Following Praxy delightful find of a Gyrfalcon's Foote (for me of course), I've been changing a lot of my active abilities around and I'm now using Phalanx.

One of the cool things about Phalanx is that it has ZERO variability on damage (at least when used with the Bowmen rune). This makes it possible to do a lot of interesting testing on all damage modifying stats in the game. Here's a list of what I've found out already:

Sheet DPS and tooltip DPS increase (for primary stat):
Comparing a set of gloves without/with strength:

• Tooltip: +5.5% damage
• Sheet DPS: 313,750 / 331,140 = 5.54% damage increase
• Phalanx damage: 658,421 / 694,914 = 5.54% increase

It seems sheet DPS and the tooltips are actually precise!

Elemental damage:
+Elemental damage is fairly straightforward, it simply adds +x% damage to any ability of the correct damage type.

Damage without/with bracers with +13% physical damage (and no other damage modifying stats):

• 817,764 / 924,073 = 13% increase

Ability damage:
+Ability damage works exactly the same as +elemental damage.

Damage without/with helm with +12% Phalanx damage (and no other damage modifying stats):

• 867,711/971,836 = 12% increase

Stacking primary stats, elemental damage and ability damage:
Damage without/with the bracers/helm used in the examples above (+5.54% sheet DPS from gloves, +12% Phalanx damage from helm, +13% physical from bracers):

• Primary stat + elemental (str. + 5.54%, +13% physical): 658,421 / 785,253 = 19.26% increase
• Primary stat + ability (str. + 5.54%, +12% ): 658,421 / 778,304 = 18.2% increase
• Elemental + ability (+13% physical, +12% Phalanx): 658,421 / 833,298 = 26.56% increase
• All together (str. + 5.54%, +13% physical, +12% Phalanx): 658,421 / 879,484 = 33.57% increase

How they stack:

• Primary stat + elemental: (1 + 5.54%) * (1 + 13%) = 19.26% increase
• Primary stat + ability: (1 + 5.54%) * (1 + 12%) = 18.2% increase
• Elemental + ability: (1 + 13%) * (1 + 12%) = 26.56% increase
• All: (1 + 5.54%) * (1 + 13%) * (1 + 12%) = 33.57% increase

So it seems everything stacks multiplicatively meaning that the total effect is always going to be bigger than the sum of the individual components. It also means that you can't just add numbers up to determine if an item is better or another, for example:

• Bracers with +25% sheet DPS and no elemental damage = 25% increase
• Bracers with +14% sheet DPS and +10% elemental damage = 25.4% increase

The differences are usually very small though, so in most cases it's fine just to add the numbers.

For the sake of completeness:

• Double strength items (+6.1%/+9.5% sheet DPS): 760,785 / 879,484 = 15.6% increase
• Double elemental items (+13%/+14% physical): 530,839 / 674,165 = 27% increase
• Double ability items (+12%/+15% Phalanx): 802,411 / 1,019,061 = 27% increase

All are additive.

Critical Hit Chance (CHC) and Critical Hit Damage (CHD):

CHC damage increase:

• 100 * ItemCHC * CurrentCHD
  1 + CurrentCHC * CurrentCHD

CHD damage increase:

• 100 * CurrentCHC * ItemCHD
  1 + CurrentCHC * CurrentCHD

Comparing amulet with no DPS stats to amulet with 10% CHC (current CHC/CHD = 35%/311%):

• 100 * 10% * 311% = 14.89% increase
  1 + 35% * 311%
• Tooltip increase: 14.9% increase

Comparing amulet with no DPS stats to amulet with 83% CHD (current CHC/CHD = 35%/311%):

• 100 * 35% * 83% = 13.91% increase
  1 + 35% * 311%
• Tooltip increase: 13.9% increase

Attack speed:
Comparing amulet with no DPS stats to amulet with +5% AS:
Tooltip increase: 5% increase

AS stacks additively with itself (i.e. two items with +5% AS = +10% damage increase).

Holy Cause (Crusader passive):
The damage component only takes effect when you are using a weapon with +Holy damage (+min - +max holy damage, not +x% holy damage). It increases damage of any ability regardless of what type of damage it is (Phalanx is physical for example).

Damage without/with Holy Cause and a weapon with +poison damage:

• 935,359 / 935,359 = 0% increase

Damage without/with Holy Cause and a weapon with +holy damage:

• 871,847 / 943,198 = 8.18% increase

Now works for any type of damage.

The tooltip states the +10% damage is applied to you weapon damage, i.e. not the damage your ability hits for, so it makes sense that the final output is somewhat different from the +10% stated in the tooltip.



Say if you think there is something else worth testing.

the base dmg from your weapon is always physical.
so the holy dmg increase is only increasing the bonus holy dmg the weapon has.

if your weapon has 2k dmg of which 1200 is holy then its safe to say the 10% holy increase will make your weapon deal 2120 dmg. which will result in a smaller than 10% increase for the total calculation. (6% in this example)

this is also why physical dmg is so cool you get a "free" bonus from the base weapon dmg.
and it also explains why +x% dmg doesn't seem to be right for any class.. it only works for physical bonus dmg weapons(+x dmg instead of +x [elemental]dmg)

I thought the + elemental damage only affects abilities though, which is what you hit things with not the physical damage of your weapon?

No, the shown damage number on your weapon (that includes +elemental damage, +damage% and +attack speed% and red gems) affect the damage of all your abilities regardless of what type of damage it is.

The +damage% is going to be fixed so that it affects all types of elemental damage as well, so it may be worthwhile hanging onto items with +damage%.

Added a section about critical hit chance/damage - can anyone explain why the numbers aren't equal? Any idea of what to trust (I'd say the math, not the tooltip)?

first we must introduce the dmg coefficient to determine the overall increase = 1+(CHC*CHD)
your total dmg with 0%CHC is 1.
if you have 5% CHC and 50% CHD, the dmg coefficient is 1.025. 1+(0.05*0.5) = 1.025
if you have 50% CHC and 500% CHD, the dmg coefficient is 3.5. 1+(0.5*5 = 3.5


now based on your information the dmg coefficient will increase by 11.3% in the first example.
if you had a dmg coefficient of 1 which will become 1.113, however you already pointed out this isnt the case you must have some number of CHC which makes the dmg coefficient higher than 1.

if you had no crit chance at all from items you would still have 5% from your base character.
the dmg coefficient for this type of character would be 1+(0.05*2.25)=1.1125.
adding 11.3% to this makes a dmg coefficient of 1.1125*1.113 = 1.238.
now we can go backwards as the CHD didnt change:
(dmg coefficient-base dmg coefficient)/CHD = CHC.
(1.238-1)/2.25 = 0.10577
0.10577-0.05=0.05577 ==> 5.577% increased critchance

so its pretty obvious you didnt have no CHC at all nor did you have the 5% base CHC.
im not gonna bother myself trying to figure your CHC out.. but the math and the tooltip increase are correct.

just noticed the attackspeed part. its not entirely correct.

compared to no attackspeed the total of all your attackspeed is exactly the amount it will increase your dps. however if you have lets say 5% from item A allready equiped and you were to equip item B with 5% aswell the increase isnt 5%. the dps is allready at 105% of normal and it will increase to 110% making the added value less then 5% effective.

110%/105%=104.7%
[new total attackspeed] / [previous attackspeed] = [effective attackspeed gain]