Two part question:
How much work have you done with deities in Pathfinder?'
I actually did some work on Paizo's recently-released Inner Sea Gods. I actually haven't seen the final product, but I was contracted to write a bunch of wondrous items.
I have designed and/or developed deities elsewhere. Two I can think of are a god we did in "The Undead Chronicles" from Louis Porter Jr. Games, and a deity in FGG's Unusual Suspects. In both cases, we were looking for a deity to fill a small niche.
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If so, what is the process of developing a deity for a world?
It depends a lot on the world. For a world like Golarian that's well-developed, it's really hard actually because whatever you come up with needs to fit into the existing canon and still make sense. In an ill-defined (or non-existent) world, it's a bit easier. You still have to consider the existing canon material, but there's likely less of it. The worst problem here is if the ill-defined world has conflicts in the existing canon; those need to either be explained away as myths, cults, etc or one needs to be excised from the canon (and then a sidebar needs to explain why, from a meta perspective).
Once the existing canon is considered, it's really not much different from developing a kingdom or country or mountain range and so on. You have to write a compelling backstory - something that works for the world, is interesting to read, and provides both GM and players some plot hooks to grab onto. Then you fill in the "crunchy" bits - favored weapon, alignment, domains, etc. You probably know alignment and at least some of the domains up front - at least for me, I find that the most common reason to make a deity is because you want something that has domains X and Y, or you want a NE deity that has domain Z, or similar scenarios.
There's really a lot of similarity to a lot of the "pieces" when you're doing campaign setting design. What do you want it to do? ("I need a NG deity who has Strength and Magic as domains," or "I need a a city that's a major trade hub along a large river, preferably away from the delta region of the river," or whatever.) How does it fit into your existing canon? ("Given my existing canon, I can make this deity the offspring of these other two deities. That will explain why she has an odd domain choice." or, "Well, I have this river over here in a fairly under-developed region. I can start expanding my material there a bit, and put my new city at the nexus point where these other two rivers combine to make the larger river.")
How can you make an interesting story out of what you have? ("What if, by the laws of the pantheon, she needed to be cast down to the world as a mortal, even with her deifiic parentage? During her lifetime, she became the greatest magus the world had ever seen. She developed a large network of followers and disciples, such that after living a long and fulfiilling life, her ascension as a deity was assured." Or, "This city started as a small garrison during the Time of Expansion. The location was deemed militarily important, so a fort was constructed, and that lead to the buildup of a small town around it. Over time, though the fort remained the actual town began to take priority over the military operation. What started off as a small fort with some fur traders developed into a large town within a mere 25 years, and now today is a large city with a popular of around 20,000 or so people. The town's population is wildly diverse, reflecting its roots as a frontier settlement. Visitors to the town are surprised to see orcs and goblins wandering the stret without incident. The military fort remains, but no longer holds the political power of the city.")
Overall, the design goals are really the same - you need to fill a need within your world, it needs to be interesting, and it needs to have story potential both for the GM and the player.
Should deities focus on roleplaying aspects? Should there be ones that give a clear mechanical advantage? Or a mix of both?
I think it's a little bit of both, with a caveat. I don't think you should go into the design seeking to have it be mechanically superior. If it happens, you should evaluate your choices and see if it's
very superior, or just slightly so. For the former, I think you should consider pulling back the power a bit.
But the RP is definitely at least as important. Assuming a d20-based game (so 3.5, Pathfinder, and even 4e and 5e) a deity is a real, tangible thing in the world, not just a concept. Gods
exist and people know gods exist. So why does
this god exist in that sort of structure? Why does she have any worshippers at all? (Even if they're all insane, you still need to answer that question.) What compelling reasons does a player have to make a cleric (or paladin or druid or oracle or...) who worships that specific deity? What compelling stories can the GM tell using the deity and/or her worshippers as the centerpiece?
Then turn those questions around to see if you're too powerful - what compelling reasons would a player have to worship
another deity? Is the only real reason to be contrary, or do other deities offer actual interesting choices? Do GMs have interesting story options if they choose another deity? Is the only compelling GM reason for this deity that all the followers are bat crap insane, and we need that for the adventure to work? (If so, I'd argue you have some bad choices, but maybe it works.)
In a more general sense, I'm a pretty firm believer that story and mechanics complement one another, rather than competing. Sure, as a game designer I can go out right now and make a 10 HD undead creature with a death touch ability and immunity to fire. I can do those mechanics pretty easily and have a reasonably balanced CR whatever (I'd guess 9-ish) creature. So what? That's only half the job. I also need the story to complete the creature; otherwise, it's just a pile of numbers. Just about anybody can make a pile of numbers. Pathfinder makes it even easier
by giving you guidelines about how many hit points a creature of a given CR should have, how much damage it should do, what it's save ought to be, and so on. Just plug and play with different numbers of HD and ability scores and you can get just about anything to fall into those ranges. so you need the flavor of the monster to bring those numbers to life.
And then turn that around. A lot of people can write a fascinating block of text about an undead creature created from the corpse of a child murderer. The sheer evilness that taints the corpse causes it to rise, and grants it the power to steal life from its target merely by touch. The writer can make it compelling and disgusting and creepy pretty easily. But without the right numbers, that "fluff" doesn't really mean much. If my creature with that background dies to the PCs in one hit every time, nobody is afraid of it, loathes it. Nobody rejoices when the evil is finally laid low. They yawn and ask if there's any treasure in the room.
But then put those together, and you have a compelling monster that player want to hate, that GMs want to build stories around, that everybody rejoices when the battle is won. And that's because you took strong numbers and strong fluff and made something that's - to use a cliche - greater than the sum of its parts.