The Bayesian winrate for this deck would be 53%. Lines up with low tier 1/high tier 2.
15 Upvotes for simple explanation of the deck and card choices:
Northshire Cleric - Goes in every Priest deck, synergizes with hero power, lets you draw closer to your combo, and contest the board early.
Power Word: Shield - More draw, and an activator for Wild Pyro. Also useful for keeping minions (especially taunt ones) alive longer.
Divine Hymn - Wild Pyro activator, and if you sequence correctly, you can get an extra pyro trigger with this and some other spells. The sustain is nice, if slightly weak by itself, vs aggro.
Mind Blast - The win condition. Play Death Knight, Alex their face, find more copies with Shadow Visions, profit. Versus certain decks you'll need the third Mind blast to burst them down before they think to heal (Even Warlock)
Shadow Visions - Find Mind Blast vs control, find whatever you need vs aggro. Pyro triggers galore.
Wild Pyromancer - Odd Paladin and Token Druid auto lose because of this card, as long as you draw it, and hold it until the latest safe moment to play it and clear board, preferably leaving it alive (using hero power, Hymn, and PW:S). Acolyte trigger vs most other decks.
Acolyte of Pain - Crappy body to contest aggro early, or Wild Pyro draws later. Filler, but the best filler.
Twilight Acolyte - If you've never seen a Mountaint Giant in your life, you can take this card out of the list. It's what seals the deal in the Evenlock matchup. Otherwise, mediocre body to stall with vs aggro, can be used to steal a minion with Cabal Shadow Priest.
Duskbreaker - Zoobreaker. Paladinbreaker.
Mass Dispel - Filler, good vs fungalmancer, Level Up, Evenlock, cycles.
Twilight Drake - Very good body, activator for Duskbreaker.
Cabal Shadow Priest - Filler, good because of how prevalent Saronite Chain Gang is, also some high roll potential because we already run Twilight Acolyte.
Holy Fire - Overcosted Mind Blasts 5 and 6 (after Shadow Visions), also decent vs Hench-Clan thug. It's reach and sustain.
Psychic Scream - A boardwipe that doesn't give a shit about the overabundance of deathrattles in this meta. Also good stall vs Shudderwock. Makes Token Druid cry.
Primordial Drake - Duskbreaker's big brother, and an activator. Everything about this card is relevant. The minion type, the taunt, the AoE.
Shadowreaper Anduin - The hero power makes Mind Blast a 6 mana 9 damage, or 2x Mind Blast is 10 mana 16 damage. This is your primary win con combo. Doubles as super versatile board control.
Alexstraza - Critical mass for Duskbreaker, and the win con combo, can also keep you alive another turn vs aggro.
How to play the deck in 10 seconds: Stall, find Mind Blasts, find the combo that does enough damage to kill them in 1-2 turns. Mulligan for AoE cards vs Aggro, and Shadow Visions/Twilight Drake vs control. Be patient with Wild Pyro.
This deck is difficult but rewarding to play, I personally think it's sleeper tier 1 as long as Zoo and Odd Pally are popular.