When one thinks of staves, they generally think of something that would empower a mage's spells. However, we haven't really had anything like that for whatever reason. With that in mind:
Does this turn Fireballs into Pyroblasts? Yes, yes it does. That's the idea.
I dabbled with the cost for a while, and I think this is the sweet spot. Any cheaper, and you run the risk of OTK cheese. More expensive, and it becomes a useless winmoar card. Also, the durability-reduction mechanic means that it rewards you for running multiple smaller, cheaper spells, such as Arcane Missiles or Icicle.
Let me know if this is useless, broken beyond belief, or just right.
Imagine if you played Arcane Explosion + Arcane Missiles + Arcane Missiles + Dragoncaster + Greater Arcane Missiles to hit their entire board for 6, then fire off six 4-damage missiles and three 7-damage missiles (total of 45 damage) for 10 mana.