How many "additional" spells can I expect as a wizard in a published adventure?

Question

Wizards in 5e gain 2 spells at each level up -- twice the amount of other arcane casters (bard and sorcerer). This gives them much greater flexibility in what they can do and what roles in the party they can fill.

The PHB entry for Wizards has a sidebar titled "Your Spellbook," which contains the following text:

...You might find other spells during your adventures. You could discover a spell recorded on a scroll in an evil wizard’s chest, for example, or in a dusty tome in an ancient library.
Copying a Spell into the Book: When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a spell level you can prepare and if you can spare the time to decipher and copy it. Copying that spell into your spellbook involves reproducing the basic form of the spell, then deciphering the unique system of notation used by the wizard who wrote it.

I understand that in most cases, this is going to be largely DM dependent, especially for home (non-published) campaigns. But, there must an average expected amount of loot for a published adventure (Curse of Strahd notwithstanding -- a bad adventure for wizards who hope to discover a few additional spells along the way!).

So, based on the currently available published adventures and AL modules, what is the number of "additional" spells a wizard can expect to encounter throughout a given adventure, say, per level gained?

Answer 1

First off, there's going to be a lot of variation here. Not all adventures have opportunities to access a spellbook, so you're likely to see whole campaigns where it never comes up and others where they're everywhere.

Lets look at some examples though, from various seasons of Adventurers League, just out of curiosity.

Season 1: 6 spell scrolls from the tier 1 adventures, most of which are on the Wizard spell list, and thus could theoretically be copied into a spellbook. In the 5 tier 2 adventures every single one of them has a spellbook or two that the players can theoretically get access to. There are also several scrolls. Apparently the authors went spellbook happy in the Tier 2 parts of this season.

Season 2: The tier 1 adventures have a handful of scrolls and 2 spellbooks. The Tier 2 adventures have a handful of scrolls and 1 spellbook.

Season 3: Tier 1 has a handful of scrolls and no spellbooks. Tier 2 has a few scrolls and 2 spellbooks. Tier 3 has a few scrolls and 1 spellbook.

In each of these cases the spellbooks in question have a number of spells, some of which you could immediately copy and some of which you need to wait till you are higher level. It's also not necessarily certain that the players will get access to the spellbooks. There's also some serious overlap between stuff in each spellbook and stuff the PCs probably already know.

Answer 2

The number very much depends on which published adventure, and your DM’s discretion.

Refer to your Player’s Companion

For a rough guideline (or perhaps, an lower limit) check out the players’ companion for your adventure, such as the Princes of Elemental Evil Player’s Companion. There are between 4 and 7 additional wizard spells for the lower levels, and then it tapers off to just one for levels 7 & 8.

The new spells introduced are typically available to be found as treasure, but often only once. So if there are 7 new wizard spells in your module, you may be able to find those 7 spells. (Note that if you find a spell scroll from a spell in the PH, your character might already know that spell.)

NOTE: You might want to ask your DM if they approve of you reading the players’ companion.

Spell Scrolls

Many, but not all, of the spell scrolls you come across will be these new spells. If you start with only spells from the PH these will all be “new spells” your wizard could learn, while scrolls for spells from the PH might already be in your spellbook. At lower levels, there will be a handful of those available to find per level, more as your increase levels.

At low levels, if you want to copy all the spell scrolls into your spell book, there are enough that you might have some difficulty (1) convincing the other spellcasters to give you all the relevant spell scrolls, and (2) getting enough gold to copy them into your spellbook.

Spell Books

In theory, when you defeat enemy wizards, you could take their spellbooks and copy the spells in it. However, the details about a wizard’s spellbook are not always defined in the offficial Wizards’ published modules.

It will be up to your DM to decide whether the wizard is carrying his or her spellbook, or if it is hidden someplace inaccessible — or perhaps they don’t have one at all. Some DM’s will simply assume the spellbook is unavailable, if it’s not mentioned as treasure. Other DM’s will assume if an NPC seems to be a wizard (even if “wizard” is not explicitly in the stat block, and it often is not) then they must have a spell book, somewhere.

If the DM decides every evil wizard is carrying their spellbook, and the party can recover them all, then your wizard is likely to accumulate a large number of spells, and this number will ramp up as you go up levels, for example, a CR 6 evil wizard might have 15 spells available (ref: Hoard of the Dragon Queen, p. 92). If you can take possession of all spellbooks from all evil wizards, the limiting factors to adding them into your spellbook may be gold (for ink) and/or time to transcribe them.