Penetration (PV)
Reason: waiting for math extention to make this page look pretty. What is a critical hit's role in all of this? TODO: add probability calculation table for quick reference
PV or Penetration Value or → is a value assigned to all weapons and plays a key part in damage calculation during attacking.
Melee Weapon PV Calculation
Melee weapons have a base PV of 4. The PV will increase by the creature's Strength modifier with an upper limit dictated by the weapon's bonus cap. Two handed weapons and the Sharp mod also increase base PV by 1.
A critical hit(natural 10) is guaranteed one penetration.
Ranged Weapon PV Calculation
Reason: is this the same for grenade launchers, thrown weapons, or bows?
Ranged weapon PV is determined by the PV of the gun itself. The PV of the bullet does not matter.
Critical hits on ranged weapons add a flat +4 PV to the shot.
Penetration Formula
To check how many times an attack penetrates, the game rolls the following value three times:
Each roll is then compared to the target's DV. If at least one roll is higher than the DV, the attack penetrates a single time. Then, if all three rolls are higher than the DV, the whole process is repeated; this allows the attack to penetrate more than once. However, each time this happens, the PV value is reduced by 2.
The chance of penetrations goes by the formula:
If PV = AV, the formula simplifies to
The probability table would be
Penetrations | Probability distribution | Probability (cumulative) |
---|---|---|
0 | 0.008 | 0.008 |
1 | 0.512768 | 0.520768 |
2 | 0.392527872 | 0.913295872 |
3 | 0.083250119 | 0.996545991 |
4 | 0.003454009 | 1.000000000 |
5 | 0 | 1 |
Derivation
is the probability that a single roll at rounds of penetration fails.
If , , , are each the probability 1 successful roll at n rounds of penetration:
The probability of n penetrations becomes a sum of the chance that that 1 or 2 out of 3 rolls hit:
OR the probability that all 3 rolls hit, but the second round of penetration fails to penetrate at all: