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Combat formulas

Posted: Mon Sep 08, 2014 5:37 pm
by Bozzax
Sigh I just noticed that Bruglirs EPIC work on warhammer combat formulas is gone. Did anyone save those posts containing all the combat formulas or are they “lost in time like tears in rain” (Bladerunner)? :cry:

Re: Combat formulas

Posted: Mon Sep 08, 2014 6:46 pm
by Idrinth
I think I got them, using them in my tank-calculator.
Will have a look, give me a sec.

Re: Combat formulas

Posted: Mon Sep 08, 2014 8:11 pm
by Idrinth
found the calculation-spreadsheet at least: ... ompare.ods

Re: Combat formulas

Posted: Wed Sep 10, 2014 7:55 am
by altgrimreaper
I think I found it:

Combat formula stuff, backed up from bioware forum!

Postby Bruglir » 20 December 2013, 19:05

let me start by sayin, sorry this has taken me so long to put online. and also that this isn't intended to be a walkthrough/step by step guide to how combat works in WAR. although it's certainly the basis for the damage calculation tools i've been building.

i'll also say that this is an ongoing work in progress, and some of the formula is things that i've tested so extensively that i know it must be that way, and other parts are theorys i haven't had a chance to completely test yet (i'll try to label those parts as i go) but "seem" to be largely correct. i'm more than open to scrutiny too, and when asked i'll provide whatever evidence i have to support theoretical data.

you will also see that "effective rank" is used in most of the formula. the way effective rank is worked out is fairly simple, if your renown rank is above 80, you do:
rank+TRUNC((renown-80)/4)=effective rank
TRUNC = truncate (round down)

for example, rank 40 renown rank 87 would be:
40+TRUNC((87-80)/4)= effective rank 41

IF at any point you see "<defender rank>", then it is the defender rank ONLY, and NOT their effective rank.

another important thing to note is that all of the combat formulas are truncated on the server end (As far as i'm aware anyway).

let's start with defences.
All defence calculations are done in two parts, the first is a statistic check made up of offensive vs defensive stats, they are coupled as follows:
Ballistics skill vs Initiative = Dodge

Strength vs Weapon skill = Parry

Intelligence vs Willpower = Disrupt

the first part of the formula is:
<defensive stat>/<offensive stat>*0.075 = base defence chance (this is capped at 25%)

the second part of the formula is:
<defenders increase in defence> - <attackers reduction in defence>

the complete formula is:
(<defensive stat>/<offensive stat>*0.075)+(<defenders increase in defence> - <attackers reduction in defence>

example of the formula in action:
(900 willpower/1050 intelligence*0.075)+(0.1-0.03)=13.42% disrupt chance.

note - your tooltip is often inaccurate as it will ALWAYS show the following as your defence chance (and therefor doesn't take into account actual enemy stats or offensive bonuses they may have):
<defensive stat>/(7.5*<your effective rank>+50)*0.075+<your defence bonus>

example of the above tooltip in action:
900 willpower/(7.5*40+50)+0.1=29.28% disrupt chance (tooltip will show).

BLOCK, is an exception to the above formula, block counters all offensive stats and is also done in two portions, the first being the block rating vs stat.
<shield block rating>/<offensive stat>*0.2 (capped at 50%)

you then add any block bonus the defender has, and deduct any reduced chance to be blocked the attacker has, remember that two handed weapons reduce block by 10%.
(<shield block rating>/<offensive stat>*0.2)+(<defender block bonus> - <attacker block reduction>)

critical hit rates are affected by defenders initiative vs attackers rank, in the following way:
(7.5*<attacker effective rank>+50)/<defender initiative>/10

you then add any crit chance modifiers from the attacker, and subtract any crit chance reduction the defender has:
((7.5*<attacker effective rank>+50)/<defender initiative>/10)+(<attacker crit bonus> - <defender crit reduction>)

again, important things to note:
in ALL cases, your tooltip will always show the ATTACKER values, as (7.5*<YOUR effective rank>+50).

any ability that says "will almost always" or "virtually", means +/- 100% (depending if it's "will almost always block/parry/critically hit" would add 100%. or "is virtually undefendable" would subtract 100%)

any absolutes such as "you will never" or "undefendable" generally mean multiply the end result (example: for healer sovereign 8 piece bonus, multiply the complete crit chance formula by 0)

the way damage is calculated, general points:
Damage appears to be calculated in sequence, starting with tooltip damage (if using abilities) which then gains a dps contribution from weapons (or not in the case of most magic abilities) and then gains stat contribution. this total is then mitigated by armour or resistances.

mitigation from toughness is calculated during the stat contribution part of the formula.

damage bonus and reduced damage are calculated from the base damage and the ATTACKING stat contribution, but before toughness is applied.

critical damage is calculated after toughness is applied but before mitigation from armour or resistances.

all bonuses to damage (base or critical) are additive.

all reduction to damage (base or critical) is multiplicative.

stats are divided by 5 for abilities, and 10 for auto attacks.

dps contribution differs depending on duelwield or single weapon.

duelwield dps contribution is: <mainhand dps> + <offhand dps> * 0.45

single weapon dps contribution is: <mainhand dps>

so a breakdown of the formula would look like this:
((<tooltip> + <dps contribution>)+(<stat coefficient>*(<offensive stat>+<power stat>)/5))*(1+<damage bonus>)*(1-<damage reduction>)-(<stat coefficient>*(<toughness>+fortitude>)/5) = <damage>

<damage>*(1+((0.5+<crit damage bonus>)*(1-<crit damage reduction>))) = <crit damage>

<damage> OR <crit damage> * (1-<mitigation from armour or resistances>) = <final damage>

Auto Attack formulas:
duelwield auto attack strikes have a main hand hit, and a 45% proc rate for an offhand hit.

two handed weapons do not get offhand procs (i've been asked so i felt the need to point it out).

for two handed weapons, calculate as a main hand weapon


so, as a general rule the following is a breakdown of auto attacks:
((<mainhand dps>*<mainhand weaponspeed>)+(<mainhand weaponspeed>*(<offensive stat>+<power stat>)/10))*(1+<damage bonus>)*(1-<damage reduction>)-(<stat coefficient>*(<toughness>+fortitude>)/10) = <mainhand damage>

((<mainhand weaponspeed>-<offhand weaponspeed>)*<offhand dps>+<offhand dps>*<offhand weaponspeed>*0.9)+(<mainhand weaponspeed>*(<offensive stat>+<power stat>)/10))*(1+<damage bonus>)*(1-<damage reduction>)-(<stat coefficient>*(<toughness>+fortitude>)/10) = <offhand damage>

multiply <mainhand damage> or <offhand damage> by the critical damage formula above, for critical strikes.

on to mitigation!
anything that says it ignores a % of armour/resistances, does so at the END of the armour/resistance VALUE calculation, and is multiplicative.

abilities that ignore a set value of armour/resistances, do so at the beginning of the armour/resistance VALUE calculation and is additive.

Resistances are pretty easy to work out, there's an "IF" calculation in the formula dependant on whether a player has more than 40% mitigation from a resistance, if they do then anything above it is divided by 3.

resistances are therefor calculated like this:
IF (<defender resistance>/(<attacker effective rank>*8.4))*0.2 = more than 0.4

THEN DO ((<defender resistance>/(<attacker effective rank>*8.4))*0.2-0.4)/3+0.4

ELSE DO (<defender resistance>/(<attacker effective rank>*8.4))*0.2

Physical mitigation values were somewhat annoying to figure out. much like everything else they're tied into a players effective rank, however it's done in a strange way. what appears to be happening (and i welcome feedback on this) is that once you move past renown rank 84 (effective rank 41 and onwards) the game adjusts the amount of weaponskill you have. if you are renown rank 83 or lower then it doesn't affect you too badly, although your penetration level will change as you rank up. the armour penetration formula looks like this:

THEN DO (<attacker WS>*(40/<attacker effective rank>))/(7.5*<defender rank>+50)*0.25=<attacker pen>

ELSE DO <attacker WS>/(7.5*<defender rank>+50)*0.25=<attacker pen>

you add any armour penetration bonus for the attacker, and subtract any reduced armour penetration the defender has from <attacker pen>

the formula for defender mitigation is:
<defender armour>/(<attacker effective rank>*44)*0.4 = <defender mit>

the complete formula then, is:
<defender mit>*(1-(<attacker pen>+<attacker pen bonus>-<defender pen reduction>))=<total mitigation>

for a complex example of the order in which the formula is carried out, we'll use a marauder who has impale, and the piercing bite tactic (ignores 50% of your opponents armour), our defender will start with 5000 armour, and impale will ignore 900.
((<defender armour>-<impale>)*(1-<piercing bite>))/(<attacker effective rank>*44)*0.4


or in the case of a witch hunter or witch elf using torment or agonising wound, that ability would do the following:
(defender armour * (1 - 1))/(40*44)*0.4

thereby reducing the armour to 0.

Re: Combat formulas

Posted: Wed Sep 10, 2014 2:24 pm
by Bozzax

Glad to see those aren't lost and thx

Re: Combat formulas

Posted: Wed Sep 10, 2014 5:13 pm
by Bozzax
Here is another post worth salvaging. The guy who wrote it was An.. (somthing).
The code basically involves the following steps:
1: The weapon dps contribution is calculated first: damage1 = weapon dps x weapon speed

2: Offensive stat term is calculated next: damage2 = (offensive stat + power)/10 x weapon speed

3: Mitigation due to toughness is calculated next: mit1 = (toughness + fort)/10 x weapon speed

4: Then they are combined: damage3 = damage1 + damage2 - mit1

5: class based percentage modifers are applied. These include such things as choppa/slayer's rage mechanic, SW's Vengeance of Nagarythe, class based tactics such as Flanking, Taste of Blood, etc.
damage4 = damage3 x class based % modifiers

6: Mitigation due to armor is calculated: mit2 = damage4 x armor% x (1 - weapon skill armor bypass %)

7: Damage after armor mit is calculated: damage5 = damage4 - mit2

8: Crit damage % modifiers to damage as well as debuffs to this damage from Trivial Blows are applied. Then other % modifiers are applied such as gear-based % modifiers, Live Event % buffs, and % debuffs from things such as detaunts, Challenge, Guard, etc. I'm not sure if class-based % damage debuffs such as Crippling Strikes and Dragon's Talon are applied here or at Step 5.:

damage6 = damage5 x (1 + crit damage %) x (1 + gear damage % modifiers) x (1 + 10% live event buff) x etc..

This is the damage value that appears in the combat log.

9: Total mitigation is calculated by applying the same % modifers from Step 8 to (mit1 + mit2):
total mit = (mit1 + mit2) x (1 + crit damage %) x (1 + gear damage % modifiers) x (1 + 10% live event buff) x etc.

This is the mitigation value that appears in the combat log.
Hmm Annaise, Anaise or somthing just cant remeber the name :mrgreen:

Re: Combat formulas

Posted: Wed Sep 10, 2014 6:44 pm
by Tesq
ye annaise had 3 different pg with almost same name, almost all of thing he wrote on combat formula are right

Re: Combat formulas

Posted: Wed Dec 02, 2015 9:53 am
by talissera
Guys, anybody have magic damage formula?
Does raw damage of staff scale with overall damage from a spell?

Re: Combat formulas

Posted: Wed Dec 02, 2015 10:22 am
by Bozzax
No Weapon DPS (of staffs) don't affect casters spell damage (1.4.8).

Was being tested/evaluated/considered in the 1.4.9 release that never made it into the game.

Re: Combat formulas

Posted: Wed Dec 02, 2015 10:54 am
by talissera
Thanks man!
Double thanks for old melee posts!!