Your rolls indicate how well, relative to your potential, a given attempt at something was. In reality, we tend to know when we’ve gotten something right or flubbed it a little, or a lot, or alternately when we just nailed it. Particularly when it’s something we know how to do well, and know the difference.
Obviously, none of us has cast fireball in real life. We don’t know how that feels—we don’t, really, even know what it means to roll for the damage. When rolling for the damage on a sword swing, it’s pretty intuitive that it represents how much force we got behind it/how much our blow landed in the “sweet spot” of our swing for maximum effect. We don’t necessarily have that intuition for fireball. But I would generally expect that it’s a similar thing: a sorcerer knows her spells, and she knows when she’s pulled the arcane threads together just right to get the maximum effect, or whatever it actually is.
But ultimately, that’s my opinion. Pathfinder, as a game, doesn’t really describe in much detail how spellcasters actually cast their spells in the fiction. They don’t really detail how that feels—and how a good roll feels better than a poor one (or doesn’t). That kind of thing is really left up to the GM—and really, a lot of GMs are going to be pretty opinionated on the subject, in my experience. How much player characters know about the numbers behind things varies heavily from table-to-table, and complaints about players assuming their characters are more familiar with those numbers than the GM wants are fairly common. Some even go so far as to call it metagaming, or even cheating!1 So it’s really no surprise that Paizo had no desire to dictate these things—it would only irritate a significant portion of their audience.
I would say, though, that a recurring complaint I have had from people with actual, real-life fighting experience (e.g. a martial artist, a former soldier), is that D&D and the like don’t give warriors enough credit when it comes to sizing up opponents. Generally speaking, it’s assumed, for example, that a target’s AC is unknown, that their level is unknown, and so on. Various classes even have special features to allow them to narrow down that information. Barring that, players are expected to figure them out by keeping track of what does or doesn’t work (“ok, a 16 missed, but a 19 hit, so it has AC 17, 18, or 19”). But I know a number of people who feel that’s kind of nonsense: any trained combatant would be able to have at least a reasonable estimate of those things within the first few moments of a fight (barring explicit attempts to feign lesser skill), whereas in D&D and Pathfinder you often never get enough data to figure that stuff out before the fight is over unless it’s a particularly tough enemy, and even then the fight is usually most of the way through. So that is something I keep in mind when I GM, and I tend to lean towards characters being more capable in their judgment than the rules seem to let on.
But again, that’s just me. You’ll have to talk to your GM, or think it over for yourself if you are the GM, in order to get an answer that applies at your table.
- And in some cases, I might agree, too; there’s a pretty wide range of possible approaches to this and everyone’s gonna draw a line somewhere.