corrected Dark Sun fluff
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minnmass
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Various settings assume different levels of access to magic. Eberron has a "magic-punk" feel, and generally assumes that magic is relatively cheap and plentiful; the Dark Sun setting vilifies arcane magic (due to the belief that it's ruined the planet), has no deities and (so divine magic is extremely rare, at bestbased on friends' tales of Dark Sun campaigns), and focuses on psionics (which, while magic-like is much more likely to focus on single-target or mind-effecting "spells" than arcane magic, IME).

Various settings assume different levels of access to magic. Eberron has a "magic-punk" feel, and generally assumes that magic is relatively cheap and plentiful; the Dark Sun setting vilifies arcane magic (due to the belief that it's ruined the planet), has no deities (so divine magic is extremely rare, at best), and focuses on psionics (which, while magic-like is much more likely to focus on single-target or mind-effecting "spells" than arcane magic, IME).

Various settings assume different levels of access to magic. Eberron has a "magic-punk" feel, and generally assumes that magic is relatively cheap and plentiful; the Dark Sun setting vilifies arcane magic (due to the belief that it's ruined the planet) and (based on friends' tales of Dark Sun campaigns) focuses on psionics (which, while magic-like is much more likely to focus on single-target or mind-effecting "spells" than arcane magic, IME).

explicitly called out the overestimation of the effectiveness of fireball against an army, using RAW
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minnmass
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The Battle of Cadzand (an "early skirmish", the first battle of the Hundred Years' War) saw 3,500 people on one side and "several thousand" on the other. Assuming the enemy stayed in nice, tight formations (and that the formations had 4 people per 5-foot square, twicea whopping 4x what normal combat rules allow), a single fireball (20-foot radius = an 8x8 square = 64 squares) could hit 256 people (probably less, I forget exactly how 5e "circles" are shaped). 5 Fireballs could hit up to 1,280, again generously. It quickly becomes hard to estimate how many would die to the fireballs (are the enemies 1st-level commoners or 5th-level fighters or paladins?); in very rough numbers, I'd expect about 1/4 to survive (assuming creatures that would survive on a successful save and need to roll a natural 16 to do so). While that's a very good chunk of the oncoming army taken out, the wizard's then done and some 2,500 enemy combatants are still on the field.

As pointed out by @Kirt, that's a tremendous _over_estimation of the firepower of a wizard. Assuming a circle is 44 squares (per this answer for 3.5/PF) and a following a strict reading of RAW, allowing each square only 1 combatant, that tops out at 44 creatures per fireball or 220 total. Even if they're all killed by the fireballs, that's less than 10% of the 3,500 people on the one side gone. If the remaining 3,280 people press on, the wizard's toast.

The Battle of Cadzand (an "early skirmish", the first battle of the Hundred Years' War) saw 3,500 people on one side and "several thousand" on the other. Assuming the enemy stayed in nice, tight formations (and that the formations had 4 people per 5-foot square, twice what normal combat rules allow), a single fireball (20-foot radius = an 8x8 square = 64 squares) could hit 256 people (probably less, I forget exactly how 5e "circles" are shaped). 5 Fireballs could hit up to 1,280, again generously. It quickly becomes hard to estimate how many would die to the fireballs (are the enemies 1st-level commoners or 5th-level fighters or paladins?); in very rough numbers, I'd expect about 1/4 to survive (assuming creatures that would survive on a successful save and need to roll a natural 16 to do so). While that's a very good chunk of the oncoming army taken out, the wizard's then done and some 2,500 enemy combatants are still on the field.

The Battle of Cadzand (an "early skirmish", the first battle of the Hundred Years' War) saw 3,500 people on one side and "several thousand" on the other. Assuming the enemy stayed in nice, tight formations (and that the formations had 4 people per 5-foot square, a whopping 4x what normal combat rules allow), a single fireball (20-foot radius = an 8x8 square = 64 squares) could hit 256 people (probably less, I forget exactly how 5e "circles" are shaped). 5 Fireballs could hit up to 1,280, again generously. It quickly becomes hard to estimate how many would die to the fireballs (are the enemies 1st-level commoners or 5th-level fighters or paladins?); in very rough numbers, I'd expect about 1/4 to survive (assuming creatures that would survive on a successful save and need to roll a natural 16 to do so). While that's a very good chunk of the oncoming army taken out, the wizard's then done and some 2,500 enemy combatants are still on the field.

As pointed out by @Kirt, that's a tremendous _over_estimation of the firepower of a wizard. Assuming a circle is 44 squares (per this answer for 3.5/PF) and a following a strict reading of RAW, allowing each square only 1 combatant, that tops out at 44 creatures per fireball or 220 total. Even if they're all killed by the fireballs, that's less than 10% of the 3,500 people on the one side gone. If the remaining 3,280 people press on, the wizard's toast.

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minnmass
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Setting matters

Various settings assume different levels of access to magic. Eberron has a "magic-punk" feel, and generally assumes that magic is relatively cheap and plentiful; the Dark Sun setting vilifies arcane magic (due to the belief that it's ruined the planet), has no deities (so divine magic is extremely rare, at best), and focuses on psionics (which, while magic-like is much more likely to focus on single-target or mind-effecting "spells" than arcane magic, IME).

So, how common is magic in your campaign setting? Even in a generally high-magic setting like Eberron, your instance might be lower-magic than most.

And, how common is high-level magic in your setting? Even Eberron's magic-punk style is compatible with a relatively small number of high-level wizards. While a high-level wizard may be needed to create a thing, that doesn't mean they're needed to maintain or run the thing. There's no way I'd trust a car I put together out of a collection of parts, but I can still drive one, change the oil, and put on the spare tire.

How common are mages?

Setting matters, part 2

It's hard to build a PC that doesn't have at least a little inherent magic (certainly possible, of course, but most classes and races have at least a little magic in them), but is that because magic is common or because PCs are blessed with magical aptitude?

Does Eberron have a magic-punk style because every street urchin can cast a few spells or because a few powerful mages got the ball rolling and muggles can mostly manage the rest?

Do campaigns focus on characters who can wield magic (both PCs and NPCs) because you can't swing a dead cat without hitting a mage or because mages are among the movers and shakers in the world? Do we follow Luke Skywalker because the movies know he's going to save the galaxy, or does he save the galaxy because the movies follow him?

Wizards are expensive

The Adventure League guidelines (per this answer) peg the cost of hiring a wizard to cast a single Fireball at 90gp. An aristocratic lifestyle can cost as little as 10gp/day, and skilled hirelings might cost as little as 2gp/day. Why would an aristocrat pay over a week's expenses for a single spell?

If a Knight wanted 10x the normal skilled hireling cost, that aristocrat could still employ 4 for the whole day for less than a single casting of Fireball would cost.

Wizards are squishy

Wizards may be masters of the arcane arts, but they're not known for riding into battle: armor gets in the way of their spellcasting, and they aren't known for their ability to take a punch. Knights, on the other hand, are well known for riding into battle and being able to take a hit.

So, either the wizard is going to ask for more than "normal" to supply their spells or they're going to need guards. Those guards are going to need to eat and otherwise be provisioned, have a place to sleep, etc..

Armies are huge

The Battle of Cadzand (an "early skirmish", the first battle of the Hundred Years' War) saw 3,500 people on one side and "several thousand" on the other. Assuming the enemy stayed in nice, tight formations (and that the formations had 4 people per 5-foot square, twice what normal combat rules allow), a single fireball (20-foot radius = an 8x8 square = 64 squares) could hit 256 people (probably less, I forget exactly how 5e "circles" are shaped). 5 Fireballs could hit up to 1,280, again generously. It quickly becomes hard to estimate how many would die to the fireballs (are the enemies 1st-level commoners or 5th-level fighters or paladins?); in very rough numbers, I'd expect about 1/4 to survive (assuming creatures that would survive on a successful save and need to roll a natural 16 to do so). While that's a very good chunk of the oncoming army taken out, the wizard's then done and some 2,500 enemy combatants are still on the field.

Archers are a thing

Fireball has a range of 150 feet. A longbow has a maximum range of 600 feet. An archer can pepper the wizard with arrows from safety before the wizard can fireball the archer.