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| Author | Attack, Defence and Damage |
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So I was curious how damage works, and how to best optimize stats, for example is more attack better than defence, or is 100 attack 0 defence better than 50 attack 50 defence and so on, however after spending over an hour I find it more complicated than I expected it to be. Does anyone have any thoughts on this?
For example one of the things I noticed is let's say your enemy has 100 stat points(by stat points I mean att or def), so let's say 50 att and 50 def. And let's assume you have 100 stat points in total as well. To be more explicit let's just say these are stats of two creatures and each gets to hit exactly once. The question is, how should you arrange your 100 stat points to best optimize the ratio of the damages you and your enemy deal? Turns out no matter how you arrange it makes no difference, so whether you have 100 att 0 def, or 50 att 50 def, or 0 att 100 def, it makes no difference.
So I initially thought no matter how you arrange stats it shouldn't make a difference, but it didn't quite convince me, as the equation when att>def is linear and when def>att (I think) is a reciprocal function. So I tried to find out what happens when you have more total stats than your enemy, how to best optimize your stats? So let's say your enemy has 100 att 100 def(I am using 100 as it might be easier to calculate with) and you have 400 stats in total. Let's say both your and your enemy's creatures have a damage range of 1-1, then the total damage your enemy would deal(without calculating any resistances or anything like that) when you have 400 att and 0 def would be 1+0.05*(100-0)=6, and you would deal him 1+0.05*(400-100)=16. So the ratio of your damages would be 16:6 or 8:3.
Now, what happens if you attack and defence are 200 each? Your enemy would deal 1/(1+0.05(200-100))=1/6, whereas you would deal 1+0.05(200-100)=6, therefore the damage ratio this time is 6:1/6 or 36:1, which is considerably more.
Now of course whether two take more attack or defence depends on a lot of other factors, for example charmers should take attack because they hit first and it helps their magic, and tribals should take defence because it helps them stack up tribal spirit, but besides all of this to the above calculations suggest that it is better to have attack and defence of a certain troop as close as possible?
By the way, further proof that it might be true, is that if you calculate the percentage of rate of change when your attack and enemy's defence is close, both equations show the % is more than when the attack and defence is far apart. | Lets say
if (att>def) then att-def= att surplus
If (def>att) then def-att = def surplus
Every att surplus increase damage by 5%, no matter how high is the att surplus it will always provide extra 5% damage per point
Now def is different, because you can't deal negative damage,even zero since the minimum damage is 1
Based on the equation in about the game section
10 deff surplus will decrease damage by 33.33%
20 def surplus will decrease damage by 50 %
30 def surplus will decrease damage by 60 %
40 def surpluss will decrease damage by 66.67 %
Notice the difference? Yes def surpluss will lose marginal effectiveness the more point in it.
But please consider that in battle we dont have same point to allocated and who strike first is matters. | Mostly depends enemy really I would say. For a lot of PvE battles the opponent has low stats (no hero) but high creature count. Frequently they will one hit irrespective of your def, so attack build is the only sensible choice, hence the most common as easiest.
Second main point is talents - namely offence and defence ones. Since they increase damage done or damage taken there impact is magnified depending on your build. So clearly offence talents become more effective with high attack, and defensive with more defence.
Frequently one does not know the opponent you are facing, so being able to second guess whether to laod attk, defence or even it out is not known. However Attack will usually prevail in this because the best form of defence is attack (or at least counter attack). Dead troops do not hit back (unless they undead of course!) The idea in any battle is to control the exchange of hits to be on your terms, defence would be used to maintain an implacable advance where ranged advantage was not present, while attack is better for those with a need to kill army before main contact.
For me the whole calculate the best is further fraught when you think of different tiers. IT is worth considering what your main units are, versus the main units of the enemy. For example if you have gobbo archers, you are always going to be hitting enemies and being hit by enemies with higher base stats than you. Plying defence would mean they just don;t hurt people, but would not probaby stop them dieing very easily, so I would think attack is better.
As a consequence I think that for many factions it is attack normally, but sometimes in pvp switch to defence or an even build. Some factions would never switch (like all elves). Some would rarely be attack (shadow barbarian). However most of this is decided by the faction, troops and talents rather than the direct damage calcs. | for krabylos:
Yes I know that, but I guess I was not clear about what I meant with percentage of rate of change
What you showed was just the percentage of change, which is the rate of change, but I was talking about the percentage of change.
Let's say when att>def the equation is f(x)=1+0.05x, and when def>att it is g(x)1/(1+0.05x). Note that x represents the absolute value of the difference between the attack and defence.
Then, we can take there derivatives:
f'(x)= 0.05 Which as you said is 5% rate of change at any point in f(x)
Whereas,
g'(x)= d/dx [(1+0.05x)^-1] = -0.05/(1+0.05x)^2
However just because their slopes are different doesn't mean that attack is superior to defence, as clearly the f and g functions are reciprocals of each other, they are equally important. However, I meant the % of rate of change, let me give you an example.
Let's say your enemy has 50 defence. When you have 70 att, you would do 2 damage. How about when you have 71 attack? You would do 2.05 damage. So by what % did your damage increase for one unit of attack from 70 att to 71? By 2.5%.
Now, let's calculate the % of change between 60 att and 61 att, it will be (1.55-1.5)/1.5= 3.33%, so it increased compared to 70 and 71 att, even though the f function itself is linear. At most it is a 5% change per attack, i.e. from 50 att to 51 att, therefore this proves that the percentage rate of change of the damage increases per unit attack as att-def approaches 0.
for Lord MilesTeg:
Yes I completely agree with you, there are many more factors that I have not yet taken into consideration yet, such as elemental damage, offence/defence talents, but I will try to soon calculate them as well :)
Other than that of course for practical purposes intuition is the way to go, such as what I mentioned before, charmers should always take more attack and tribals should take more defence :) | | Btw sorry for so many typo's! Hopefully it should get much in your way for understanding what I wrote :) | You need defence equal with enemy attack(i mean every creature attack, not just hero attack ).
Put all the rest in attack. | So clearly offence talents become more effective with high attack, and defensive with more defence.
I doubt the defensive talents work like that. At least from description of one of the example talents - basic defense says that it reduces melee dmg by 10%.
If you have high defense, the damage received by the player with this talent will already be less regardless of talent. Then a 10% further reduction seems less effective.
The exception would be if the 10% reduction from talent is factored before defense stat of the unit being attacked. | The exception would be if the 10% reduction from talent is factored before defense stat of the unit being attacked.
Even if this is the case, which i doubt.. the effect of talent will make the defense stat to be less efficient. See how in post 2 krabylos said Yes def surpluss will lose marginal effectiveness the more point in it.
| for virtual_vitrea:
I don't understand what you mean by The exception would be if the 10% reduction from talent is factored before defense stat of the unit being attacked.
It should make absolutely no difference to the damage, a*b*0.9 is the same as a*0.9*b.
The effectiveness of the talents always remain the same, i.e. if you mean the % of damage reduced or increased. The magnitude reduced obviously decreases if defence is higher as you are taking 10% of a smaller damage then. | I think what he means is that someone with 0 defence will take 90% of melee damage, 1 - (0.1*1)
So if the damage is initally 100 (0 talents) afterwards it'll become 90.
But if you have some defence, let's say enough to make the damage go down to 90 with no talent, after the 10% reduction it'll be 81 damage.
1 - 0.1 - ((1-0.1)*.1) or something. | Why did you write it like this? 1 - (0.1*1)
Shouldn't it simply be 100*0.9
If you include attack and defence, one possible way to write would be this:
100(1+0.05(0-0))*0.9
And when you deal 81 damage:
100/(1+0.05(20/9-0))*0.9
PS: Obviously 20/9 defence is impossible, but the only way you can get exactly 90% of initial damage by increasing defence is by increasing it by 20/9. | Dead troops do not hit back (unless they undead of course!)
Lol MilesTeg.
Regarding this Thread, why do Tribal boys maximize Defence Stat Btw?
They are supposed to deal more Damage than they receive.
Actually... Any Faction is supposed to deal more Damage than they receive. xD
Except UN I guess. | for Ipsen:
Triabl's units are fragile.
Compare HP with any other same tier unit of other faction, you'll see.
On the other hand, going full defensive let them survive longer and increase tribal spirit level which makes them stronger. | The magnitude reduced obviously decreases if defence is higher as you are taking 10% of a smaller damage then.
Yes, this is what Virtual Boy meant.
I think its a Plot Twist then:
Defence Talent Branch is more effective when maxing Attack :P
Didnt know this, I thought it was the other way round Tbh. | | I see, Ty 13# |
Regarding this Thread, why do Tribal boys maximize Defence Stat Btw?
Because the loss of tribal spirit depends on damage taken, and so long that they have enough spirit it is virtually impossible to kill it. So, by going defensive, they loose spirit less quickly and it can easily end up in a situation where it is impossible to make it loose spirit faster than it gains it, see commanders once they get up to 3 attacks per move (plus rapid and morale for 2/3 moves per hero turn ie. up to 900 spirit per hero turn). | | This becomes obvious if you are defensive build and deal low damage, then it is almost impossible to beat tribal because you don't make it loose enough spirit. | for randomr1:
I think you understand what i meant now, correct? | Tribal boy go defence build so their troop last longer and snowballing with their racial ability.
They dampen percentage of damage according to their fsl (very high percentage in fsl 8+) with the cost of spirit. The Higher current total hp in a unit means lower spirit cost.
If they last longer, they can perform more attack, they gain more spirit than it loss and on top of that they get bonus once hit 200,500,800 spirit.
Tribal is one of the best faction to go defence | for virtual_vitrea:
No I don't :O didn't quite understood what you meant before 10% is calculated before/after.
Defence Talent Branch is more effective when maxing Attack :P
Well same for dark and holy. If expert offence is attacking expert defence 1.3*0.7=91% of damage is dealt not 100%.
Similarly if 40% delay and rapid are cast on a creature overall it will have 1.4*0.6=0.84 of the initial initiative. |
This topic is long since last update and considered obsolete for further discussions.
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