While fighting Morgan she special did way more damage than what is listed on her card. Her card lists it as 672, during the battle is was listed as 780, and once fired it was actually 912. Am I missing something? Screenshots attached.
Two effects happening here.
- There is an unlisted defender bonus of about 20%, to make raiding less one-sided in the attacker’s favor.
- The point value in a Damage over Time special isn’t actually a fixed value, despite what it looks like on the card. Behind the scenes it is based on the hero attack score, which can be boosted by troops. The better the troops, the higher the DoT special damage will actually be, exceeding the listed value on the hero card.
The combination of these factors causes the discrepancy you see.
Dont forget the bonus you get from troops 
While I understand what your saying I think you may be missing what I’m saying. I’ve been hit with other DoT and the numbers don’t vary that greatly, especially not while in battle. There are three different numbers going on, 2 of which occurs during the battle itself.
The value shown for the special power in the battle in your first screenshot is based on the extra attack percentage from a troop. It’s about 16%.
The additional discrepancy between the damage shown in the first screenshot and the damage shown in the second is that unlisted 20% defender bonus.