I depends on the type of games:
Games like stationmaster or free cities dont really need a background as you are playing a sandbox and not a story.
Story based games do need a background explaining why stuff are as they are:
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The important thing is to only add what is important for the story.
I myself dont like main charaters with a mind of there own.
And with that i mean main charaters that make there own choices.
Lets use billy from superpowered as example:
He is well written:
He wants to be a hero.
He got lucky with his dna and has no limet to the amount of power he can get and because of money he doesnt get monitors 24/7.
Basicly he got free reign aslong he doesnt do something stupid that would attracted heroes to attack him.
His personaly is well written enough that him not seeing his villian behavior or lack of proper use of mind control can be blamed on his dislision of being a hero(he is a glory houd who just want to be a famous hero and compleetly lacks morals tho you can make him heroic or vilianus given how easly he justify mind controling his teacher into fucking his friend he is anything but a hero... Seriously he lacks morals even when you play him heroic.)
His powers makes him horny 24/7 which create's an interesting gameplay challange.
Getting too horny makes him jerk off in public(Which is one of the few ways to lose if it happen to often)
Or fate of irena.
The dialog is enjoyable and while not my kind of game(i dont like linear visual novels)
The mind control/break is done well and the story is nice to read.
Lab rats 1 and 2 also has good background stories.
The key about creating a background (for me atleast) is to use simply facts and shove your opions where the sun doesnt shine.
I hate it when the main charater deside he wants to fuck his mother.
I the player make the desicions.
The main thoughts and words shoud be limeted to facts.
Likewise a stupid main charater like the main charater from the headmaster just made me want to shoot him.
His intro was so bad.
All but saying on stage that he is training 18yo girls as sex slaves
If he wasnt the main charater who would probley be shot for it.
From:
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You can ask an audience to believe the impossible, but not the improbable.
I find that the best stories are those where the main charater has no opinions of its own.
Instead the player makes the decisions.
Dialog shoud be kept to a minimum and avoid uneccery details.
For example:
That is a green rock.
Yeah i know i got eyes.
That is just wasting my time.
Marian lives on alms street 12.
Meaby i shoud visist her this sunday.
This is subltle use of thoughts to tell players about the next trigger.
And you shoud give them the option to ignore the trigger and change the story baised of there choice.
Likewise avoid choices that lead to a game over.
If i lose because i pick the wrong choice i just get frustated at the fake choice.
Losing because i dont have the right stats?
Perfectly fine.
Losing because i wasnt fast enough?
Perfectly fine.
Losing because only one dialog choice continue's the story.
Take this writter behind the shed and put him out of my misery.
To take a none porn game example:
In dragon age origian i cared for jowel my ingame mage friend.
I spend some time helping with with his love life.
In dragon age 2 you have a sister and a brother and one of them dies withing the opening scene.
I never got to get to know them so i had no attachment to them.
I know they where hawk's family but i was never given any reason to care.
Short version(and again this is all personal preference):
I find that background helps me invest in my charater as having a reason to care.
Likewise a personaly can help me relate to the main charater.
However the challange for any writter is to not favor one playstyle over an other.
Many games are bad because the only right way to play is how the writter wants the story to go.
For example i cant stand waifu acadamy because it has next to no gameplay and several game over choices.
If i want to read a story i go read a story.
I want to play a game.
The main charater is also unlikeable.
He motivation is to rape and mind break inocent girls to get revenge on the people that harmed his father?
Dude i am all for revenge but leave the inocent alone.
I wish you luck.
And remember: You cant please everyone.