Buff/Debuff math

The wiki isn't super clear on this topic and [previous] [questions] don't appear to source from anything other than that same wiki. I would like some clarification on the order and math behind each thing that can cause a change in battle stats.

 

According to the Status Effect wiki page:

Additive modifiers are always displayed in percentages, while multiplicative modifiers are always displayed in fractions.

 

We can start with the examples from Kenzo's post by ignoring all other perks (such as faction) and bonuses (such as education) and focusing solely on five things (and we'll go with speed since it has items in each of these categories):

1. Base Stat
2. Buff bonus weapon (quicken)
3. Debuff bonus weapon (slow)
4. Buff temporary item (melatonin) 
5. Debuff temporary item (flash) 

 

1. Base Speed: 100m

2. Quicken is not a status effect and the only info provided on the Weapon Bonus page is that it provides "Increased speed while using the weapon (%)". We'll go with a 50% bonus to make things easier. Should we assume it is also (additive?) based on it using a "%" sign?

3. Slow is 25% (additive?) up to 3x using a status of Slowed. Is it 75% total (25%+25%+25%) or is it 57.8125% (25% and then 25% more and then 25% more which is the equivalent of saying [original value]×75%×75%×75%).

4. Melatonin is 500% (additive?) by applying a status of Quickened.

5. Flash is 1/5 by applying a status of Blinded and differs from the other things on this list because it is described as reducing "effective speed" rather than "passive speed" which aligns with the note on the wiki to make it so this should be (multiplicative?).

 

The question about order and math makes more sense when looking at examples that highlight the difference. 

100m Speed with 50% Quicken, 75% Slowed (3 stacks), 500% Quickened, and 1/5 Blinded could be: 

100,000,000 × 1.5 × 0.25 × 6 × 0.2 = 45m

Or

100,000,000 × (+50% - 75% +500%) × 0.2 = 115m

Or

(100,000,000 + (100m × 1.5) + (100m × 0.25) + (100m × 6)) * 0.2 = 175m

 

Could I get a response that includes a quotable source such as the wiki or a staff forum post? Thank you!

Slow x 3 would be 75% reduction.

Flash Grenade would be down to 1/5, so 80% reduction.

Can't comment on quicken.

 

I am sure there formula somewhere in the forums.

 

With flash(multiplicative), mela (additive) and slowed (additive) being in action you get:

 

100 million * (0.25 + 5 and any other additive bonus )  * 0.2 = 105,000,000 with quicken possibly then 115

 

regarding quicken. 

https://www.torn.com/forums.php#/p=threads&f=3&t=16538963&b=0&a=0&start=20&to=27002774

 

Edit: sorry I forgot to include this isn't just a random source. They're  also to be credited with RW reference guide which is still a tool I use today. Someone who's more competent and driven to provide the data and references the rest of us are too lazy to.

As far as I'm aware, giving and example, it's additive.

 

If the opponent has 0% passive speed increase and you slow them 3 times, they'll be at -75% of their speed.

 

If the opponent has +50% passive speed increase and you slow them 3 times, they'll be at -25% of their speed. If they are running a 50% quicken, they should be sitting at +25% speed.

Your middle answer.

 

Base x (combination of all additive buffs/debuffs) x multibuff1 x multibuff2, etc.

(although your education passive bonuses and any drug effects are also additive so would be in that "combination" section alongside the others)

 

 

It is why temporary items are the most effective stat modifiers.

(needles due to them being such bigger additive bonuses than all the others, and temp weapons due to them being multipliers and affecting their entire total bonus)

Thank you all for the detailed responses. The terms "additive" and "multiplicative" really aren't sufficient description but this helps (especially the response by IndyCision that includes an example equation showing the types of modifiers).

 

Base stat + (Base stat × (add all additive modifiers)) × (multiply any multiplicative modifiers)

 

It's weird because you still have to multiply the base by the additive modifiers before adding it to the base. The only gotcha is that you have to SUM the additive modifiers first. That's why calling it "additive" by itself is confusing. 

 

It would be fantastic if the wiki could be updated to better describe this.

 

To demonstrate this using the same example as earlier:

 

100m + (100m × (+50% -25% -25% -25% +500%) ) × (1/5)

 

100m + (100m × 475%) × (1/5)

 

100m + (475m) × (1/5)

 

575m × (1/5) = 115m

If you just think of the multipliers as decimals, with 1.0 being 100%, 0.5 being 50%, etc.

 

100m  x  ( 1 + additive multipliers ) x multiplier bonuses

 

100m x ( 1 + 0.50 - 0.25 - 0.25 - 0.25 + 5.00) x 1/5

 

100 x (5.75) x 0.2 = 115

 

 

Edit: You always start with your additive multipliers being as 1 (representing naturally being at 100%)

Edit2: Fixed my maths error, 5.75, not 4.75 haha

Somehow if you also want to calculate delta armor also into it. It seems following:

 

effective stats - (effective stats - (effective stats - negative buffs) x multiplactive debuffs ) x (100 - delta armor bonus)/100

 

600% - (600% - ( 600% - 3 x 25% slow) x 0.2(flash grenade) x ( 100 - 40) / 100 = 303 million in speed, when base stat is 100 million

 

Gets more complicated when you add second flash grenade.

Isn't that because the RW bonuses are multipliers the same as temps? (which is what my "x multibuff1 x multibuff2 .." was in my earlier response to him)?

 

Edit: The RW Armor bonuses, not weapons :)