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does it gain anythign from wisdom
I made a test with divine armor.
Damage taken without divine armor: 74
Damage taken with divine armor: 66
Damage taken with divine armor and a bit increased wisdom: 54

I guess the same goes for ethereal intervention
This wiki frequently uses "magical" damage interchangeably with arcane damage, bit annoying. Anyone know if this shields against elemental magic, fire lightning etc, or just arcane?
When it's not precise (like this spell), it's all source of magic (arcane, fire, lightning, holy)
It's enemies using magic In their attacks, as well as if someone uses a spell in pvp.
Tested at 12 Wisdom Reduced damage of Court Sorcerer spells by 30%
This page is wrong in some way or another. I am lvl 130, on NG+, have 33 wisdom and an ArcaneDef stat of 249.6. The percent arcane is reduced is 55.5%. This is before E.I. If this page was correct my ArcaneDef should increase by ~160. By doing some math, each point is worth about 0.2%. So, after using E.I. I should have a rating of ~415 ArcaneDef. Thus have a percentage reduction of ~92%. However, this clearly isn't the case as if I get hit by any magic I still take a meaningful amount of damage even though it should be real close to none. I think it either is because Def has Decreasing Returns or whatever it's called and each point into it is worth less OR this 160 it provides is split between the Def's it increases.
Update: The former theory about Decreasing Returns is true. I wanted to check my other defences and look at what it would do to those and swiftly notice that despite my FireDef having nearly 50 points less than ArcaneDef is still only 5% behind ArcaneDef in the percent catagory. Or in other words, from 0 - 200 Def, you gain 50% but from 200 - 250 you gain only 5% for a total of 55%. I'm not sure on the exact rate of decreasing but just using these numbers, every 50 before 200 is worth 12.5% while every 50 Def after 200 is worth 5%. This would mean I only gain probably about 15% from the 160 Def E.I. gives me. So this spell is actually far better suited for those who are using light armor with low defence rather than someone like me who wears heavy armor and already has high defence which is a little weird as most clerics are slower, heavy armor and big weapon users while the actual light armor users are wizards and thief type classes that typically would never use Prayers.
The comment that should be below this one is also mine. It's a long block of text and I wanted to summarize. This prayer is better suited for people who already have low defence as defence has decreasing returns and the less armor you have the better this is.