I meant the GM having backstory in mind ahead of play.
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I mean pre-authored campaign material that the GM comes up with prior to play, but which is used not to thwart the players introducing story elements or declaring actions for their characters.
If this is genuinely setting material - as opposed to ideas that might seem useful in play - then what prevents it from affecting player action declarations?
If the material deals with the locations of things, or the dispositions of NPCs, or the hidden forces at work in some game-relevant situation, how does a GM
avoid it coming into collision with player conceptions of the shape of the fiction?
If we can imagine a GM who creates an interesting and compelling story that incorporates or at the very least does not contradict or suppress player goals, then I think that's all that is needed in order for the idea to have merit. Perhaps the Gm has come up with a villain that he has worked into each character's stories in some way, connecting them all but without forcing them along certain paths. The GM has a loose idea of where things will go or what some characters may or may not do, but leaves plenty of room for change along the way.
I'm not sure how "interesting and compelling story" and "loose idea of where things will go" yet a"without forcing them along certain paths" and "plenty of room for change along the way" fit together.
For instance, how do we know that the NPC introducec by the GM is a villain? What if the players have their PCs ally with the NPC? Or what if some do and some don't?
Story tends to suggest a sequence of events with rising action, climax, resolution, etc. If the GM has an idea for such a thing, where exactly do the players fit in? Conversely, if the rising action, climax and resolution are the results of actual play, then what is the role of the GM?
This is why the "standard narrativistic model" emphasises framing and consequences. Compelling framing does not require the GM to envisage, in advance, what the compelling story might look like. Robust action resolution mechanics mean that these can be relied upon to generate consequences, again without the GM needing to envisage, in advance, what the compelling story might look like.
So my players gave me a good idea of what each of them wanted for their characters.
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I then took those ideas and some that I had, and weaved them together. Some of my ideas were inspired, or further inspired, by ideas of the players. I also had some stories that I wanted to bring about in play, so I connected those to the players' stories. The ideas I had and the ideas my players had have blended quite a bit. There are some elements about which I can honestly not say who came up with them. Others I know are mine, or a specific player, or the group.
So there is a larger story at play, some of which the players are unaware of, and they discover through play.
To the extent that the players discover a GM-authored "larger story" through play, it seems to me that it is the GM rather than the players who is exercising agency in respect of those contents of the shared fiction.
And
discovering a GM-authored story through play seems to me to mean that, at certain points of play, the players make moves that lead the GM to reveal (= tell them) some bits of that story. Eg maybe the players declare that their PCs spy on some person or event, and the GM reveals (= narrates) what transpires.
Perhaps you mean something else by the idea of "a larger story at play, some of which the players are unaware of, and they discover through play." I am just trying to make sense of what you are describing, including the contrast that you draw.
to introduce an element wholly unexpected by the players because it is not directly connected to their stated desires
I think it is self-evident that this is an example of the GM, and not the players, exercising agency over the content of the shared fiction.
to take many story threads offered by the players and make a cohesive narrative out of them
This can cover a very great range of things, from approaches to framing, to narration of consequences of failed action declarations, to "behind the scenes" manipulation of backstory to generate particular outcomes.
Having a failed search for the mace reveal that the mage's brother was apparently manufacturing black arrows - one of which killed the master of the elven ronin PC - might be an instance of what you have in mind.
So would the GM deciding, as an item of pre-authored setting detail that the only way to free the brother from possession by a balrog is to gain the help of the dark naga - thus linking the fate of one PC (the one whose brother is possessed by a balrog) with that of another (the one dominated by a dark naga).
It seems obvious to me that these are very different sorts of thing: the first affirms player agency over the content of the shared fiction, whereas the second is the GM establishing some setting element that seems likely to serve as a limit on subsequence player action declarations for their PCs.
I don't use the pre-authored material to force them down certain paths, or to thwart their ideas. I use it to hopefully enhance the story and play.
I am not in a position to judge whether or not what you do in your game enhances the story and enhances play. I'm just trying to analyse techniques, not make aesthetic judgements.