How does damage reduction and defense work exactly?

[den4ikus1917]

So 75% damage reduction is the maximum one can achieve, I assume a lot of people know that, but how does it work exactly?

Let us say that a monster deals 1000 damage to me. The 75% reduction decreases it to 250.

But how does it work with defense? Would it reduce the damage to 250 first and let the defense do it's thing (decrease 250 further)?

Or does defense first decreased the 1000 damage and then the 75% reduction decreases the damage that the defense decreased first?

[tummuthr2]

My understanding is defense is taken off first. Then damage reduction. Then legend gem damage reduction.

[R2109499284]

Prepare for MATH.

The order tummthr2 wrote down is correct - but that barely matters for how it acutally works. It wouldn´t change a single thing if legend gems or damage reduction were calculated first. The only important part is that defense is taken into account before the %-reduction.
If you don´t have any %-damage reduction you can (in theory) simply subtract your defense from the damage you take. The most reliable way to test this is against a player with 100% critchance and a high luck stat (I don´t remember if 100 is enough to always proc it) as you want to minimize the damage fluctuation (for example: Some bosses deal anything between 2 and 3.5 million damage against me without crits).

Damage reduction is where it get´s interesting and to get it out of the way: Legends gems and damage reduction work multiplicatively. What does that mean ? The higher one stat is the less "effective" the other stat becomes (this is not entirely true). Let´s get to an example: You have 75% damage reduction, 0 defense and 3 level 5 legend gems socketed (that´s 11,6%) and you receive 100 damage. Now let´s get to the math.
100 * (1*(1-0,75*1-0,116)
= 100 * 0,221
= 22,1
So you´re reducing 77,9% of the damage as the 11,6% only affect the remaining 25% damage you take. Since we´re reducing an additional 2,9% we can double check this by multiplying.
25*0,116 = 2,9
The math checks out so the formula i used above should be correct.
How does all of this affect defense ?
Let´s say your taking 100 damage,50 defense and 0% damage reduction.
100-50 = 50
You should on average take 50 damage from that source (once again, damage fluctuation makes this kinda hard to test).
If we say that you´ve got 50% damage reduction and 0 defense while normally still taking 100 damage it would look like this.
100 * 0,5 = 50
So in both cases we´ve reduced 50 damage (the %-damage reduction being extremely high compared to the defense and the fact that reaching 50 defense is way easier than reaching 50% damage reduction doesn´t matter because we´re working with percentages.
If we apply both at once it´ll look like this:
(100 - 50) * 0,5 = 25
Since both alone reduce 50 damage but both together only reduce 75 damage we´re "loosing" 25 damage that we would normally reduce somewhere. Now the question is, are we loosing damage that is reduced by the defense or the %-damage reduction ?
If we write this down differently we can change it up a bit.
100 - 50 = 50
50 * 0,5 = 25
This would make it look like the defense is reducing the amount of damage that get´s reduced by the damage reduction, if we write those two steps down differntly though:
100 * 0,5 - 50 * 0,5 = 25
This is still the same (not only the result is the same but it´s still the same calculation as the next step to make that shorter would bring you back to where we started ((100 - 50) * 0,5 = 25).
This means that your defense is basically lowering the damage that is reduced by your defense even though the defense is calculated before the damage reduction and this is only made worse by legend gems as those basically only increase the amount of damage that is percentually reduced which then again affects the damage that is reduced by your defense.
If you somehow manage to get three LOT gems to level 10 you would get 12,8% damage reduction for every stone for a total of 38,4% which would get your total damage reduction up to 84,6%.
So yeah, your defense would only be reducing 15,4% of the damage that it would reduce without LOT gems and damage reduction which is one of the reasons why "some" people feel like defense is somewhat useless (if I increase my def by like 100k I take roughly 20k damage less). I remember that xProtoypeT wrote something similiar, here is the quote.

'MDEF and PDEF are broken stat(in bad way, not good) They don't work well what so ever, I've tested it and 100k mdef/pdef only reduces about 20k Damage recevived which is super low and getting MDEF/PDEF is not easy either.'

(Sry for getting this into your inbox because I quoted you)

Increasing your defense and damage reduction will always lower the damage you take no matter what, increasing your damage reduction does not mean that you suddenly take more damage because your defense is less effective (some people were confused about that when I explained it to them so I´ll just put that here).

And now to get back to the part above where I said that LOT gems and damage reduction work multiplicatively and that they reduce how effective the other stat is. That´s acutally only correct in the sense that the added damage reduction is lowered, the stats acutally scale exponentially with each other (and themselfs for that matter). What do I mean by that ? Every single %-damage reduction you get that get´s you closer to 100% acutally makes able to take more damage than the previous %. Let´s say you have 100 health and make two examples where you´ve got 10% damage reduction and one where you´ve got 20% and calculate the amount of damage that you could acutally take (basically the amount of HP that would be equal to your current HP and %-damage reduction without the damage reduction). Let´s take 100 HP as a baseline.
100 / 0,9 = 111,11...
So 10% reduction means that you can take slightly more than 11% more damage than without damage reduction. So 20% should be 22,22% ? Nope
100/0,8 = 125
That´s already 25% more. If you would make this into a graph you would see that it scales exponentially which means that your defense is getting worse and worse the more damage reduction you have while you´re HP gets better and better. At 75% damage reduction your HP is 4 times as valuable as without damage reduction while your defense get´s reduced to 1/4 of it´s originial value (16 times difference compared to 0% damage reduction)

If you were to acutally get full legend gems your HP would be nearly 650% more valuable while your defense would be sitting at 15,4% of it´s orginial effectiveness (your HP is now 42,17 times more effective than with 0% damage reduction). Throw in armor pen for PvP and your defense is even less effective unless you have the Sunder debuff on you or the Bloodpool debuff from a priest (at which point you´re most likely at 0% damage reduction. On the other hand: your LOT stat be completely negated by your enemies LOA stat which means that your defense will realistically be slightly "better" even without debuffs.

[xPrototypeT]

never thought i'd get quoted on that kek, but basically mdef/pdef only good for pvp when you have enough crit def to counter all crit dmg obtainable in game and even then you're gonna need some millions