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What is so cool about 4 of each per day at 4th level? Why don't wizards EVER get more than 4 cantrips a day?
Looking at 1st-level spells, if the original pattern was kept up, at 20th-level wizard would have 10 1st-level spells per day. That's a lot, but would it screw things up? I guess a better question would be if it would make anything better?
(For the record, clerics and druid seem to cap out a 4 of each, while bards cap at 5 per, and sorcerers at 6 per. Paladins and rangers have a split cap, w/ 4 1st and 2nd-level spells per day and 3 3rd and 4th.)
Short answer: Bonus spells for Int and balance.
Long answer: Once ability score advancements and stat boosters start having a significant effect (around 8th-10th level), the 4 spells per spell level is more like 5 or 6. An effective stat of 20 in a spellcasting ability grants 2 bonus 1st level spells and 1 each of levels 2nd-5th; an effective stat of 28 (attainable at 16th level with a starting score of 18, all advances in that ability, and a +6 boosting item) grants 2 bonus spells each for 1st-4th and 1 bonus spell each for 5th-8th. If you start adding inherent bonuses from tomes and miracle/wish, it can get really obscene*. Wizards, like clerics and druids, have fewer spell slots and must prepare their spells in advance in exchange for a wider selection of possible spells when compared to a sorcerer (vice versa from a design standpoint, since sorcerers were new with 3.0). Bards are even more limited in their spell selection than a sorcerer, but have more non-spell options. Paladins and rangers have small lists, few spell slots, and slow progression, but they can prepare any spell on their lists and spellcasting is only a minor part of their abilities.
*- Consider that a wizard, with Craft Wondrous Item, fox's cunning, and wish can effectively have an Int 16 points higher than the starting score by 20th level (+5 advances, +5 wishes, +6 stat booster).
Good explanation, thanks. It just seems weird to me that a 20th-level wizard can know the same number of 1st-level spells and 9th-level spells per day.
If by "know" you mean "memorize", that's not quite true. A 20th level wizard has at least 36 spell slots (not counting bonus slots) and he could memorize 1st-level spells in all of them, if he wanted.
And don't forget the permie bonus slots.
Another point to consider is if wizards could cast all their spells all day long why play a fighter?
A fighter can use his talents all day everyday every way they want. A wizard's powers take more umph and give more back to. From a design stand point it's about giving everyone something and some time.