I'd phrase it as "control" instead of "involvement"
That seems fair to me. In some other recent posts I've started to talk about "joint creation" of the fiction. Which is (I think) gesturing in the same direction as you.
"narrative control" is synonymous with "I do what I want regardless of how much sense it makes."
I don't think that's what [MENTION=1210]the Jester[/MENTION] meant. It's not what I meant.
You've framed it in ingame terms - the "I" in your sentence is spoken by the PC, talking about the PC's success or failure with the PC's actions.
But narrative control isn't an ingame thing. It's a metagame thing. It's about who gets to determine the content of the shared fiction. Different rules can distribute this power in different ways among the participants. 4e does it differently from (say) 3E, or 2nd ed AD&D, and gives more of that power to the players.
That has no real bearing on the ingame question of whether or not the PCs achieve their goals. It's perfectly possible to have a game with a high degree of player narrative control yet a high degree of PC failure (I've GMed a Rolemaster game that had this feature; I think quite a bit of Burning Wheel could go this way too.
First off, its primary function is to neuter DM control of his game as rule-arbiter (referee) and shielding yourself in the "Almighty Letter of the Rules" to justify never losing, or even the illusion of letting your character be in danger.
Can't use your favorite tripping attack because you're facing an arthropod? BOOM! Rules says I can trip anything!
But only once per encounter. That is, the mechanism of limitation is different. So provided you need to trip twice per encounter, you'll still be in danger, and might even lose.
The logical extension of the battle between player and DM for narrative control ends up with DM, no longer rule arbiter <snippage> the DM becomes one thing: monster-runner.
There's no battle; at least not at my table. There's a distribution of roles.
But characters going for their dramatic needs with every fibre of their being and us seeing what happens when they do IS the story!
This.
The story arises when we see what happens, but there is more than one way to go about that process.
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With a stronger "simulation" (means have primacy over effects) bent, I think the process is rather as follows.
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3) The player/PC examines what in-world means are available for achieving these goals. Even mechanical abilities are considered in this light. Physical pushing is likely to result in movement, so pushing is a sensible thing to pursue. If none of the available means seem likely to succeed, go back to step 2. At this point the fictional means are essentially fixed.
4) The action is resolved, but the DM considers whether the in-world circumstances merit a bonus/penalty/other to the process. The DM tries very hard to be impartial about how the in-world circumstances are applied to the process. The DM also tries very hard to be impartial about any changes to effects (e.g. only half normal distance moved).
With a stronger 4e-like approach (effects have primacy over means) I think it looks more like:
<snip>
3) The player/PC examines what game-mechanics means are available for achieving these goals. If a suitable power fits, it is selected. If not, return to step 2 or examine whether a scene resource can justify a stand-in. At this point the (probabilistic) effects are generally fixed.
4) The action is resolved, and the player and/or DM optionally indicates how the effects correspond to the in-world actions the PC took. Both try very hard for this result to make sense within the fiction.
That seems fair to me.
The technical term I use for your second approach (which I learned at The Forge) is "fortune in the middle" ie in the middle of the narration - your (4) captures that, because we resolve first and narrate second. The phrase I learnd from [MENTION=54877]Crazy Jerome[/MENTION] to describe your first approach is "process simulation".
One rationale of fortune-in-the-middle is to give the player a bigger role in creating the fiction around their character - instead of "trying", and perhaps having the resolution make them look like a chump, we resolve first and then retrofit the narrative around that - so the reason for success or failure can be narrated afterwards, and preserve the players' authorship of his her character (eg I didn't miss becaue I suck - I missed because I'm so awesome, that I'm duelling with someone who's even more awesome than me, and therefore beat me!)
You also correctly note that it can be a weakness of a fortune in the middle approach that it may not actually force us to finish off the narration, and thus the fiction becomes "gappy" and we potentially degenerate into a boardgame rather than RPG. That's why I think getting the role of keywords, p 42 etc right is pretty important. And why I think the sometimes-derided 4e battlemat is actually pretty signifcant for providing an anchor to the fiction that 4e is really responsive to (like position, terrain etc). Another technique I use, as a GM, to make sure we push through with the narration is to have the responses of the NPCs/monsters to reflect (even if it's just in their witty dialogue) the after-the-dice-roll narration of what happened.
