OOOH ohh oh! A thread where I can spill my terrible philosophy at 
Well, for starter, indeed stats is such a “minefield.”
Treat it wrong, and your story will turn into standard RPG (altough it’s not a bad thing per se, cue on The Great Tournament)
But for now, let’s talk about how to make our story more “story” rather more “gamey”
So, stats. 
They give IF the privilege of non-linearity and customization, unlike other text mediums.
Indeed you can make a CYOA game without stats at all (and it still counts as CYOA!). But remember, adding stats also allows your player/reader the customization aspect of their MC (or other NPCs. Basically anyone the author allows to).
That being said, I’ll divide stats into 2 categories:
-
Flavor stats
Name, Favorite food, and Eye color usually fall into this category.
They don’t affect the “branching” of the story. In fact, if pulled well, you can make a totally linear story without the reader realizing that the story is actually railroaded.
Did the NPC refers to you as “Hey, Bob! Over here!” and not “Hey, over here!”? That is the doing of the Flavor stats.
They make your story feel livelier and more believable.
Oh! The king forgot if you’re a lefty and he awkwardly pull his right arm, frantically switch to his left arm for a handshake! -
Check stats
Strength, HP, and Mana. Pretty self-explanatory.
If you have a lot of Strength, you can throw the boulder away from the road.
Low of HP? You’re dying.
Etc.
Those 2 are the basics, but keep in mind that certain stats can have their characteristic (and functions) overlap between the two.
Oh, you’re silver-haired girl. You’re a witch! Enjoy the power of the moon. MP++ 
Oh, you’re in relationship with that tall black guy with a cool scar on his face. Now, you can ask him to accompany you on your every journey and flirt with him.
Oh, you have a black eye, you’re the demon! 
Now, you have your stats. But how do you use them?
Know your story.
It’s pointless to add HP to a youtube-simulator game.
It’s pointless to add Favorite Weapon to a story about basketball.
But, is it worth it to add Gender to a story about being a lampshade?
Is it worth it to add Name to a story about being a mute protagonist solving mysterious case?
Add the stats which are required by your story, consider the stats which are optional, and avoid having too much stats for fillers (unless you know what you are doing)
Aand… that’s pretty much it, for this topic at least.
Of course, there’re still some interesting topics that I not discussed at there 
(such as stats balancing, stats introducing, and stats naming), but I think they deserve their own comment slot. Or even their own topic/thread.
But for now, I’ll leave it at here 
BTW, here’s a reply which have a quite radical view regarding stats.
I’ll just leave the link 'cuz it’s quite a textwall (but it’s a worthy read)
A reply on Balancing Stats