Is the (Shadow)Priest the better Mage in WOW?

[savaughn]

Of mage and shadow priest, talking solo play, the mage has only one advantage - polymorph.  Shadow priests put out more single-target DPS than mages (especially after Shadow Form), but may have trouble taking pulls of more than one beast due to lack of poly.  Humanoids, however, can be MCed and made to fight each other; undead can be shackled.  Priests also need to buy water instead of getting it free.
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Disagree. Frost Nova is an immobilize, frost everything else is a snare, blink is a movement bonus. In solo play a mage has many ways to escape when things go wrong. A priest must scream and hope the shield holds while running. Especially up through the 40's, priests end up dead more often. Substantial down side.

DPS output is an argument for Priest over Mage, surprisingly enough.  Mage benefits are basically poly.  Teleports for convenience, but that doesn't really apply in combat.
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After Shadowform, this can be the case (depending on the build and assuming you stay maxed as a shadow priest). You get shadowform at level 40 - 48 if you couldn't wait that long for Improved Shield. Until then you are VERY behind mages. A level 32 fire/arcane mage will run the following sequence: pyroblast, fireball, fireblast, arcane missiles. Starting with the cast of the first spell (since the opener time occurs before the pull) the first 4.5s generates around 770 points of damage. Afterwards, the mage will do about 83 dps with arcane missiles.

Compare this to a similar priest pulling with Mind Blast, SW:P, Mind Flay generating around 364 damage in the first 4.5s and following up with continued Mind Flays+SW:P for around 55 dps.

The Mage uses 545 mana to pull this off and 64m/s for missiles. The Priest uses 585 mana (including the initial shield) but only around 30m/s. This means that for mobs of roughly equal level the Mage will have killed the mob in about 10s. The Priest will kill the mob in about 20s. They will both be down virtually identical amounts of mana. This will allow them both to kill 2 mobs before being out of mana. If the priest decides to allow let Spirit Tap work, it will restore roughly half the mana used over a 15s period but meaning that the priest is killing less than 2 mobs per minute. Including time spent recovering mana, the mage will kill around 3.5 mobs per minute.

Please note: these are optimistic estimates. Costs for additional shields and inner fire haven't been included.

The priest can improve the dps by Mind Blasting. Even with Spirit Tap the priest will not be able to get through three mobs without drinking and will likely need to drink after two. A typical mob at this level drops just over 1s in cash. Nectar costs 1.8s per bottle. The priest spells all improve substantially over time, eventually eclipsing the equivalent fire spells - but you have to get through 50 levels before that happens.