An in depth look at the effects of Spell Speed and Black Mage

Spell Cast/Recast
Fire - 2.5/2.5
Fire III - 3.5/2.5
Fire IV - 3/2.5
Flare - 4/2.5
Blizz III - 3.5/2.5
Blizz IV - 3/2.5
Thunder 2.5/2.5
Thunder III 3.5/2.5

Astral I,II,III - +50%, +75%, +87.5% - Reduces the cost of Ice Spells by 50%, 75% (No further reduction from AS3)

Umbral I,II,III Reduces the cost of Fire Spells by 50%, 75% (no further reduction from UI3. While increasing the amount of MP Recovery per tick.
Leylines - Reduces Cast/Recast by 15%

Special notes about Astral Fire III and Umbral Ice III
Astral Fire III - Reduces the cast time of Ice Spells by 50%. This does not include the Recast time so you are still bound by how long the recast of a spell is.

Umbral Ice III - Reduces the cast time of Ice Spells by 50%. This does not include the Recast time so you are still bound by how long the recast of a spell is.

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Potencies

Fire - 180 - 337.5 Under AF3
Fire III - 240 - 450 Under AF3 - 168 (70% Potency)
Fire IV - 280 - 525 - Under AF3 - 551 Including Enochian
Flare - 260 AOE - 487.5 Under AF3 + Stacking 10% less per mob up to 50% less for 6+ Mobs - 468 under AF
Blizz III - 240 Potency - 168 Potency Under AF3 (70% Potency)
Blizz IV - 280 Potency
Thunder - 30 Potency + 40 Potency DOT for 18s (240)
Thunder III - 70 Potency + 40 Potency DOT for 24s (320)
Thunder III Proc - 390 Potency + 40 Potency DOT for 24s (320)

Potency Per Second (Astral Fire)
Fire - 135 Potency/s
Fire III (Umbral) - 67 Potency/s
Fire III Proc - 180 Potency/s
Fire IV - 175 Potency/s (Not including Eno 5% Bonus)
Fire IV (SwiftCast) - 210 Potency/s
Flare - 122 Potency/s - 195 Potency/s with Swiftcast
Blizz III - 67 Potency/s under AF
Blizz IV - 93 Potency/s under UI
Thunder - 108 Potency/s
Thunder III - 111 Potency/s
Thunder III Proc - 284 Potency/s @ 0 DOT Clipping
Thunder III Proc - With 100% Clipping (24s on DOT Timer) 156 Potency/s
Thunder III Proc - With 75% Clipping (18s on DOT Timer) 188 Potency/s
Thunder III Proc - With 50% Clipping (12s on DOT Timer) 220 Potency/s

Take note that the Potency/s values will change depending on Spell Speed values reducing the Cast/Recast values as well as DOT Potency.

Thunder/Thunder III and Spell Speed

Because Spell Speed increases the Potency of DOT's by a rate of 0.95% per 66 Spell Speed it drastically changes to the potency of Thunder and Thunder III Procs.

Compare these two skills Fire IV and Thunder III using a value of 1344 Spell Speed (12% Reduction of Cast/Recast and 11.4% increase in DOT Potency

Comparison of F4 and T3 using Enochian and Maim + Mend II for both values.

Fire IV - 2.64 Cast @ 717 Potency (280x(1.3)(1.875)(1.05) = 271 Potency/s

Thunder III Proc - 532 Potency + (52*1.114) * 8 (486 including 5% from Enochian) Combined Potency = 1018 Potency

Thunder III Proc - 2.2s Recast - 463 Potency/s
Thunder III Proc - With 100% Clipping - 242 Potency/s
Thunder III Proc - With 75% Clipping - 297 Potency/s
Thunder III Proc - With 50% Clipping - 352 Potency/s