Confused about when you multiply and when you add

I've read the mechanics thread, and I'm still confused about when you add multipliers together and when you multiply them. So I'm going to try and do all of these calculations, and hopefully someone will find the errors for me.

Let's say you have a Lightning Strike gem linked to a Lesser Multiple Projectiles gem linked to a Faster Projectiles gem linked to a Melee Damage on Full Life gem.

I'm choosing these skills because I have access to them, and because the projectile portion of the Lightning Strike isn't shown anywhere, so there's no way to find it out in game.


(Assume the Faster Projectiles is a level 1, I couldn't find a level 1 to link, stats are 30% increased speed, 10% increased damage)


Lightning Strike says:
2 additional projectiles
50% of Physical Damage converted to Lightning Damage
20% Less Projectile Damage

So, with absolutely no skills or stats, and a pure physical damage weapon, if you hit someone with a 100 physical damage weapon a melee hit would be 50 physical damage, and 50 lightning damage, and the projectile that flies out would be 40 physical damage and 40 lightning damage. That's fine, that's easy.

Lesser Multiple Projectiles says:
30% Increased Projectile Speed (we're going to ignore this one)
10% Increased Projectile Damage

So now we have a 10% increase to the projectile's damage. According to the mechanics thread:

"

In general, integer modifiers are applied before percentages. Percentage modifiers using the words "% increased" or "% reduced" stack additively with one another, while "% more" and "% less" modifiers stack multiplicatively.

So, we would increase the damage first, and then lessen it, right? At this point the order doesn't matter.
Hit: 50 phys, 50 light
Projectile: 44 phys, 44 light (80% of 55 damage, or 110% of 40 damage, either way works)

Next up is multiple projectiles:
2 Additional Projectiles
30% less Projectile Damage

Less modifiers should multiply together, so now our projectiles are only dealing 56% of the original damage (Right? 80% * 70%?).
Hit: 50 Phys, 50 Light
Projectile: 30.8 Phys, 30.8 Light (100 * 1.1* 0.8 * 0.7 * 0.5)

Now we get a multiplier increase, Melee Damage on Full Life:
30% More Melee Physical Damage When on Full Life

According to Mark_GGG conversion take place first, but all effects that would have applied to them originally still apply. Source.

Hit: 65 Phys, 65 Light
Projectile: 40.04 Phys, 40.04 Light (100 * 1.1 * 0.8 * 0.7 * 0.5 * 1.3) or (65 * 1.1 * 0.8 * 0.7)

Now we have all the simple stuff out of the way. Now lets add in passives, and a real weapon.


Related Passives:
125% Increased Elemental Damage
63% Increased Lightning Damage
54% Increased Physical Damage

An Apex Rapier starts at 25-57 Physical Damage (from now on we're going to deal only with the minimum to reduce the calculations by half).

25 Physical Damage
15 Cold Damage

The weapon adds an additional "Increased" 114% physical damage and Quality adds an additional "Increased" 19% physical damage.

So for Physical damage, we have 25 base, 114% increased, 19% increased, 54% increased and 30% more.

25 * (1 + 1.14 + 0.19 + 0.54) * (1.3) = 93.275 applied physical

Lightning Strike converts half of the base physical into lightning damage, but because it's a conversion, it recieves all of the previous physical modifiers as well as the 125% elemental, and 63% lightning.

25 * (0.5) * (1 + 1.14 + 0.19 + 0.54 + 1.25 + 0.63) * (1.3) = 77.1875 applied lightning damage

Cold damage is easy to calculate, 15 * (1+1.25) as it doesn't get any of the physical damage increases.

So a melee hit with Lightning Strike would deal:
Physical: 46.6375 damage
Lightning: 77.1875 damage
Cold: 33.75 damage

The projectile that flies out should have an additional 10% "increased" from the Faster Projectiles support gem, and a 20% "less" and a 30% "less" from Lightning Strike and Lesser Multiple Projectiles.

So now Physical damage would be: 25 * (1 + 1.14 + 0.19 + 0.54 + 0.10) * (1.3) * (0.8) * (0.7) * (0.5) = 27.027 applied physical

Lightning: 25 * (1 + 1.14 + 0.19 + 0.54 + 0.10 + 1.25 + 0.63) * (1.3) * (0.8) * (0.7) * (0.5) = 43.225 applied lightning

Cold: 15 * (1 + 1.25 + 0.1) * (0.8) * (0.7) = 19.74 applied cold

Projectile hit would deal:
Physical: 27.027 damage
Lightning: 43.225 damage
Cold: 19.74 damage

What's interesting to me is that the projectiles are composed of a different percentage of each element than the main hit. The melee hit is 29.6% physical, 49.0% lightning, and 21.4% cold. The projectile is 30.0% physical, 48.0% lightning, and 21.9% cold. This is because of where the 10% increase is applied, because it isn't 10% more.

Doing all of these calculations made me realize just how much more powerful straight damage increase mods are compared to % increase mods. Note that the weapon I linked SAYS it deals 58-133 physical damage. If it actually had a mod on it that was +33 physical damage instead of the 114% increase and 19% quality, so that the weapon still read 58 minimum damage the damage would be:
Melee hit:
58.058 Physical
128.934 Lightning
33.75 Cold

Projectile:
34.6237 Physical
74.3142 Lightning
19.74 Cold

That's a 40% increase to melee damage and a 43% increase to projectile damage. Just by changing a % increase mod to a flat damage mod.



So, can anyone catch any mistakes in there? This should be as close to a real situation as you could get (other than the fact that all the gems are level 1).

I didn't read it all, but it looked good.
For someone supposedly confused you didn't appear that way.

Yes + damage mods can be good, but more so when you have fast weapons that are low damage. Slower weapons like 2 handed hammers aren't that great for +damage mods.

"

Xapti wrote:

I didn't read it all, but it looked good.
For someone supposedly confused you didn't appear that way.

Yes + damage mods can be good, but more so when you have fast weapons that are low damage. Slower weapons like 2 handed hammers aren't that great for +damage mods.

Ya, I'm still not sure why anyone would want to use a slow weapon. The % multipliers affect your DPS by the exact same amount as a faster weapon, meanwhile the + addition modifiers give you a much much smaller DPS increase than they do for faster weapons.

Two (possible) reasons: mana cost and damage-per-hit, assuming equal DPS numbers.

The first one is straightforward enough: the faster you go, the more mana you spend. Spending less mana to get the same DPS output should come with some sort of tradeoff.

The second one is simply a function of the way armor works.

Now, it may well be the case that these factors are not enough to offset all the "straight" +damage mods you can stack, in which case the baseline DPS on slower weapons will have to be tweaked upwards. But there are reasons to take it slow sometimes.

Ok, I can see your point. You would pretty much have to plan your build on the foundation of using slow weapons it seems. Seems easier to just plan on attacking fast and keep trying to go faster.

"

Skivverus wrote:

Two (possible) reasons: mana cost and damage-per-hit, assuming equal DPS numbers.

The first one is straightforward enough: the faster you go, the more mana you spend. Spending less mana to get the same DPS output should come with some sort of tradeoff.

The second one is simply a function of the way armor works.

Now, it may well be the case that these factors are not enough to offset all the "straight" +damage mods you can stack, in which case the baseline DPS on slower weapons will have to be tweaked upwards. But there are reasons to take it slow sometimes.

3rd reason would be the way stun is implemented.
High damage hits have a higher chance of stunning the target.