Can we build the math from the ground up? (And does Vancian help or hurt that?)

[Ignimortis]

Does PF2 advertise itself as "make muggles great again", lie that "the math just works - all hail balance", or is this a silent feature of the game?

Just a thing, I think. I'm still not sure myself whether their complaints are overblown and they're too used to casters utterly dominating the 3e/PF1e (and to a lesser extent, 5e) metagame with save-or-dies and such, or if it's really something like this. From some descriptions, I can glean that caster party members feel like the encounters would be cleared just fine without them, and if they just rolled a Fighter or a Champion, they'd be of more help than they are now. That's a major and persistent complaint for 3e/PF1e/5e, except it usually worked the other way around with Fighters being better off replaced by mages.

In my experience, 90% of class choice comes down to "I like this class". That's why there's so much damn hue and cry over the Fighter sucking. People like the Fighter and want it to be good. If people just wanted to bring necessary abilities to the table, they would simply ignore the classes that sucked. People's class choices need to give them the opportunity to contribute in most situations, and to tailor their capabilities to the group. These are things the Wizard does.

Sure, but that's exactly the paradigm you want the game to have, isn't it? You've got Beguiler stuff that the Beguiler is better off doing, and Wizard stuff the Wizard is better off doing. What does it matter that the Wizard's solution to the Beguiler stuff is a 6/10 instead of a 1/10? The Beguiler still does a better job of it. The only time that comes into play is if there isn't a Beguiler around, and at that point it's the difference between the adventure continuing and not. Where's the problem?

So what? The Beguiler still has the toolkit to overcome pretty much any challenge, because challenges aren't just "do X damage". Having or not having a particular tool doesn't matter. What matters is being able to overcome challenges.

Because it doesn't matter 90% of the time if your solution is 10/10 or 6/10 - what matters is whether you can do it at all. Like I said earlier, it's binary, and there are not enough situations where distinctions between abilities serving the same general function are important - unless you levy the ones that exist currently with more restrictions.

Your position is that a party of Wizard, Cleric, Fighter and Rogue would have a choice between certain abilities that are all on the same general level as each other, for any situation. I instead presume that a party might actually just be two Wizards and two Clerics, or two Rogues and two Fighters, or anything else - it all depends on which ability is generally the best (Teleport is still superior to Shadow Walk, or vice versa for general means of travel that don't involve lots of additional stipulations). People would just pick classes that allow them to solve as many of generic problems as they can. I've seen enough all-fullcaster parties to know this happens, perhaps not very often, but still.

In other words, having one 10/10 and five 6/10s is generally better than having three 6/10s and five 2/10s. Having seven 6/10s might even beat both of those, too. It all depends on whether that 6/10 is enough to contribute enough in most situations.

It depends what you mean by "spell". Fabricate certainly needs different mechanical constraints than Fireball does, but "magic up some non-magic goods" is absolutely the kind of effect that can and should exist in your system.

Well, make it a ritual, at least. Fabricate is certainly not a thing that should be on spell lists and cast with a single level 5 slot in a few minutes.

That's not the point. The point is that you don't need to take away the Wizard's toys to give other classes a niche. You can instead give them toys that are more efficient in their particular niche. If you want to rely on the Rogue for stealth, you don't need to nerf the Wizard, you need to make the Rogue as effective at stealth as the Beguiler.

If you want to rely on the Rogue for stealth, they have to be better at stealth than Invisibility starting at level 3. That means either getting even more absurd bonuses to stealth than Invisibility grants you, or having some good bonuses and, for example, sharing them with the whole party. Wait, that's Pass without Trace in 5e. Unless you want the Rogue to auto-solve the stealth minigame, I don't see how much of an improvement you can make here without nerfing spells, because level 2 slots are already providing effects that do, for the level, almost automatically solvie stealth. Of course, you could go the 3.5 route and say "but Invisibility doesn't make you move silently, so that check is still bad" - but that bumps into design bloat by the way of "having so many skills that spells can't cover them all at once, and giving players lots of skill points so that they can". Complexity can solve the problem, but it's like firing a nuke at bandits - the solution might be worse than the initial problem.

Of course not everyone should learn Teleport. Some people should learn Shadow Walk or Tree Stride or any of the other fast travel abilities that exist in D&D and the rest of the genre. What shouldn't happen is telling the rest of the players that this is the Wizard's turn (or the Fighter's turn or the Rogue's turn) to get to solve the problem, so they all get to sit down and shut up. That experience is the worst part of the game, and I categorically reject the notion that there is any problem that is solved by making it more common. Any problem that is interesting enough to spend table time on needs to be interesting enough for there to be tradeoffs between viable solutions.

See above. Those problems are usually too binary to involve tradeoffs. Making a plan and having tradeoffs comes from the world most of the time. The way you make everyone able to contribute isn't by having binary switches, it's by making team play work.

So instead of just positing a problem (we need to be there quickly), you need to present additional challenges that another member of a team is equipped to handle. Something like "we need to be there yesterday, Wizard can handle this with Teleport, then we need to persuade the king that the devils are coming in full force, Fighter can do that, while the Rogue finds info on cultists in the town and Cleric sets up defensive wards around the city to minimize civilian casualties". This way, everyone still got to contribute to the plan, and they didn't need to have Teleport/Shadow Teleport/Divine Teleport/Smash Teleport on their sheets. Having everyone contribute to the same one task that is solved with one action isn't fun, it feels like everyone can do something without you even needing to be there. Kind of like current Fighter.

Of course, we also need to make sure that it's not something that's best solved with "the Wizard can teleport us there, and then charm the king into believing us, and scry on the cultists, and then set up wards". Because that would be the current situation, perhaps with Cleric finding the cultists through divine aid, and them setting up wards together, while Rogue and Fighter are basically there to hit stuff.

Those creatures both have more than double the HP of our Bugbear, which means Fireball is falling behind against them too, just to a smaller degree.

Bugbears are by default not equipped to deal with Fireballs, since Fireball is a level 5 thing. Compare a Bugbear to Magic Missile or Scorching Ray - they also won't die from one of those. Monster HP doesn't scale linearly with CR - HD gain is way faster that CR gain.

"Contribute significantly" seems like a phrase that is doing a lot of work there. What exactly does that mean? I could imagine a standard by which a 9th level Warblade "contributed significantly" in an 11th level party. That doesn't mean I'd pick a 9th level Warblade over an 11th level character given the choice.

Having solutions to problems that couldn't really be handled without them. Or making it way easier to handle problems the party did encounter.

Such a system also makes it impossible to have Lightning Bolt, Fireball, and Cone of Cold without also having Line of Cold, Lightning Ball, and Cone of Fire. Like many things, there is a place for it within the rules, but it doesn't seem especially appealing as a core part of the system.

Frankly, I see no problem with Line of Cold (Ridge of icy spikes), Lightning Ball (shock explosion) or Cone of Fire (hey, that's Burning Hands, but bigger!). It might not lend itself well to certain spellcasting ideas (especially those involving unique effects like Fabricate or Magic Circle), but most generic spells fit into this well enough.