How does defense/attack work? An analysis
Jun 8, 2019 23:06:18 GMT
Sorbet, Nobunaga Oda, and 2 more like this
Post by acridbrimistic on Jun 8, 2019 23:06:18 GMT
Skip to the end if you don't care about math.
As you probably know, units in the game have differing stats, including attack, defense, mobility, range, etc.
But what difference do they actually make? Let's analyze this.
TEST 1:
Attack - 27 atk MI vs 5 def Howitzer:
Both in plains. Tested in Axis mission 6.
1: 27 dmg
2: 25 dmg
3: 29 dmg
4: 20 dmg
5: 24 dmg
6: 25 dmg
7: 20 dmg
8: 22 dmg
9: 26 dmg
10: 24 dmg
Dmg. Range: 20?-29?
Mean (from range): 24.5
σ = 2.7495454169735
TEST 2:
Attack - 27 atk MI vs 2 def Assault Infantry
Both in plains. Tested in Axis mission 6.
1: 27 dmg
2: 24 dmg
3: 26 dmg
4: 22 dmg
5: 30 dmg
6: 25 dmg
7: 29 dmg
8: 22 dmg
9: 21 dmg
10: 24 dmg
Dmg. Range: 21?-30?
Mean (from range): 25.5
σ: 2.8635642126553
In these tests, it seems as if compared to 2 def, 5 def only reduces damage 1 extra.
But what if the defense is just 1?
Attack - 27 atk MI vs 1 def Light Infantry
Infantry in forest, but this shouldn't affect anything as infantry are immune to terrain debuffs.
Tested in Axis mission 2.
1: 31 dmg
2: 30 dmg
3: 25 dmg
4: 25 dmg
5: 31 dmg
6: 29 dmg
7: 25 dmg
8: 25 dmg
9: 30 dmg
10: 26 dmg
Dmg. Range: 21-31?
note. in a later test i noticed that i got very lucky in this test. the mean is closer to 27. the min dmg is 21.
Mean (from range): 26
σ: 2.5709920264365
TEST 4:
Attack - 27 atk MI vs. 0 def MT (landing craft)
Attacking MI on forest, but shouldn't affect anything.
Tested in Allied mission 4.
1: 32
2: 32
3: 22
4: 30
5: 26
6: 31
7: 24
8: 32
9: 31
10: 30
Dmg. Range 22?-32?
Mean (from range): 27
σ = 3.5832256659105
From this data it's possible to conclude some facts.
Defense is pretty obviously just subtracted from the raw damage, which is variable but it seems that the attack value lies in the median.
My theory is that the raw damage formula goes something like this:
ⅅ = (ℕ∩[-5,5] + a) - d,
where;
ⅅ represents raw damage total.
ℕ∩[0,10] represents a random variable following the discrete uniform distribution over the set {-5,-4,-3,-2,-1,0,1,2,3,4,5}.
a represents value of the attack stat
d represents value of the defense stat
Therefore, ⅅi = ⅅ * (1-t) + f
Where ⅅi represents true damage,
t represents terrain bonus in decimal
f represents the sum of all other factors (generals, etc.)
In summary:
To calculate raw damage of an unit, simply subtract defense from attack, then add a random value between -5 and 5.
What this means in practice is that for a defensive unit, HP is more important against high-damage units, while defense is very useful against low-damage units. High defense may negate almost 40% of an attacker's attack, but against high-damage units it negates less than 10%.
Think of it like this: your 8 defense reduces the enemy attacker's attack from 23 to 15, shaving off nearly 35% of the enemy's damage. But against a howitzer it reduces it from 46 to 41, only ~11%.
On attack, you should use your heavy damage-dealers to first wipe out the enemy bulks, then support your weaker comrades. For example, say you have 2 weak units and 1 strong one, against an enemy with the same force. Use all units to defeat the enemy strong unit, then take out the weaker units one-by-one.
Thanks for reading. I hope you learnt something new.
