As I continue making my way through Frasier
Good man. Frasier is the best American sitcom.
@Spirit makes a good point about how spin-offs work very differently in different media, and I agree. What makes a good TV spin-off isn't the same as what makes a good video game spin-off, etc. Since you mentioned Frasier, I'll start with my thoughts on TV spin-offs.
Frasier succeeds tremendously as a spin-off, arguably surpassing Cheers in popularity. I think the reason for this success is down to the choice of character to follow for a spin-off. When you think of Cheers, you've got Sam Malone who will own the bar until he dies, Carla who'll work the bar until she dies, Norm who'll drink at the bar until he dies, and Cliff who'll soothe his loneliness at the bar until he dies. Frasier was the only member of the cast with the narrative potential to carry his own story. He wasn't dependent on the bar, he had a clearly defined life outside of the bar, and so he was the only character who could exist, narratively, away from the bar. Frasier doesn't
need Cheers to be an excellent show. You can watch it and love it without even knowing what Cheers is (though some of the cameo episodes will be better if you do). Frasier can stand alone.
Compare that with Joey. Friends was huge, but looking at the main cast, what can you do with them? Ross and Rachel are together and raising a child, Monica and Chandler are together and raising three childs, and Phoebe is married to Mike and probably soon going to be raising childs of her own. The only character who wasn't in some blissfully generic domestic paradise was Joey, so a spin-off follows him. But who is Joey? He's a dumb actor who sleeps around. By the end of Friends, that was basically it (Friends has some of the most blatant examples of Flanderization in TV). So they sent him to LA to pursue his acting career, which was basically what he'd been doing for ten years in New York. Joey, as a character, didn't have the narrative potential to carry his own story, there was nothing they could
do with him, and I think that's the fundamental reason why Joey didn't work. It's only appeal was that we knew him from Friends.
On British TV there's a police drama called Lewis which is very popular. It's a spin-off of Inspector Morse, perhaps the best loved British police drama of all time. I think Lewis manages to succeed because it's basically the same exact show. Lewis was Inspector Morse's partner, and so when Morse died Lewis took over the role. For audiences, it was a character they knew well and loved, and Lewis, the show, was able to continue in much the same manner as Inspector Morse because of that.
Again, the key factor, I think, is the central character. Lewis succeeds because audiences are familiar with Lewis as a character, whereas Frasier succeeds because Frasier has enough narrative potential to exist independently of his original series. Joey fails because there isn't enough character to him and there's definitely not enough narrative potential to him. TV spin-offs, in my mind, succeed and fail based on how compelling their central character is. Better Call Saul would be another great example of a show built around a character with a strong story to tell. If the character can support a robust story, then the spin-off will likely do well. If not, well, you get crap like Joey.
As for video games, I feel this is where writers take minor characters and base entire games on them more so than anywhere else. When I think of video game spin-offs the first that comes to mind is Halo Wars. Halo Wars is decent enough, I guess (I'm personally not a huge fan of real-time strategy), but I think the reason it does well as a spin-off is that it isn't based on the story of the main Halo games, it's a stand-alone story set within that wider fictional universe. That way it will entice Halo fans who want that sweet, sweet lore and enjoy the aesthetic, while also appealing to RTS fans who perhaps haven't played Halo. Halo Wars doesn't need the branding to survive — if it was the first game ever set in the Halo universe it still would have pulled an appreciative audience interested in the world and genre.
In comparison, spin-offs like Resident Evil Umbrella and Darkside Chronicles
do rely entirely on prior familiarity of the main series to succeed. As arcade rail-shooters they don't appeal to too many people and the entire draw is to relive the earlier Resi games in more direct, concise chunks. They abandon pretty much everything that made those games popular, the only exception being story (which Umbrella Chronicles mangles anyway). These games require the main series to exist and won't have anything to offer people without experience of it.
I'd say video game spin-offs have more room to manoeuvre because they can shift genres and find stable footing in that way, but it still comes down to whether or not the spin-off can stand on its own two feet. Spin-off games that can, I feel, tend to do better than those that don't. Relying too heavily on familiarity with the main series almost guarantees a spin-off will have limited appeal and not feel like its own complete experience. Spin-offs that use the main series as a jumping off point to build something solid that can stand on its own merits will be much more likely to succeed.
As for movie spin-offs, I'd say the same basic idea applies. The spin-off has to be able to carry itself. Something like The Scorpion King doesn't do that. It's just a generic pseudo-historical movie built entirely from a brief scene at the start of The Mummy Returns, a much more interesting, fun, and enjoyable movie all round. It banks entirely on the box office draw of The Rock, who wasn't the beloved star he is today, and doesn't deliver a compelling story with an interesting central character.
A movie like Creed (aka Rocky VII) manages to succeed because it gives us a character with a story to tell. Creed is kind of a movie version of Lewis (I doubt
anyone ever thought someone would say that) by which I mean it's a fairly smooth continuation of the series it spun-off from. If you liked Rocky for its character and themes then Creed will serve you well. It takes the narrative core of the Rocky franchise — a societal underdog showing that they have what it takes to prove themselves worthy — and says 'Ok, you saw how Rocky did that, now let's see how Creed does it.' In this way, Creed appeals to fans of Rocky, but it can also stand alone because it is, basically the first Rocky film again, in a thematic sense. You don't need to be familiar with the six Rocky films to enjoy Creed. It helps, but it's not necessary because the story and character are solid and compelling on their own.
I think this is a big factor in the divisive reception of the Star Wars spin-offs, Rogue One and Solo. Rogue One tells a story we already know the end of with characters who are so unbearably boring that you don't care if they live or die (and kind of hope they die). There's nothing compelling there, and the story requires A New Hope in order to feel dramatic. Solo tells us the story of a character whose growth we already saw. It doesn't matter what happened to him before hand, and the only appeal is to simply see a younger version of characters we already know from The Empire Strikes Back. Both of these movies
need the original trilogy to have any kind of appeal. Imagine if Rogue One was the very first Star Wars movie ever made for a minute. Would you have been satisfied? Would you have been interested enough to see a sequel? Was any excitement you felt at the end the result of the story you'd just been told or because of the explicit connection you were shown to a film you've loved for years? Would parts of the story even make sense without your prior knowledge of older films? Rogue One and Solo don't stand on their own. Obviously, in a mega-franchise like Star Wars they don't need to (well, maybe Solo did), but I think the less-than-glowing reception of them is testament to that core problem: They need the main series to be a crutch for them.
So, for one final time, I'd say that while different media can and need to handle spin-offs in different ways, the fundamental key to a
good spin-off is whether or not it can stand as its own complete creation. If you can enjoy and get everything you're meant to from a spin-off without any prior experience of the series it spun-off from, then you've got a winner on your hands.