Would somebody explain how Immortal Call works with expendable Endurance Charges?

https://pathofexile.fandom.com/wiki/Immortal_Call

"The less physical damage taken per endurance charged removed skill modifier is multiplicative with the innate less physical damage taken skill modifier.
For example, Level 1 Immortal Call with 5 endurance charges will give you a total of 81.25% less physical damage taken, not 100%."

So, this doesn't make sense to me, since .25 * 1.75 =/= .8125

In fact, I haven't found a calculation that plugs these numbers in and gets 81.25%

Would somebody help me understand?

Edit: I'm getting the "1.75" from the 1 + 5 (end charges) * 15% (less physical damage taken per endurance charge removed).

Without any reduction you take 100% damage.

With 25% innate reduction, you take 75% damage, as

100 * .75 = 75

With a further 75% reduction (multiplicative) you take:

75 * .25 = 18.75

So you end up taking 18.75% of the original hit, or a 81.25% reduction.

"

kaijyuu2 wrote:

Without any reduction you take 100% damage.

With 25% innate reduction, you take 75% damage, as

100 * .75 = 75

With a further 75% reduction (multiplicative) you take:

75 * .25 = 18.75

So you end up taking 18.75% of the original hit, or a 81.25% reduction.

So I've seen this explanation before, and it isn't correct in how it looks at this.
The mistake here is thinking that 18.75% further reduction is subtracted from 100 instead of added to 25.

This interaction is a mystery to many it seems, since nobody has a refutation to what the wiki says, but conversations I've had with people on the PvP scene says something along the lines of an actual 43.75% less damage taken.

If there was enough experimentation done to clear this up, we should get this wiki article changed.

"

So I've seen this explanation before, and it isn't correct in how it looks at this.
The mistake here is thinking that 18.75% further reduction is subtracted from 100 ins.tead of added to 25.

There is no 18.75% reduction. It is a 81.75% reduction as correctly stated and calculated in the first response. I disagree with your point.

It is true, that the wiki is written by normal people who can make mistakes. Nevertheless kaijyuu2 correctly explains what the gem states. And the gem text can hardly be ignored. "PvP Players have said" does not really convince me, since PvP applies PvP damage scaling.


@op kaijyuu2 looks at a lv1 IC, the math changes/improves on higher levels.

"

Lightelder wrote:

"

So I've seen this explanation before, and it isn't correct in how it looks at this.
The mistake here is thinking that 18.75% further reduction is subtracted from 100 ins.tead of added to 25.

There is no 18.75% reduction. It is a 81.75% reduction as correctly stated and calculated in the first response. I disagree with your point.

It is true, that the wiki is written by normal people who can make mistakes. Nevertheless kaijyuu2 correctly explains what the gem states. And the gem text can hardly be ignored. "PvP Players have said" does not really convince me, since PvP applies PvP damage scaling.


@op kaijyuu2 looks at a lv1 IC, the math changes/improves on higher levels.

The "18.75%" comes from multiplying the innate 25% by an additional 75%. 25 * 0.75 = 18.75.

What?

"

Base duration is 1 seconds
(25-34)% less Elemental Damage taken
(25-35)% less Physical Damage taken
15% less Physical Damage taken per Endurance Charge removed

There is a 25% less phys damage taken mod in line 3. To calculate damage, multiply unmodified damage with 0.75 (you only take 75% of the damage).

There is a different 75% less damage taken mod in the last line; removing 5 endurance charges will grant you 5*15=75% less phys damage taken (5 is max as stated in the skill).

So you have two less-modifiers which are multiplicativ with each other (they do not get added together, thus not granting 100% less phys damage taken).


25% * 75% = 18,75% of damage taken


(or 0.25 * 0.75 = 0.1875 if you don't like %)
(or 100 * 0.25 * 0.75 = 18,75 if you want to know how much damage you will take from a 100dmg phys hit)
(or 81.25% less phys damage taken)

"

Lightelder wrote:

(or 100 * 0.25 * 0.75 = 18,75 if you want to know how much damage you will take from a 100dmg phys hit)
(or 81.25% less phys damage taken)

It's this line right here that doesn't make sense.
It's essentially taking the innate 25%, reducing it to 18.75%, (which isn't what the description says the charges do), and then takes that number and subtracts it from the top down, instead of adding it from the bottom up.

Does that make sense?

It doesn't say "This is how much % damage you'll take". It says "You take this much% LESS damage."

"

Noble_Seiken wrote:

It's essentially taking the innate 25%, reducing it to 18.75%, (which isn't what the description says the charges do), and then takes that number and subtracts it from the top down, instead of adding it from the bottom up.

No, that's not what's happening it all. It's taking the innate 25% and realizing that that means that the amount of damage you're taking is 75% of what you would otherwise take. Then, it takes the 75% and further reduces it (or "lessens it" to be more thematically appropriate with the increased/reduced more/less theme) by 75%. 75%, once lessened by 75%, results in 18.75% of damage.

"

It doesn't say "This is how much % damage you'll take". It says "You take this much% LESS damage."

Those two statements are functionally the same. Any increased/more/reduced/less is a multiplier to a base value. Increased/more refers to things that make the value go bigger or higher, whilst reduced/less refers to things that make the value go smaller or lower.

You start by taking 100% of damage. Then, a 25% reduced damage taken or 25% less damage taken modifier multiplies that value by (1 - 0.25), thus causing you to take 75% of damage. At this point, reduced-stacking would change the 0.25 within the parentheses, whilst less-stacking would add a separate multiplier.

The math I mean by adding a separate multiplier is: base value * (1 - 0.25) * (1 - 0.75) = 0.1875 of base value, which is economically equivalent to granting 81.25% less damage as shown by (1-0.8125) = 0.1875 of base value; hence, the economic equivalence of stacking 25% less and 75% less together is best expressed as 81.25% less damage.

To phrase it differently, any x% less or x% reduced means you're multiplying by 1 minus that amount, so x% less stacks with y% less in the form of x% less * y% less.

Oh, alternatively, you're saying that 25% less damage taken gets reduced to 18.75%, which is not what anyone was saying. If we want to compare donuts to donuts and donut holes to donut holes, you should say that the 25% less damage taken gets increased to 81.75% via the magic of multiplicative math. Trying to say that 25% less damage gets reduced to 18.75% is like trying to compare a donut to a donut hole; x% less damage taken vs y% damage taken multiplier (which I don't think exists on any current mechanics) are additive complements if I'm remembering my math terms right.

That is - part of the confusion arises because if (1-x) = y, then (1-y) = x is also true. So that is how you can start comparing donuts to donut holes and not donuts to donuts - if you use the (1-x)=y form in one context and then swap to (1-y)=x in the next context, you're just flipping things around incorrectly.

Sorry, just came up with yet another way of phrasing it if that helps.

"

The "18.75%" comes from multiplying the innate 25% by an additional 75%. 25 * 0.75 = 18.75.

That's flipped around. In fact, what's happening is you're "multiplying the innate 75% by an additional 25%."

25% less is a 75% multiplier, and 75% less is a 25% multiplier.

Another fun thought experiment - who else uses "x% less" or "x% reduced"? Businesspeople. Suppose we're talking about profits. If at first you make $100 per widget, and there's a 25% decrease in profitability, you make $75 per widget. That's just how reductions/less work. Every $1.00 made in the past now only generates $0.75. Given that you're now generating $75 per widget, suppose your profitability then decreases three times as quickly in proportion with a 75% decrease in profitability.

For a 75% decrease, again we must use the consistent definition we used before. For every $1.00 made in the past, we now only generate $0.25, because that's the same ruleset we used for the 25% decrease.

Given those $75.00 you then apply $0.25 for each of those $1.00 and now you are making $18.75 per widget.

Hence, 75% reduction * 25% reduction on $100.00 per widget results in $18.75 per widget.

What else can cause $100.00 per widget to drop to $18.75 per widget? That's right - 81.25% reduction.