The Game Winner for Disney+? Slapping Down the Sports Clichés.

A cantankerous coach. A team of misshapen outcasts and weirdos, built around maybe one competent player. League rivals stacked with as many bullies as it has championship trophies. An improbable Big Game ending.

The story has written itself since “The Bad News Bears” set the standard for underdog little leaguers back in 1976, and it would seem to have written itself again in two new kid-sports series, “The Mighty Ducks: Game Changers” and “Big Shot,” which have had overlapping runs on the streaming service Disney+.

That cantankerous coach? He lightens up a little. Those perennial losers? They get better. The Big Game? Bet against the Vegas oddsmakers on this one.

Yet “The Mighty Ducks: Game Changers,” which drops its final episode Friday, and “Big Shot,” which will see new episodes through mid-June, are better and more surprising family shows than one might expect, in part because they’re familiar enough with the playbook to tear a few pages out — or at least scribble around at the margins. The winning formula still holds, but they tweak it in big and small ways that make a cumulative difference, starting with key casting choices at the top and continuing in minor subplots and character details that wouldn’t fit into any movie. These are TV shows. They have the benefit of time.

They’re also not about sports. Not entirely. As Alex Morrow, the single mother of a 12-year-old youth hockey player in “Game Changers,” Lauren Graham plays a sports agnostic who doesn’t understand why winning even matters at this stage of her son’s life. She just wants him to have fun with his peers. Maybe get a little exercise. Give her some time to herself.

“I don’t understand being so invested in your children winning,” Graham said over a video call from her home in Los Angeles last week. “That was not part of my upbringing. I don’t even remember my dad staying for one soccer game. I think that was, like, an hour when you got to go do your own thing.”

Graham calls it “light neglect,” a parenting philosophy in which caregivers are there for pickups and drop-offs, but otherwise leave their kids alone. (She fondly recalls her father’s saying he did “nothing” whenever asked how he raised a successful actress.) But Alex doesn’t have a choice. In the first episode of “Game Changers,” her son, Evan (Brady Noon), is cut from a joyless, hypercompetitive team, so mother and son form their own team of castaways, the Don’t Bothers. The twist of the series is that the name of the cutthroat team is the Mighty Ducks — once underdogs, now the Death Star.

The current model for this little switcheroo is “Cobra Kai,” the Netflix series (it debuted on YouTube Red) that flipped the script on the 1984 martial arts favorite “The Karate Kid” by turning the dojo of the title — “Strike first. Strike hard. No mercy.” — into a refuge for the picked-on. And Gordon Bombay (Emilio Estevez), the once-slick lawyer who led the Ducks to glory across three Disney films in the ’90s, is now a long-in-the-tooth sourpuss managing a dilapidated hockey rink. As it was with the beer-swilling Johnny Lawrence in “Cobra Kai,” adulthood has been for Gordon a humbling experience.

According to one of the series’s creators, Steven Brill, who conceived the Mighty Ducks and wrote all three films, it was a natural place for the series to go. After all, the Mighty Ducks (now just the Ducks) have been an N.H.L. franchise in Anaheim, Calif., since 1993. They aren’t underdogs anymore.

“When I saw ‘Cobra Kai,’ it immediately validated the idea that you could take people from the past and you could turn the heroes into the villains,” said Brill, who said the two shows were developed concurrently. “After the last movie, I only saw the Ducks as turning into this conglomerate, this franchise, this out of control competitive league. It got away from where it was at.”

Humility is also the major theme of the basketball-themed series “Big Shot,” on top of the excruciatingly difficult lesson that sports may not, in fact, be everything. As the player empowerment era continues to shift the balance of power on the professional level, college sports are the one place where dictatorial coaches still hold sway over their programs.

The chair-throwing incident that knocks Marvyn Korn (John Stamos) from his Division I perch in “Big Shot” references the former Indiana University coach Bobby Knight’s infamous temper tantrum in a game against Purdue in 1985. But Stamos more closely resembles Rick Pitino or John Calipari, slick floor generals who turn out pros and win N.C.A.A. championships. For someone like Marvin to coach a high-school girls team at a California private school is a special kind of a purgatory.

Based on an idea by the actor Brad Garrett and developed by the TV veterans David E. Kelley and Dean Lorey, “Big Shot” is a fish-out-of-water story with endlessly renewable conflict between a bullheaded coach, a school that cares more about academics than athletics and the helicopter parents pulling the strings. There’s a delicate balance on the show between how temperamental Marvyn is allowed to be without alienating his players — and, by extension, the audience. He can’t be an irredeemable jerk, but he can’t shelve his win-at-all-costs mentality, either.

“John really protected the rough edges of this guy because he didn’t want him to flip and become a teddy bear by Episode 2,” Lorey said on a video conference with Stamos earlier this month. “And so it was inspiring to see him, very often, pushing back against the petting-the-dog scene and just let this guy be this guy for a bit.”

For his part, Stamos took Marvyn’s prickliness to Method extremes.

“I purposely didn’t hang out with the girls in the beginning,” he said. “I didn’t want to have any cutesy [expletive] with them. At the end of the day, I came home and told my wife, ‘I hate it. I don’t even know the girls’s names.’”

Though “Big Shot” seems loath to allow Marvyn’s mistakes to linger much longer than an episode, the series isn’t about the softening of Marvyn Korn, which would not only drain the tension but put him constantly in the wrong. He isn’t always the blowhard in need of comeuppance or a good talking-to. He also empowers his team to play with unity and confidence and to be their best possible selves, which figures into their conflicts off the court, too.

Formula dictates that the teams in “Game Changers” and “Big Shot” eventually stop losing and have their Big Game confrontations, but what unifies these shows is a surprising thoughtfulness about what sports are for, and the difficulty of drawing a line between healthy competition and a misplaced obsession with winning. There was no analog to Alex in “The Mighty Ducks” movies — adding Graham’s character to the formula “violates the reboot laws,” she joked. Alex is a rare voice for the sports parent who believes that sports have their limits.

“My cousin’s husband was the coach of a girl’s basketball team that lost for, like, four years in a row,” Graham said. “They lost like every single game. And I was like, ‘That’s a show I would watch.’ Like they just kept losing.

“And then, I don’t know, I guess; where does it go? This is why I don’t run networks.”

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