==[Maths]== Armour value to damage absorbed conversion

[Yekaterina]

damage1.xlsx

Proportion of damage absorbed (out of 1) = 1 - e ^ ( ln(0.9)* armour value )

@nani

 

[Yekaterina]

@alre

Edited July 25, 2021 by Yekaterina

[alre]

Obviously, the proportion of damage dealt is obtained by taking out the "1 -" and is 

e^( ln(0.9) * armour value of the target ).

If one tries to compute the proportion of damage dealt to two different units whith two different armor values, it comes out that a unit whith 1 more armor than another, take 90% (0.9) of the damage that the less armored unit takes. 

Computing the inverse of the proportion of damage that a unit takes from enemy blows gives us a measure of 'durability' of that unit. That's the proportion of damage one have to deal to that unit to overcome its armor. One additional level of armor increases the durability of some unit by 1/90% ~= 11%. Two additional levels of armor increase durability by 1/(90%)^2 ~= 23%.

[alre]

durability increase = (damage necessary to kill a unit with improved armor / damage necessary to kill that unit with base armor) - 1

armory techs level 1 and 2 -> durability increase of 11%

armory techs level 3 -> durability increase of 23%