Shadow is the priest's damage spec, and it plays as upkeep. You keep 
Shadow Word: Pain and 
Devouring Plague on the boss, cast 
Mind Blast and 
Shadow Word: Death each time they come off cooldown, and channel 
Mind Flay in every gap between them. Forever's 
Shadowform halves the mana cost of all five, so against one boss you finish with mana to spare. Its searched build scores 755.2 DPS on a one-minute single-boss fight, which places Shadow 14th of 25 damage specs.
Strengths and weaknesses
Strengths
- Fight length barely moves it. No part of the rotation is a burst window that a long fight waters down. One minute gives 755.2 DPS and three give 741.5 DPS, so the rank climbs from 14th to 10th.
- No mana worries on one boss. With half-price spells, the
Major Mana Potion and 
Meditation both measure as nothing on a three-minute fight. - Several bosses at once. Shadow Word: Pain goes on every boss in reach. Its share of your damage goes from 20.5 % with one boss to 48.2 % on a three-minute fight against three bosses.
- It heals itself. Devouring Plague heals you for all it deals, more over a fight than Shadow Word: Death's backlash costs.
Weaknesses
- One small cooldown.
Inner Focus is the build's only cooldown, and over three minutes it adds 0.2 %. - Hit is hard to find. A level-63 boss shrugs off 17 % of your spells before any hit.
Shadow Focus gives 5 % and the pre-raid set only 2.0 %, so about one Shadow spell in ten still misses. - Less for the raid than in Classic.
Shadow Weaving now raises only your own Shadow damage, so the warlocks in your raid gain nothing from your stacks.
On every fight
Shadow gains ranks as fights get longer, because almost none of its damage waits on a long cooldown. Against three bosses the extra Shadow Word: Pains lift the score to 969.7 DPS, but specs with area spells gain more, so the rank stays in the middle. The table's fight names switch the whole guide.
Races
For the Horde, Undead leads the single-boss fights. 
Touch of the Grave adds a Shadow drain worth 5 % of your maximum health to one landed spell in ten, and 
Dark Sacrifice, the Undead priest's own spell, turns health into mana before the pull. Troll takes the three-boss fights with Berserking, which casts 10 % faster for 10 seconds every three minutes.
On the Alliance side Night Elf is first on every fight thanks to 
Elune's Light: 15 seconds of 10 % extra crit every three minutes, pressed together with Inner Focus. Gnome, with Eureka!, runs close behind on the three-minute fights. Night Elves also learn Starshards, a 30-second Arcane channel that none of our rotations casts. It gets none of your Shadow talents and should lose to Mind Flay, though nobody has simulated it.
What a Priest brings to the raid
Your raid buffs are 
Prayer of Fortitude, 
Prayer of Spirit and 
Prayer of Shadow Protection. Below, each buff is priced for the damage specs that gain from it here. Vampiric Embrace's party healing isn't in it, because our rotation never casts Vampiric Embrace.
Prayer of Fortitude+0.4 % to 3 of 25most: Mutilate Rogue +0.5 %
Prayer of Spirit+0.3 % to 3 of 25most: Elemental Shaman +0.4 %
Changes
Every row is one release of our simulator or of the game data, with this build's result on this fight after it. What each release changed is on Updates.