Arcane Spell Failure: Armor interferes with the gestures that you need to make to cast an arcane spell. Arcane spellcasters face the possibility of arcane spell failure if they're wearing armor, so wizards and sorcerers usually don't wear armor. Bards have a hard choice because they're more likely to get into combat than wizards and they cast fewer spells, so getting some armor makes more sense fo them than it does for a wizard.
Casting an Arcane Spell in Armor: When you cast an arcane spell while wearing armor, you often must make an arcane spell failure roll. The number in the Arcane Spell failure column on Table 7-5: Armor is the chance that the spell fails and is ruined. If the spell lacks a somatic (S) component, however, you can cast it without making the arcane spell failure roll.
Shields: If you are wearing armor and using a shield, add the two numbers together to get a single arcane spell failure chance.
Player's Handbook p. 105
Reading this section from the book, it is easy to miss the section about somatic components. For example, a bard wearing Chainmail (30% arcane spell failure) can cast a spell like feather fall without the 30% chance to fail. A sorcerer may take the Armor Proficiency (heavy) feat to wear Full Plate armor in combat and get the Still Spell feat; then he could simply cast a fireball or magic missile spell without worrying about the armor getting in his way.
The following listing comes from the Sorcerer/Wizards spell list and is a compilation of the spells available to them without a somatic component. A character with the Still Spell feat may cast any of his spells without somatic components (within the feat's restrictions).
0 Level Spells: Flare, Light 1st Level Spells: Feather Fall, Hold Portal, True Strike, Ventriloquism 2nd Level Spells: Blindness/Deafness, Blur, Knock 3rd Level Spells: Displacement, Suggestion, Tongues 4th Level Spells: Dimension Door, Lesser Geas, Polymorph Self, Shout 5th Level Spells: Contact Other Plane, Teleport 6th Level Spells: Geas/Quest, Mass Suggestion 7th Level Spells: Phase Door, Power Word - Stun, Teleport without Error, Vanish 8th Level Spells: Mass Charm, Otto's Irresistible Dance, Power Word - Blind 9th Level Spells: Mordenkainen's Disjunction, Power Word - Kill, Prismatic Sphere, Teleportation Circle, Time Stop, Wail of the Banshee, Wish
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