### Multiplicative vs Additive

First Riot Post
Comment below rating threshold, click here to show it.

Cryser

Senior Member

I'd like some clarification as to the difference. I know that it's generally seen that multiplicative is generally a higher number than an additive amount, but i'm a little confused as to how that works. Let's use the upcoming Zilean buff as an example:

Zilean
Reduced the movement speed modifier on Time Warp to 55%, from 65%.
Time Warp's haste effect is now a multiplicative movement speed modifier

Let's assume a base speed of 300.

With the buff on, how does the number 300 change when it's multiplicative as opposed to additive?

Comment below rating threshold, click here to show it.

Tyrfang

Senior Member

300 base speed
375 with boots 2

Old:
300 * 1.65 = 495
300 + 75 + 300 * 65% = 570

New:
300 * 1.55 = 465
300 + 75 + (300 + 75) * 55% = 581.25

Comment below rating threshold, click here to show it.

Cryser

Senior Member

Ah, so basically multiplicative basically just takes item stats into account when determining the final number.

Thanks for the quick reply =P

Comment below rating threshold, click here to show it.

Phreak

Shoutcaster

Order of buffs go like this

Static bonuses: 300 move speed, +90 from boots, etc. Examples: Characters' base stats, boots.

Additive % bonuses: Multiplies the sum of whatever is one level above this one. %ages are added and subtracted, then multiplied against the above value. Examples: Ghost, the Utility thing, Quintessences, Janna's passive.

Multiplicative % bonuses: Same as above, the %ages are added/subtracted within this group, then multiplied by the product one level up. Examples: Any slow, Zilean's Time Warp.

Comment below rating threshold, click here to show it.

Delicious Donut

Senior Member

Ok, so Tyrfang is wrong?

Comment below rating threshold, click here to show it.

Phreak

Shoutcaster

Pretty sure Tyrfang is wrong.

I know for a fact that the Utility 3% movespeed multiplies my Boots movement speed. I can't say I've done hard math on the other small move speed buffs, which is hard to do properly because you get diminishing returns on high move speed.

Comment below rating threshold, click here to show it.

joesyuh

Senior Member

Still not 100% clear on how this works.

I understand the difference between multiplicative and additive.

From that understanding I take the fact that a additive stat will end up being less then if it was multiplicative. Just the same as if you were going from Exponential to Multiplicative. I think... haha.

Comment below rating threshold, click here to show it.

Bagration

Senior Member

Comment below rating threshold, click here to show it.

Phreak

Shoutcaster

No. Both stats do the exact same thing, unless you're slowed.

A 50% move speed bonus that is "additive" is the exact same as a 50% move speed bonus that is "multiplicative"

The difference comes if you get slowed, because all slows are "multiplicative"

If you move at 300 MS, get a 50% "additive" boost, you reach 450. If you then get hit by a 50% "multiplicative" slow, you drop down to 225.

If you move at 300 MS, get a 50% "multiplicative" boost, you reach 450. If you then get hit by a 50% "multiplicative" slow, you drop down to 300.

Comment below rating threshold, click here to show it.

wildfire393

Senior Member

From what the Mechanics FAQ says, Phreak is correct.

Boots count as "base speed" when applying % modifiers like Zeal, Phantom Dancer, Movespeed Quints, Swiftness Mastery, etc.

Multiplicative bonuses are applied over this. Most of the abilities that grant Movespeed have recently been changed to be Additive, but some of them are still multiplicative.

Let's compare Zilean's new one to his old one to demonstrate the difference.

Say we've got an Ashe (300) with boots of Swiftness (90), Zeal (8%), and the Mastery (3%). She's been struck by Phage's Passive (-40%), and has Zilean's buff on her:

Old ability: (300+90)*(1.76)*(.6) = 411.84
New Ability: (300+90)*(1.11)*(1.15) = 497.835. Though this will suffer a little from diminishing returns, because it exceeds the threshold.

12