Magic Damage formula edits

Something completely changed or I'm doing something completely wrong. Neither formula is working anymore. I feel like they nerfed the spell constant for firebolt at some point or something, but I'm not sure. It feels like a completely different formula is being used for bolt spells since I know I tested this with Lightning Rod when it came out...

EDIT: Strangely, this formula works fine if I use my Savage Fire Wand. Is there some weirdness going on with the phoenix fire wand? It used to reduce damage itself instead of magic attack when upgraded for speed, so maybe there's some sort of bug with lingering effects?

EDIT: NEVERMIND I'M STUPID. Corrected my math. Everything is fine. Results are still a bit off and neither formula matches perfectly, so there's still something missing with the formula somewhere. I'll analyze this deeper over the weekend.

Test Results

Char stats/equipment:

• 348.2~348.4 magic attack (taking into account rounding done by the game)
• 0 damage enchants
• Phoenix fire wand
• No Hebona set bonus
• Rank 1 magic weapon mastery
• Rank 1 bolt mastery
• Rank 1 fire mastery

Old formula after plugging in values for firebolt:
{120 + [5 * (1 + Charge Multiplier)] + (0.5 * 348.2~348.4) + (0 * 0.4)} * [1 + (0.15 + 0.15 + 1.5 + 0 + 0 + 0)] * Charge Multiplier * Full Charge Multiplier * 1 * 1

Old formula simplified:
{(294.1~294.2) + [5 * (1 + Charge Multiplier)]} * 2.8 * Charge Multiplier * Full Charge Multiplier

New formula simplified (just missing the 1 + before the first charge muliplier):
[(294.1~294.2) + (5 * Charge Multiplier)] * 2.8 * Charge Multiplier * Full Charge Multiplier

Expected max damage with old formula:

• 1 charge: 851.48~851.76
• 2 charges: 1730.96~1731.52
• 3 charges: 2638.44~2639.28
• 4 charges: 3573.92~3575.04
• 5 charges: 5898.62~5900.44

Expected max damage with new formula:

• 1 charge: 837.48~837.76
• 2 charges: 1702.96~1703.52
• 3 charges: 3436.44~3437.28
• 4 charges: 3517.92~3519.04
• 5 charges: 5807.62~5809.44

Actual test results against a brown fox - highest non-crit value over multiple trials:

• 1 charge: 843
• 2 charges: 1714
• 3 charges: 2614
• 4 charges: 3541
• 5 charges: 5845

Doing math with these results while at work because this is really bugging me. Instead of multiplying the Wand Bonus with the Charge Multiplier, I think it'd be easier just to list the Wand Bonus at varying charges for each bolt. Obviously, the "each bolt" part only REALLY matters with Firebolt. As such I propose revising the formula into this:

[Base Damage + Wand Bonus + (Spell Constant * Magic Attack) + (Damage Enchants * Damage Constant)]
* [1 + (Bolt Mastery Bonus + Elemental Mastery Bonus + Magic Weapon Mastery Bonus + Staff Elemental Level Bonus + Hebona Set Bonus + Rosemary Glove Bonus)]
* Charge Multiplier * Full Charge Multiplier * Thunder Multiplier * Distance Multiplier

And then changing the description of Wand Bonus into this:

• Wand Bonus is a constant for bolt spells while using a wand of the same element.
  • The value for Spirit Weapon wands depends on the Social level of the spirit. Actual values are unknown, but generally equal or higher than non-spirit wands.
  • For non-spirit wands, the values are as follows:
    • Icebolt with any non-spirit Ice Wand at 1 to 5 charges: 10.0
    • Firebolt with any non-spirit Fire Wand varies depending on number of charges:
      • 1 charge: 7.0
      • 2 charges: 12.0
      • 3 charges: 17.0
      • 4 charges: 22.0
      • 5 charges: 27.0
    • Lightning Bolt with any non-spirit Lightning Wand at 1 to 5 charges: 7.0
  • All other cases, including with Bare Hands or Staff: 0

I need to do further testing with bare hands at different numbers of charges to make sure about this formula though.

Just realized these results are wrong because of my ALO Asuna title that I was wearing at the time (or at least I think I was wearing it this morning), which adds 2% damage to bolts somewhere. I'm going to have to retest without that title to get the real Wand Bonus, and figure out after that where the title adds its bonus.

Okay, the wand bonus at 1-5 charges for firebolt appear to be 5, 10, 15, 20, 25. This means that Sephard's edits to remove the "1 +" and double the icebolt and lightning bolt wand bonuses are actually correct. However, even though you happened to be right this time, I still don't think people should be changing something just because it looks wrong until they test it and prove that it's wrong.