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| Author | Enchants and Damage Formula |
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https://www.lordswm.com/help.php?section=34
>>If "Attack" (A) of the attacking stack is bigger than "Defence" (D) of the defending stack, then
Damage = [1 + 0,05 (A-D) ] * [1 - 3*Y/100]
>>If (A) is smaller than (D), then
Damage = [1 - 3*Y/100] / [1 + 0,05*(D-A)]
I have a lot of questions regarding how the damage formula works. In the above 2 simplified formulas I'm looking for an explanation of how the damage formulas and enchants work.
1. Does variable Y work against neutral creatures (hunts, merc quests, caravans, survival tournaments, events, etc)?
2a. How do weapons with increase in melee/range damage affect above formulas?
2b. How do armors with decrease to melee/range damage affect above formulas?
3a. How do talents that increase melee/range damage affect above formulas?
3b. How do talents that decrease melee/range damage affect above formulas?
4a. How do elemental weapon enchants affect the formulas? I know that E5 + E5 is less than E10, so no need to explain this.
4b. How do elemental defense enchants affect the formulas? I know that again E5 + E5 on armors is less than E10. It works in the same exact way as weapon enchants do. But how do elemental defense enchants, magic resist from arts, and resist from talents work together?
5a. How does [I] weapon enchant affect the formulas?
5b. How does [D] defense enchant affect the formulas?
And lastly how does all the above variables I brought up affect each other?
And bonus question: At what defense point does [I10] and [F10] enchants do the same damage? Please show your work. Prove your answer. | | I have a feeling that you already know the answers, at least the one to the bonus question. | From Arctic Infos :
Let's say something would do 100 damage with the benefits of a simple Mithril Longsword without enchants.
Then a 5*12% would deal this much:
- First, physical damage. Defense is decreased by 12%, so the damage would be: (Z is number of attackers in stack, take it 10 for this example)
100/Z=RND(Min,Max)*(1+0.05*(Attack-Defense))= 100/10=RND*+0.05*Att*RND-0.05*Def*RND.
New_damage/Z=N/10=RND(Min,Max)*(1+0.05*(Attack-0.88*Defense))= N/10=RND(Min,Max)*+0,05*Att*RND-0.044*Def*RND
Subtract one from another:
(N-100)/10 = (RND-RND)+(0.05*Att*RND-0.05*Att*RND)+(0.05*Def*RND-0.044*Def*RND);
N-100 = 10*0.006*Def*RND.
New damage = 100 (the old one) PLUS 6% of Defense of the target * Random (minimal damage; maximal damage) of the attacking creature.
Let's say we attack Behemoths with Shrews. Shrew damage is 5-7; Behemoth defense is 22. Shrews would normally deal 100 damage with some determined RND(min damage; max damage) (their damage is 5-7) - let's say it was 6. Thus,
N = 100 + 0.06*6*22 = 107.92 physical damage.
After that, all elemental coefficients apply.
Extra 12% with fire is 12.95 damage with fire
Same bonus damage with air, water and earth.
If those behemoths have no resistances, total damage will be:
107.92+4*12.95=159.72 rounded up to 160 damage.
5*12%... 60% extra... sounds quite right, eh? ;-)
NOW WHEN THERE ARE ENCHANTMENTS OF ONE TYPE ON MULTIPLE WEAPONS - that's when that formula comes in.
If there is a longbow with another 5*12% - that's where you use the formula, but not to do what you do, rather to understand what is the final effect of "Extra fire", "Extra air damage", "Ignore defense of target" and all other. After all, when you are in combat and Shift+Double click your character, you are able to see only the final effect, not the effect per every item you are wearing.
THAT is where you start counting with the help of commutative formula.
You have 2 weapons of 5*12%. That means, there are two sources of Extra air damage, and all other. What is the final effect of extra air damage?
It is not 1.12+1.12=1.24!!
It is 2-(1-0.12)^2=1.2256.
So, those two weapons with 5*12% will give a final effect of
22.56% extra fire elemental damage
22.56% ---- air ----
---
---
22.56% ignore target defense.
In this case, the previous formula would become
N-100 = 10*6*22*(0.05*0.2256)=14.89,
so the new damage is 114.89.
THen elemental coefficients are 22.56%*4 of that much, so the final damage in case of no elemental resistance is
114.89*(1+4*0.2256)=218.56 rounded up to 219 damage.
Two enchants of 5*12%? hmm that's extra 120% damage, right?
Still sounds rational ;)
Now you can do the same calculations for the third weapon with 5*12%.
I can foretell =) The damage would be somewhere around 280,
(3 weapons of 60% each) but you can check =)
So now let's start the debate with pantheon. | A1: Y does not work against creatures in hunts, so I assume it doesn't work for neutral creatures in general. Proof is in my fight against magi:
https://www.lordswm.com/warlog.php?lt=-1&warid=21251246
54 magi (A - 10) attack my magi (D - 16). Damage is 7-7. So, ignoring Y:
Damage = 54*7/1.3 = 291 which is what actually happens.
2 and 3a: Just multiply by the factor (1 + p), where p is the percentage. If there are many different factors, multiply by them all: (1 + a)(1 + b)(1 + c)...
2 and 3b: Similarly, just divide by the factor (1 + p). Again, it scales to many factors.
Example: 50 Hobgoblins, with advanced offense, battle fury and a ruby gladius (+ 7% melee damage), with attack 25, attack shrews, defense 19, basic defense and wearing platemail (- 5% melee damage).
Hobs base damage (taking attack and defense into account):
Damage = 50*3 * (1 + (6*0.05)) = 150 * 1.3 = 195 damage.
Taking the factors into account:
Damage = 195 * (1.2 advanced offense) * (1.07 ruby gladius) / ((1.1 basic defense) * (1.05 platemail))
So damage = 217.
4: already answered. One clarification though, is that it only comes out to around 60% because you chose behemoths as the defender. If it was something like goblins, it would be only 48% more damage, so 148 damage.
5: Ignore defense does exactly that - ignores some defense.
eg. If the defending stack has 30 defense, then I10 reduces it to 27 defense during damage calculation. Again, covered in post #3.
Bonus question:
At defense = 20, I10 ignores 0.1 * 20 = 2 defense. So (A-D) goes up by 2. Since each (A-D) contributes 5% extra damage, the I10 effectively increases damage by 10%, which is exactly what F10 does. But this isn't entirely true, because the extra damage done by I10 can be compounded, as you see in post 3, whereas the damage done by F10 does not (and can be reduced by immunities, or increased by grotesques). | Bonus question:
It is not possible to conclude without knowing the attack parameter of the attacking stack. As qulows has covered, at defense = 20, I10 contributes to (A-D) to go up by 2. However it is wrong to say that it increases damage by 10%.
Attack 40 attacks Defense 20: (A-D) was initially 20, I10 will calculate (A-D) to become 22. Hence, the multiplier increases from 2 to 2.1, which is a 5.0% increase in damage by having I10. F10 would have resulted in 2 x 1.1 = 2.2 damage multiplier.
Attack 20 attacks Defense 20: (A-D) was initially 0, I10 will calculate (A-D) to become 2. Hence the multiplier increases from 1 to 1.1, which is a 10% increase in damage by having I10. F10 would have resulted in 1 x 1.1 = 2 damage multiplier.
So as you can see, when using ignore defense enchants, different attack parameter values have different results in the percentage increase in final damage. | | Does that mean ignore defense is useless when Xbow is in aimshot situation? | 5: Yeah, I forgot about the fact that F10 affects the whole damage.
Suppose we have attack A, and defense D (which we want to find), and a base damage M (Just the result of multiplying the number of creatures by the damage).
Assume A >= D.
Original damage = M*(1 + (0.05 * (A-D)))
F10 increases damage by 0.1*damage, so damage = 1.1*M*(1 + (0.05 * (A-D)))
I10 decreases defense to 0.9D, so damage = M*(1 + (0.05 * (A-0.9D)))
These two are equal. So, 1.1M (1 + 0.05A - 0.05D)) = M (1 + 0.05A - 0.045D)
Cancel the M, and multiply out:
1.1 + 0.055A - 0.055D = 1 + 0.05A - 0.045D
1.1 - 1 + 0.055A - 0.05A = 0.055D - 0.045D
0.1 - 0.005A = 0.01D
D = 10 + 0.5A
But this is only when A >= D, which is when A >= 20.
When A < 20, we will need A < D. Then, with the same variables:
Original damage (no enchants) = M / (1 + 0.05(D-A))
With F10: damage = 1.1M / (1 + 0.05D - 0.05A)
With I10: damage = M / (1 + 0.045D - 0.05A)
(Assume reduced defense is still larger than attack)
Equating the two, cancelling the M's, and cross-multiplying:
1.1 + 0.0495D - 0.055A = 1 + 0.05D - 0.05A
0.1 - 0.005A = 0.0005D
Multiply by 2000
200 - 10A = D. This is when 0.9D >= A, i.e. 180 - 9A >= A, 180 >= 10A, A <= 18
So, from A<=18, D = 200 - 10A. | To summarize:
For A >= 20, D = 10 + 0.5A
For A <= 18, D = 200 - 10A
For A = 19, I tried to solve the equation but it doesn't seem to work
@6: Ignore defense does the same thing in aimed shot for xbows, it's still useful. It's useless on low defense creatures (like lizard charge). | #6
Yes, aim shot means 100% ignore defense, so for aim shots additional ignore defense from enchants is useless. | | I always thought aimed shot increased the amount of damage (like , as opposed to ignoring the defense, but obviously I was wrong. Did this change recently, or was it always there? | | It's always been ignore target defense | Well, if you need the exact numbers (i.e. with a proof in battle) then I give you some calculations I did earlier.
From: tony1745
To: Robai
Subject: why my dmg is so low
https://www.lordswm.com/warlog.php?warid=494918427 -my low dmg battle
https://www.lordswm.com/warlog.php?warid=491680831 -you super high dmg
From: Robai
To: Re: tony1745
Subject: why my dmg is so low
In your battle:
Swordsmen deal 227 damage to Spawns. 38 perish.
Your Swordsmen had 15 attack.
Spawns had 2 defense, so the difference was 15-2 = 13.
It means that your Swordsmen had bonus 13*0.05 = 0.65, i.e. 65% bonus to damage.
Base damage for Swordsmen is a random number from 2 to 4.
So you your 51 swordsmen was able to do
min damage = 51*2*1.65 = 168.3
max damage = 51*4*1.65 = 336.6
And indeed the number 227 is between 168.3 and 336.6
Now let's look at my battle.
Swordsmen deal 335 damage to Titans. 1 perish.
My Swordsmen had 26 attack.
Titans had 30 defense, so the difference was 26-30 = -4.
It means that my Swordsmen had penalty -4*0.05 = -0.2, in such case the damage is divided by 1.2, the exact formula is here:
https://www.lordswm.com/help.php?section=34
Base damage for Swordsmen is a random number from 2 to 4, but I had GH set, which gives +1 to damage, so it was random number between 3 and 5. But they had Bless (+50% min dmg), which brings it to random number between 4 and 5.
But GH set gives +40% to damage. Moreover, it was enchanted by +17% dmg.
I also had GH sword, which gives additional +15% dmg to melee.
So my 45 swordsmen was able to do
min damage = 45*4*(1/1.2)*1.4*1.17*1.15 = 282.555
max damage = 45*5*(1/1.2)*1.4*1.17*1.15 = 353.19375
And indeed the number 335 is between 282.555 and 353.19375
Best regards | 5b. How does [D] defense enchant affect the formulas?
I don't believe anyone answered this one yet. Does anyone know does this enchant decrease the attacker's Attack parameter, increases the defender's defense parameter, or affects the formula some other way? | @13:
The description seems pretty self-explanatory to me. Is there any reason for your thinking that it's more complicated than it seems? | | It decreases the attack parameter of the attacking stack by the stated percentage. Quite the opposite of ignore defense. | for Geryon:
Yes, the basic damage formula given to us has no explanation or includes any other variables for all the various things that we know affects damage: enchants, special weapon modifiers (increase melee damage%), talents, creature abilities, etc.
I have yet to really fully dive into and pick apart the above explanations. But you can easily see nothing is really all that simple.
In my original post I purposely left my questions open ended so people are free to come up with different comprehensive answers. In the end what I'm really looking for is a simple formula (as simple as can be in this situation) that includes all variables that affect damage. For example [F10][F10][F10] is F 27.1% and not F 30%. This type of calculation isn't officially stated anywhere. Also it is pretty simple that 27.1% extra damage is 27.1% extra damage. But let's put in talents that increase physical damage as well. Or what about arts/talents that increase F damage? We have many different variables that affect damage. How each are calculated or where they are inserted into the formula would affect the final outcome. | It decreases the attack parameter of the attacking stack by the stated percentage.
Again, where's the complication? | Okay, to give a formal formula for the effect of the defense enchant:
Assume the net defense enchant is d (as calculated in post #3 I believe), then:
Replace any instance of the variable A with the variable (1 - d)*A
For example, for the most basic damage with defense enchant (and in the end attack is larger than the defense):
Damage = Base damage * [1 + 0.05 (((1-d)*A)-D) ] | #18
Thanks. Now with all the other variables added, the formula can be complete. There are just too many assumptions how everything fits into that formula. And there's the complicated interaction of the different variables. | Many things that increase damage (say, +10%) work this way:
- you just multiply the previously calculated damage by 1.1
But this is not always true.
For example, let's say you already have "Advanced Offense" talent and now your melee stack can do some damage d.
"Expert Offense" would give you 10% more damage, but wouldn't be d*1.1, because 1.3 is not the same as 1.2*1.1 = 1.32, it means that it would be (d/(1.2))*1.3 instead.
As Pantheon mentioned, we have many assumptions.
I'll try to list some of them (I'm not 100% sure if they all are correct).
1) Weapon enchantment E8A9 increases damage this way:
- if there are no other enchanted weapons then you multiply previous damage by 1.17 (i.e. not by 1.08*1.09 = 1.1772)
2) If you have three weapons E8, E9A7 and E10A6F5 then you multiply damage by
1 + (1-(1-8*0.01)*(1-9*0.01)(1-10*0.01)) + (1-(1-7*0.01)*(1-6*0.01)) + (1-(1-5*0.01)) = 1.3386
3) Usually if you have damage bonuses from different sources (enchantments, bonuses from weapons like melee, talents, etc.) you just multiply corresponding factors.
Example:
For
E8, +15% melee (like GH Sword) and Advanced Offense talent
you multiply everything by 1.08*1.15*1.2 = 1.4904, not by 1.43 (8+15+20=43).
4) My guess is that even for "Cold Blade" talent (+15 Water dmg) you just multiply.
For example, if you have GH sword [W8] with Advanced Offense and Cold Blade talents you multiply the damage by 1.08*1.15*1.2*1.15 = 1.71396
I'm not sure if W8 + Cold Blade gives 1.08*1.15 = 1.242, maybe it should be 1.23 instead. Or maybe this way (since both are Water dmg bonuses):
1 + (1-(1-8*0.01)*(1-15*0.01)) = 1.218
I'm also not sure if Advanced Offense and Cold Blade gives 1.2*1.15 = 1.38, maybe it should be 1.35 instead (since they are both talents).
5) For Luck or Critical you multiply the overall damage by (1+Luck+Critical).
If Luck=1 and Critical=0 then you get double damage.
If Luck=0 and Critical=1 then you get double damage.
If Luck=1 and Critical=1 then you get triple damage.
(of course, for non Elf faction always Critical=0)
6) Any hunter set (H, MH, GH, Beast) gives +1 to damage and that is added to the base damage BEFORE any other effect takes place.
For example, GH set bonus (+1 and +40%) is added this way:
- if you apply +1 bonus and after that +40% then your Sprites will do (2+1)*1.4 = 4.2 dmg
not this way:
- if you apply +40% and after that +1 bonus then your Sprites will do 2*1.4+1 = 3.8 dmg
By the way, it interesting to note that it doesn't matter which you add first: +1 bonus to min and max or Bless spell effect (with any efficiency):
- if we apply +1 bonus and after that Bless spell (with t efficiency) then:
min_dmg = a+1 + ((b+1)-(a+1))*t = a+1 + (b-a)*t
max_dmg = b+1
- if we apply Bless spell (with t efficiency) and after that +1 bonus then:
min_dmg = a + (b-a)*t + 1
max_dmg = b + 1 |
This topic is long since last update and considered obsolete for further discussions.
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