# Is “+% chance” additive or multiplicative?

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?

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Let's hope it's not 5% * 5% :) – Alex Sep 21 '12 at 8:18
in BL1, it was additive. I would assume its the same in BL2 – z ' Sep 21 '12 at 12:58
I do assume/hope it's additive, but the Badass token bonuses got me wondering, since some of those (% damage) are clearly multiplicative but there's no difference in how they're presented. – Ben Brocka Sep 21 '12 at 13:35
Either way we can assume that stats will only ever increase. I was making a poor maths joke :/ – Alex Sep 21 '12 at 13:39
@Alex oh, I didn't notice the joke; regardless I'd be disappointed in 5% * 105% as well (which is what I assumed you meant) – Ben Brocka Sep 21 '12 at 14:17

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.

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The logical thing would actually to be multiplicative, 1.05*1.05 = 1.1025 so a bit over 10% increase even. However, it probably means 5% increase over base damage, so hence additivity.

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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.

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Formulas can be created to take other variables into account, even if they're missing sometimes; just set their value to make no change to the formula when missing. – Frank Nov 5 '12 at 20:59