I'm personally of the opinion that the mechanics should come first, the explanation after. You give a wonderful, in-character, dramatic speech to try to persuade a group of farmers to help you fight the bandits who oppress them, and then roll a 1 on your check. Better, I think, to roll the dice and then make a speech appropriate to the result - in this case, persistently calling the village by the wrong name, or something similar.
Here's how I handle that:
After the player makes the speech for his PC, I consider the reaction of the NPCs. If the words are
obviously enough to convince the NPC, there's no need for a roll. The opposite is also true - if the words are
obviously not going to work, there's no need for a roll. If I think the NPC's reaction is in doubt, then I ask for a roll.
A simple example:
A simple farmer's toiling in his field. The PCs are tired, wounded, and looking for rest at the nearest inn. They hail the farmer: "Hail!" I make a reaction roll to set his initial disposition and get something low. I decide that the reaction roll means that the farmer doesn't like wandering mercenaries, is busy, and needs to get his harvest in before the frost; he doesn't want to waste any time talking. The farmer looks up, grunts, and ignores them.
One of the PCs grabs the farmer by the hair and puts a knife to his neck. "Where's the closest inn?"
I use my DM's judgement, considering what I know about the NPC, and decide that he'd tell them.
Or: One of the PCs calls out to the farmer. "I know you're busy, but if you direct us to the nearest inn, there'll be a shiny silver piece in it for you."
I use my DM's judgement, considering what I know about the NPC, and decide that he'd tell them.
Or: One of the PCs calls out to the farmer. "Where's the nearest inn?"
I already know that the farmer isn't going to talk to them, so he continues to ignore them.
More complicated:
The PCs are trying to rally the peasants to take up arms against some bandits. The PCs might make a great argument, but asking people to risk life and limb is difficult, so I'm not sure as DM how they would react. I call for a check.
They key for me is: did the actions of the PCs trigger any kind of internal conflict in the NPC? In the first three examples I don't think they did; the farmer wants to tell the PCs, or not, based on their actions and the farmer's disposition. No need for a roll. In the latter example, I think there is a conflict there - the farmers would rather not fight, but they are being oppressed and the PC's words are convincing, so we roll the dice to see which way that plays out.
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I'm not sure if there's a big difference between the two approaches. In my experience, if you roll first and narrate after, there's a danger of omitting the narration, or having it feel tacked on. (I have been through too many Duels of Wits where it went something like: "What are you doing? Point? Me too. I'm rolling Persuasion, how about you? Same thing, eh. Cool. I got 4 successes - you? Okay, I'll reduce my Disposition by 3. Great. Next round - what are you doing?")
However, one danger in the way I do it is that the actual words can get lost after we add up modifiers to the roll. There have been times in my hack where I have to ask the player, "Okay - what did you say again?"