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[egruntz]

There are many different games I've been playing that use these terms to describe how their bonuses stack. My problem is that it seems "multiplicative" means something different depending on the game and I'm wondering if there's a standard by genres or perhaps for game design as a whole? Can you please me figure this out?

In my mind, additive means 50% damage boost + 50% damage boost = 100% damage boost.
In my mind, multiplicative means 50% damage boost x 50% damage boost = 125% damage boost.
So multiplicative is better.

League of Legends though is saying additive > multiplicative. Looking at their wiki:

Stacks multiplicatively
When effects stack multiplicatively, the cumulative effect can be calculated by multiplying the effects together. Note that the game interface rounds champion statistics, so what is shown in-game may be slightly different than what is calculated.

It is important to understand that most champion statistics that stack multiplicatively are displayed as the opposite of the actual numbers that are multiplied. For example, 10% damage reduction should instead be understood as 90% damage taken, and 25% damage reduction should instead be understood as 75% damage.

10% damage
reduction   10% damage
reduction
⇨
19% damage
reduction
↓ ↑
Damage ×0.9 × Damage ×0.9
=
Damage ×0.81
Example: If your champion has armor granting 10% damage reduction and an item granting 10% damage reduction, you multiply the damage factors—0.9 and 0.9—to get 0.81, which means your champion has 19% damage reduction (against physical damage).

Huh?

Diablo 3 seems to also have "multiplicative" stacking that is worse than pure additive?

Anyway can you help me out understanding this? Am I understanding this completely wrong and multiplicative actually is what I think, and LoL/Diablo 3 is just...different?

 

[Earthstrike]

Yeah, the main issue is that better or worse are matters of the context. Damage reduction is worse for you if it were to stack multiplicatively instead of additively, however, damage amplification is better for you if it were to stack multiplicatively instead of additively. Remove the notion of good and bad from your mind and just get a grasp of the mathematics. Then from there, determine which would be better or worse in each case as it can vary in each case.

 

[Septimus Prime]

I think I've also seen it to mean multiplicative of the bonus amount instead of the total, so if you stack two 50% bonuses, this way, the second will give you 50% on top of the additional 50%, which is an additional 25%.

So 100% + 50% + (50% x 50%) = 175%

 

[NawtKool]

I can't say I really understand the context of the numbers, but in general, I believe if you're aiming to go towards 0%, additive is better. If you're aiming past 100%, multiplicative is better.

For instance, with damage reduction, you want to be closer to 0% damage taken.

Wtih a 50% damage reduction source and a 40% damage reduction source, the differences look like this:

Multiplicative:

0.5 * 0.4 = 0.2 = 20% damage taken.

Additive:

1 - (0.5+0.4) = 0.1 = 10% damage taken.

If these factors interact additively, it results in half the damage taken compared to multiplicatively.

However, if you're looking at damage increase, then 50% and 40% looks like this:

Multiplicative:

1.5*1.4= 2.1 = 210%

Additive"
1+(0.5+0.4)= 1.9 = 190%


That's probably it. Right? Someone logic check me?

Sneak edit:

Nobody's here right? Cause I totally failed the damage reduction one multiplicatively. It's not 0.5*0.4=0.2 .
It's 0.5*0.6 =0.3.

 

[Earthstrike]

I can't say I really understand the context of the numbers, but in general, I believe if you're aiming to go towards 0%, additive is better. If you're aiming past 100%, multiplicative is better.

For instance, with damage reduction, you want to be closer to 0% damage taken.

Wtih a 50% damage reduction source and a 40% damage reduction source, the differences look like this:

Multiplicative:

0.5 * 0.4 = 0.2 = 20% damage taken.

Additive:

1 - (0.5+0.4) = 0.1 = 10% damage taken.

If these factors interact additively, it results in half the damage taken compared to multiplicatively.

However, if you're looking at damage increase, then 50% and 40% looks like this:

Multiplicative:

1.5*1.4= 2.1 = 210%

Additive"
1+(0.5+0.4)= 1.9 = 190%


That's probably it. Right? Someone logic check me?

Yeah, my post combined with yours resolves it entirely. Again the main confusion is the concept of one being better or worse than the other when it's context dependant.

 

[chillybright]

Most of these are because of balancing issues to prevent item/effect stacking to be overpowered and promote item/strategy diversification. In your example, imagine the dmg reduction is percentage additive, there could exist an op tank build that stack dmg reduction to be 100%. The same could be said about dmg amplification. I remember there was a pre season in league where black cleaver's passive was not unique (25% armor penatration iirc). Brusiers like pantheon were op as fuck for the whole patch and all they had to do was build 6 black cleavers and one shot anyone else.

 

[serversurfer]

In my mind, additive means 50% damage boost + 50% damage boost = 100% damage boost.
In my mind, multiplicative means 50% damage boost x 50% damage boost = 125% damage boost.
So multiplicative is better.

In this example, yes.

League of Legends though is saying additive > multiplicative. Looking at their wiki:

Huh?

Looking at the example, I'm guessing that they're saying you don't add 10%DR to 10%DR to get 20%DR, because that's "too much" DR. When you add, it gives you a bigger number than the proper result, which is 0.9^2=0.81, or 19%DR.

Diablo 3 seems to also have "multiplicative" stacking that is worse than pure additive?

I think adding first gives better results for damage reduction, while multiplying first gives better results for damage bonuses. That should be true regardless of the game, pretty sure.

Anyway can you help me out understanding this? Am I understanding this completely wrong and multiplicative actually is what I think, and LoL/Diablo 3 is just...different?

HTH <3

 

[SomTervo]

Damage reduction is worse for you if it were to stack multiplicatively instead of additively, however, damage amplification is better for you if it were to stack multiplicatively instead of additively. Remove the notion of good and bad from your mind and just get a grasp of the mathematics. Then from there, determine which would be better or worse in each case as it can vary in each case.

... I'm going back to No Man's Sky.

 

[egruntz]

Yeah, the main issue is that better or worse are matters of the context. Damage reduction is worse for you if it were to stack multiplicatively instead of additively, however, damage amplification is better for you if it were to stack multiplicatively instead of additively. Remove the notion of good and bad from your mind and just get a grasp of the mathematics. Then from there, determine which would be better or worse in each case as it can vary in each case.

Yeah, my post combined with yours resolves it entirely. Again the main confusion is the concept of one being better or worse than the other when it's context dependant.

Sorry, I still don't understand. It's not a thing about context for me, but the math formula behind it.

So 100% damage reduction (if I'm the attacker) is obviously bad.
100% damage amplification (if I'm the attacker) is obviously good.

But the connotation of good vs. bad, whatever the effect is, doesn't change the math behind it. That's what I"m getting at here. I'm looking for the standard of what "multiplicative" means in game design. Because as others have said:

I think I've also seen it to mean multiplicative of the bonus amount instead of the total, so if you stack two 50% bonuses, this way, the second will give you 50% on top of the additional 50%, which is an additional 25%.

So 100% + 50% + (50% x 50%) = 175%

This is what makes sense to me when I think of "multiplicative." However, I've seen several games now that use the term to define their formula of diminishing-returns-stacking, like LoL and Diablo 3 (I think). I don't understand the logic of, "If it's 10% damage reduction, it's actually 90% damage dealt, which you multiply to this other thing for a lesser effect."

Does that make sense what I'm confused on?

Sorry for the late reply btw. Made the thread and then had to bail, priorities. Thanks for all the help so far.

 

[Krappadizzle]

Me right now:

 

[uncredited male]

In Diablo 3 offensive bonuses are all eventually multiplied together but certain things are added together and treated as a single value before the final multiplication. These things are referred to as additive as they have diminishing returns.

Multiplicative means it is a totally separate modifier in the context of D3.


You do 100 damage and have 50% damage boosts.

One boost additive (same as 1 boost multiplicative):

100 x (1 + .50) = 150 damage (50% more damage)

2 boosts additive:
100 x (1 + (.50 + .50)) = 200 damage (second boost only adds 33% more damage than first formula)

They are both multiplicative:
100 x (1 + .50) x (1 + .50) = 225 damage (second boost adds 50% more damage than first formula)


For defense damage resist is a % of damage mitigated. All different sources of DR are also multiplicative as if they were additive you could stack enough DR to have over 100% which would make your character invincible.

So in D3 multiplicative modifiers are preferred for offense. While additive would be preferred for damage resist.

The point is that it is just mathematical behavior that will have different effects for the player.

 

[Ferrio]

edit: Disregard, huge brain malfunction

You're treating percentages as if they're whole numbers, when they're actually a representation of fractions of 100.

50% * 50% does not equal 125%.

Instead it's

additive: 0.5 + 0.5 = 1.0 = 100%
multiplicative: 0.5 * 0.5 = 0.25 = 25%

 

[Wulfram]

You're treating percentages as if they're whole numbers, when they're actually a representation of fractions of 100.

50% * 50% does not equal 125%.

Instead it's

additive: 0.5 + 0.5 = 1.0 = 100%
multiplicative: 0.5 * 0.5 = 0.25 = 25%

Two 50% damage boosts does mean a 125% damage boost in a multiplicative system. Because its 1 * 1.5 * 1.5 = 2.25%.

 

[Ferrio]

Two 50% damage boosts does mean a 125% damage boost in a multiplicative system. Because its 1 * 1.5 * 1.5 = 2.25%.

Shit you're right, that's embarrassing. Not sure what the hell I was thinking.

 

[cakely]

Two 50% damage boosts does mean a 125% damage boost in a multiplicative system. Because its 1 * 1.5 * 1.5 = 2.25%.

This is it!

I've done enough diablo 3 math to know. I even have a tiny python library for calculating DPS for my Wizard.