%increase of elemental effect chance [duplicate]

For items and Badass Tokens that boost things like Elemental Effect Rate (which is a % itself), is the added percent applied multiplicatively or additively?

For example, the Siren's skill that adds 5% elemental chance. If I get +5% chance and I use a gun with 5% chance to burn do I have 10% chance now or 5.something%?

Are Badass tokens the same as the skill/item boosts in this regard?

From some testing I noticed vastly reduced elemental effect occurrence rates when not using the Siren skill that adds +30% elemental effect chance. That skill alone makes elemental weapons vastly more viable.

The same was true with class skills; a +25% boost takes an SMG from about 10% chance to about 35% chance, so the % chance is definitely additive there as well. If it were multiplicative the benefit would have been extremely minor.

Not sure about Badass rank yet, but I assume it's the same.

It's additive... flat-out...

Start with your gun's damage = X

You find a relic with +10% damage and put it on = X + (X*.1)

You find a class mod with +10% damage... but you think it might work better with a different relic, so you take that off first... = X

... then put on the class mod = X + (X*.1)

...then realize the other relic won't work with your build, so you put the damage relic back on = X + (X*.1) + (X*.1)

In the actual coding, X is most likely something like "gun_base_damage" and is being referenced by each individual instance where X is needed to fill a variable. Since the X variable doesn't actually change, and the bonuses do not reference eachother, each bonus is added independently.

To do otherwise would require an absurd amount of coding because you would be checking for variables that aren't neccesarily present all of the time... variable variables, if you will.