I couldn't find info on this on the web, so I decided to test this out. I equipped a few different staffs with one level 4 mage, and also looked at a level 15 Vivienne, without the +50% bonus. Here are the numbers:
Weapon damage 17: Max barrier 996
Weapon damage 20: Max barrier 1140
Weapon damage 38: Max barrier 2004
Weapon damage 62: Max barrier 3156
This gives four equations with two unknowns, each of the form
A + Weapon Damage * B = Barrier
Many other stats were changing between these different staff checks, including Magic, Willpower, Constitution, and level. If those other stats affected Barrier, the system of equations above would be inconsistent. Instead, there's an exact solution:
Barrier = 180 + Weapon Damage * 48
So, it appears Barrier is a function of weapon damage, and nothing else (except abilities).





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