?

Trick question: It’s not possible. Not for me, anyway. After years of writing up Top 10 rosters (and sometimes fudging the numbers with ties), I cry uncle. For my sanity, my year-end best-of-TV list has to contain 20 entries. (Some of these entries are discussed in a new Talking TV podcast with Hitfix critic Alan Sepinwall.)

Even with that expanded roster, it was once again very difficult to come up with the list you see here. Hence the creation of more lists: Here’s my list of the year’s best new shows, and I’ve also published a rundown of the best returning shows of 2015. All told, around 50 shows and dozens of TV providers will be represented in these lists (which, I should add, don’t even contain all the great, good, pretty good, decent and not-great shows I watched this year; these were just the list-worthy contenders).

Faced with a smorgasbord of options, it’s only appropriate that a food-related word kept occurring to me as I wrote up this list: Umami. Beyond sweet, salty, sour and bitter, food aficionados have come to appreciate a fifth basic food descriptor. It’s hard to pin down what “umami” is, but most definitions describe it as a savory richness — a complex flavor that isn’t easy to describe but enhances a dish and makes it truly come alive.

There’s so much variety in the TV landscape that there’s no way to define what makes these shows special. Some shows are just bursting with umami.  

“The Americans,” FX: Every year, it seems impossible for this drama about Soviet spies to get better. But every year, it becomes more evocative, exciting and emotionally rich, because it continues to find new and even more effective ways to tie espionage plots to stories of relationships in danger. “The Americans” has figured out how to deftly combine moral dilemmas with bittersweet tales of loyalty and disappointment, and this fiendishly addictive show keeps making it look easy. (I wrote about season three here and here.

“Black-ish,” ABC: This reliably good sitcom got better this fall, as its cast and writers locked into even more entertaining grooves. The whole cast is outstanding, but Tracee Ellis Ross is giving a performance that, in its game physicality, multi-layered tenacity and cheerful intelligence, makes her seem like a modern-day Judy Holliday. Sometimes Rainbow Johnson has five different reactions in a scene, but they all make sense and they’re never just for show (and at least three of them are hilarious). “Black-ish” weaves cogent, necessary and truthful statements about race and class into many of its scenes and premises, all of which gives it extra heft and energy, but it’s also a warm-hearted family comedy that has a lot to say about human nature and middle-class American life. It’s terrific.  

“BoJack Horseman,” Netflix: One of TV’s most interesting sub-genres revolves around depression, being annoyed by people who do improv (or who are connected to the media industries in any way), and the fact that being in a relationship in Los Angeles or New York is not for the faint of heart (see also “Togetherness,” “You’re the Worst,” “Casual,” “Girls” and “Master of None”). “BoJack” hits all those notes and yet it’s so much more than the sum of its cumulatively affecting parts. This sharply observed animated show unites the surreal, the goofy and the profound, and makes the adventures of a depressed horse and his odd collection of friends and frienemies absolutely mesmerizing. (Also, what most people don’t realize is that it’s actually a show about Diane Nguyen and Princess Carolyn. Fact.)

“Catastrophe,” Amazon: Instantly captivating and almost indecently charming, this sweet and saucy show is part of a wave of rom-coms that eschew fake sentiment and rote formula and end up with knockabout, human-scale stories that are winningly rich and real. Someone put season two in front of my eyeballs right now, please and thank you. 

“Fargo,” FX: If this show had only given us Nick Offerman as a drunk Libertarian lawyer, that would have been enough. If it had only given us Bokeem Woodbine as a philosophical gangster and Jesse Plemons as a butcher who seems to be made out of a slab of meat, that would have been enough. But this year’s edition of the tart drama gave us all those wonderful things and much more, including a tragicomic performance from Kirsten Dunst that is every bit as precise and impressive as Billy Bob Thornton’s work last year. “Fargo” is likely to win a bunch of awards again in the next awards cycle, and that’s just swell, you betcha, because even if it is a little chilly or clinical at times, its cast is tremendous and it’s a heck of a lot of fun.

“Fresh Off the Boat,” ABC: It’s unfair to single out one person from this very strong ensemble, but I’m going to do just that: What did we do with our lives before Constance Wu was on our screens every week? Her comic timing and detailed characterization are joys to witness, but there are so many more “Boat” elements to savor. Randall Park’s deft performance as an enthusiastic and loving dad is tremendously endearing as well, the show’s kids are sharply observed characters in their own right, and the comedy’s writing, which weaves pointed social and cultural commentary into a well-crafted sitcom framework, is reliably excellent. New one-hour dramas at the broadcast networks have been frequently disappointing in the last few years, but in the realm of comedy, the broadcast networks haven’t lost their mojo, and “Boat” is proof of that. 

“Hannibal,” NBC: Every year, this drama got better and better at creating nightmarish dreamscapes, to the point that this year, its mood of surreal fantasia seemed familiar and even comforting at times — and that in itself was a little unsettling. Few shows in TV history have been better at creating enthralling atmospheres; “Hannibal” doesn’t necessarily lay out stories as much as it weaves spells. From the lush interiors to the perfect clothes to the mouth-watering (and terrifyingly sourced) food, every element of this show is part of a seduction, which is exactly the point — and also the problem. Hannibal’s core idea — that one should live in devoted service to specific aesthetic and philosophical ideals — sounds good, but in practice it’s a brutal, sociopathic nightmare. When the pursuit of aesthetic ideals is not accompanied by compassion and empathy, well, you get Hannibal Lector. Though it faded a little in the home stretch, “Hannibal” once again found enthralling ways to explore a Jungian terrain of horror, beauty and twisted love. It was beautiful while it lasted.

“The 100,” CW: I’ll crib from a (non-spoilery) piece I wrote after the show aired its second-season finale: “I’ve rarely seen a program demonstrate the kind of consistency and thematic dedication that ‘The 100’ has shown in its first two seasons.This is a show about moral choices and the consequences of those choices, and it’s been laudably committed to those ideas from Day 1. …Who do you become if you sacrifice others in order to survive? When do the needs of the many outweigh the needs of the few? When is taking a life — or many lives — justified? …What gives ‘The 100’ a particularly rich flavor on the character front is that very few people on the screen are in a position to judge anyone else. No one occupies the moral high ground. There is blood on the hands of just about every person on the screen.” It’s not the only piece I’ve written about the show, but I’ll stop now and remind you that the first two seasons of the drama, which returns Jan. 21, are on Netflix.

“Inside Amy Schumer,” Comedy Central: In a year in which an varied array of half-hour shows did exceptional work, Schumer’s wickedly funny show stood out, not just for classic sketches like, “12 Angry Men Inside Amy Schumer” and “Last F—kable Day” but for a host of other moments that delivered Schumer’s smart, raunchy brand of feminism in memorable and hilarious ways. 

“Jane the Virgin,” CW: This show is basically perfect, and if you don’t agree, I will fight you (not with fists — with emojis, of course). My thoughts about this show’s technical, aesthetic and emotional mastery — all of which place it in the highest tier of television accomplishment — are here and here.

“The Leftovers,” HBO: By moving the show lock, stock and knitted brow to Jarden, Texas, and injecting a new array of characters and conflicts into the show’s rich brew of supernatural, mundane and profound events, “The Leftovers” raised its game significantly in season two and turned itself into essential viewing. In “The Leftovers,” showrunner Damon Lindelof unites the heartfelt and finely honed commercial storytelling moves he used on “Lost” with a wilder and weirder set of concerns, and the result is a show that’s entertaining, sincere and movingly abstract. Let’s hope the show, like Kevin Garvey, keeps on returning, despite the odds. My thoughts on the season are here and my recent interview with Lindelof is here, here and here.

“Mad Men,” AMC: “What you call love was invented by guys like me to sell nylons,” Don Draper declared in the “Mad Men” pilot, and the show spent seven seasons revealing what a liar he was. Don — or Dick — absolutely believed in love, to a degree that was self-destructive and delusional at times. Time and again, he lunged at love and sex and money to fix what was broken inside him, and despite all those bad choices, he finally ended up realizing that people did love him, and that he might be capable of love as well. Don Draper, you magnificent bastard, I miss you and all your ad-industry friends, and I always will. (My thoughts on the show’s finale are here and here.)

“Marvel’s Jessica Jones,” Netflix: This bracing drama dwelled on the fallout from abuse and sexual assault, and in doing so, it broke with many of TV’s most deplorable traditions when it comes to those subjects. “Jessica Jones” didn’t show us the rapes its title character endured: It simply accepted that they happened, it depicted the aftermath from her point of view, and it showed how infuriatingly hard it was for Jessica to get anyone else to believe that her attacker was a dangerous sociopath who needed to be stopped. It’s not that violence against women should never be shown on TV, but like many viewers (male and female), creator Melissa Rosenberg was tired of assaults being casually used as prurient sideshows meant to signal “grittiness,” and she went out of her way to avoid cliches and superficial scenarios in this surprisingly complex Marvel drama. The quality of the show’s pacing and characterization falls off in the final few episodes of the season, but “Jessica Jones” works like gangbusters before that, and it’s to be lauded for its smart use of atmosphere, whipsmart dialogue and film noir conventions. Star Krysten Ritter, it should be said again, did tremendous work.  

“Master of None,” Netflix”: Very few series emerge this fully formed and assured, and it was simply a blast to watch “Master of None” plunge straight into challenging territory with vigor, wit and irreverent curiosity. It ended up being one of the funniest and most vital shows of the year, in part because it was willing to explore ideas and points of views that TV typically relegates to the sidelines.

“Mr. Robot,” USA: An exceptionally ambitious meditation on technology, voyeurship and the mediated life we all live now. If Rami Malek had not imbued the lead character with depth, intelligence and finely calibrated suffering, in addition to sly wit and steely resolve, the show simply wouldn’t have worked. Also doing terrific things: Christian Slater, who was restrained when he needed to be but who also unleashed the glorious Full Slater when necessary; the show’s directors, who played with point of view and perspective in ways that enhanced every frame; and supporting players like Michael Cristofer, B.D. Wong, Stephanie Corneliussen and Martin Wallström. Now that “Hannibal” is over, we’ll have to rely on Corneliussen and Wallström to take up the mantle of “TV’s most terrifying couple.” (Further thoughts on the show’s first season are here.)

Rectify,” Sundance: It’s not just one of the best dramas of 2015, it’s one of the best TV dramas of all time. Each season, the show’s characters are ever more richly realized and each encounter is more movingly chronicled. Standout performances from Clayne Crawford, Adelaide Clemens, J. Smith-Cameron and J.D. Evermore enhanced the poignant and incisive third season, and as always, Abigail Spencer and Aden Young were incredibly committed and impressive as Amantha and Daniel Holden. Seriously, “Rectify” offered up a perfectly realized season of television this year, one with a boundless heart and yet a clear-eyed view of limits and the necessity of compassion. If you love “Friday Night Lights,” “The Leftovers” or “Enlightened” and haven’t seen this, well, you know what to watch next. If you do watch the show, check out this interview with creator Ray McKinnon.

Transparent,” Amazon: One of “Transparent’s” greatest qualities is its deceptiveness; at first glance, it seems like nothing more than a sharply observed indie comedy about the overly privileged members of Los Angeles family, but then it quietly gathers its strength and emotionally sucker-punches you in the best possible way. It can be enjoyed on so many levels: As a wry family comedy; as a meditation on inheritances and the damage done by secrets, lies and willful obliviousness; and an artful exploration of what it’s like to feel both deeply alone and joyfully connected. The new season arrives Dec. 11; here’s my review.  

“Unreal,” Lifetime: Many TV shows find it difficult to supply viewers with one complicated, morally questionable female character, but “Unreal” found a way to give us two, and Shiri Appleby and Constance Zimmer dug into their roles with inspiring gusto. Also impressive: The show explored the tropes and cliches of dating reality shows without serving up condescending judgments of those who participate in or watch those programs. The word “game-changer” gets tossed around a lot, but “Unreal” did truly change the game for Lifetime, which wasn’t in the conversation about ambitious television until this show arrived.

“Wolf Hall,” PBS/Masterpiece: From my review of the canny adaptation of Hilary Mantel’s novels: “This Masterpiece drama has intelligent observations to make about about how people in power — kings and queens, but they might as well be studio executives, CEOs or presidents — want their dirty work done without having to be reminded of just how dirty and deceitful it can be. Powerful people… believe they are better than they are and try to ignore the fact that people are being kneecapped (or worse) just offstage. Doing something for the greater good is easier if you make other people bear the moral cost of repugnant but debatably necessary acts. [Mark Rylance’s] Cromwell silently bears that weight — in his posture, in his delivery, in his eyes, Rylance makes you see what carrying that burden does to the man.” Not only that, the hats on this show were incredible. The cast, the writing and the direction was very good, but “Wolf Hall’s” hat game was next level. 

“You’re the Worst,” FX: This nimble show was one of my favorite shows of 2014, so imagine my surprise when it easily surpassed the accomplishments of its first season. Thanks to a first-rate cast and smart writing, “You’re the Worst” is not only consistently funny and smart but also deeply emotionally engaging and even tear-inducing at times. Despite having interviewed the show’s creator and cast, I still don’t know how they did that.

The latest edition of the Talking TV podcast features TV critic Alan Sepinwall and myself discussing the new edition of his book, “The Revolution Was Televised,” and talking about some of the entries in our 2015 Top TV lists. That podcast is here and on iTunes. Several recent Talking TV podcasts with myself and Ryan McGee delve into “Transparent,” “Jessica Jones” and other shows on this list.