Spells

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"Spells" is an informal term for skills that are cast as magical attacks, rather than skills that modify weapon-based attacks. Spells are largely used by mage characters; the Wizard and Witch Doctor in Diablo III.

The term is nebulous; virtually everyone would agree that skills like Electrocute and Swarm of Locusts are "spells" but skills like Ground Stomp and Impenetrable Defense might not be considered as such.

There's no game importance to the term; it's purely a piece of terminology.

Spell Damage

There are two major changes to how spell damage is calculated in Diablo III. In addition to the spell itself increasing in damage with more points in it, and various passive skills boosting all or some group of spells, the Wizard's stats are factored in when determining damage, and +%spell damage, found on many items, is essential to maintaining a rapid killing speed.


Attributes

Just as strength and dexterity are a crucial part of the damage calculations for the accuracy and damage of most physical skill attacks, the attributes will matter for spell accuracy and damage in Diablo III.

Which stats, and how they'll be calculated, is not yet known.


+% Spell Damage

The biggest change to spell casters in Diablo III is the addition of +% spell damage modifiers. These sorts of modifiers were found on some passive skills in Diablo 2, as well as on a very few uniques and runewords, but they were uncommon, and were not required to kill effectively. As a result, casters in Diablo 2 were much less item-dependent than the combat classes, and found it easier to concentrate on Magic Find, resistances, hit points, and other non-damage bonuses.

This will not be the case in Diablo 3, where mages must add considerable +% spell damage from modifiers to stay ahead of the monster hit point curve. A high level Wizard or Witch Doctor in Diablo 3 will no more be able to kill quickly with no +spell damage than a Barbarian or Monk could succeed with a junk weapon.

A quote from Flux's post-Blizzcon 2009 Wizard write up explains this in more detail: [1]

When viewing the listed damage on each spell, it’s important to keep in mind that those are not absolute numbers, in D3. They’re much like weapon damage; modified by your wizard’s attributes, your character level, by other skills, and also by your equipment. Lots of types of items in D3 carry modifiers that boost spell damage, usually by a percentage.
I found numerous wands, staves, and even pieces of armor with values between +5-25% spell damage, and that was just in the early stages of the game. We know nothing about higher level equipment bonuses, and it’s entirely possible that the D3 team is projecting high level characters to have +100%, +200%, or who knows, +500%, spell damage. If so they’ll be adjusting the base spell damage accordingly, which might make it look very low to our untrained eyes.
Here’s an example from early in the game, that was mentioned in the Witch Doctor skills report. The skill tree listed damage on my level 2 Skull of Flame spell was 6-9, yet with a level 12 Witch Doctor my Inventory screen showed 19-29 for that spell. I don’t think I had more than +50% spell damage from equipment, so assuming the display values aren’t wrong (in D2’s infamous LCS style), there are considerable bonuses added to damage from character attributes, which are then further boosted by the spell damage bonuses on your equipment.
This is all part of the D3 team’s plan to make all of the attributes useful to all characters, and to make more types of modifiers useful/essential to spell casters. We don’t know enough yet to judge how well it’s working, but it should be a substantial change from how spell damage was calculated and scaled up (or not) in D2.


Scrolls

One type of "spell" that can't be considered a skill is something cast by a scroll. There are only a few of these in Diablo III, and all characters can use them.

The Scroll of Identify returns in Diablo III. As in previous games in the series, all magical, rare, legendary, set items are found "unidentified" and must be IDed to see their stats. UnIDed items can not be equipped in Diablo III.

The Scroll of Wealth is a new scroll in Diablo III. These items allow a character to sell items without returning to town.

The Scroll of Town Portal is not in Diablo III. It was, during much of the game's development, but was removed after the team decided that allowing an easy escape to town was defeating their efforts to make combat more meaningful and intense. See the Town Portal page for more details and quotes from the developers.