How Vulnerabilty interact with saving halev or absorbing effect ?

[Julien Dien]

B1 305 wrote:

Vulnerabilties (Ex or Su) A creature with vulnerabilities takes half again as much damage (+50%) from a specific energy type, regardless of whether a saving throw is allowed or if the save is a success or failure.

(1) Acconding to the bold part, several players insist the additional 50% damage of Vulnerability should not be halved by successful saving.

I don't think so.

(2) When interact with Protection from Energy and Resist Energy, which goes first?
I always follow the rule "multiply before adding", so the order is
original damage * 1.5[Vulnerabilty] - Protection from Energy - Resist Energy.
some friends thought the Vulnerabilty should be go last. If the damage is absorbed, it has nothing to do with the target, which do not "trigger" the Vulnerabilty. So the order is
(original damage - Protection from Energy) * 1.5[Vulnerabilty] - Resist Energy.
some friend even put the Vulnerabilty to the last, which is
(original damage - Protection from Energy - Resist Energy) * 1.5[Vulnerabilty] .

[Mysterious Stranger]

The normal order of operations is to first do everything inside parentheses, then exponents, then multiplication and division and last is addition or subtraction.

The way you have been doing it looks to be the correct way. Since multiplication and division are at the same level it does not matter if apply the vulnerability before or after the saving throw. (20 * 1.5)/2 is the same thing as (20 / 2) *1.5.

[Chell Raighn]

Your players have an odd way of looking at that… and a complete lack of understanding for not only math, but the rules. You are doing it correctly. While most things on pathfinder tend to stack in a way that is most beneficial to the players, damage calculations do not. Damage, resistances, and vulnerabilities have a fairly standard order of operations. The order benefits the players when THEY inflict damage, but disadvantages them when damage is inflicted to them.

That means you follow this formula:
((Damage * Vulnerability) - Protection) - Resistance

Reduced damage on saving throw is applied to the base damage before anything else applies. Of course, because (X/2) * Y is the same as (X * Y)/2, it really doesn't matter if you apply vulnerability before or after saving throw, but the standard order is saving throw applies first. Note: Saving throw being first is the only thing here ordered to be advantageous to the players when receiving damage.