Square root attrition model
Posted: Fri Aug 23, 2024 6:13 am
It is intriguing to compare the combat resolution systems in TOAW and PZC, particularly noting that both games share some fundamental concepts, such as victory conditions driven by morale checks. However, a notable difference lies in how losses are calculated for the target units:
In PZC, the target's losses are directly proportional to the attacker's assault value:
target loss ratio = k * attacker's assault value / target defense value
Contrastingly, in TOAW, the attrition value, based on information scattered across the internet, is proportional to the square root of the attacker's attrition value (which is the sum of their AP or AT values):
target loss ratio = k * sqrt(attacker's AP or AT value) / sqrt(target defense value)
When the attacker is sufficiently powerful, the square root function in TOAW's attrition model resembles the maximum attacker mechanism in DC, which reduces the attacker's strength after multiple attacks within a single combat round. This can be represented as a piecewise function with both linear and logarithmic components:
loss ratio = k * attacker's fire value (linear if the threshold is not reached)
loss ratio = k * thresholded attacker's fire value + k2 * log(extra attacker's fire value)
Regarding defense values, consider the effect of bombardment. Doubling the strength results in approximately a 2 * 1/sqrt(2) = sqrt(2) ~=1.41 losses increase, assuming no stacking limit penalties apply (in PZC, a linear relationship would prevent such a increase (2 * 1/2 = 1)). It looks that TOAW just assumes the target units are uniformly distributed within the combat zone and that artillery fire strikes randomly across the area.
In PZC, the target's losses are directly proportional to the attacker's assault value:
target loss ratio = k * attacker's assault value / target defense value
Contrastingly, in TOAW, the attrition value, based on information scattered across the internet, is proportional to the square root of the attacker's attrition value (which is the sum of their AP or AT values):
target loss ratio = k * sqrt(attacker's AP or AT value) / sqrt(target defense value)
When the attacker is sufficiently powerful, the square root function in TOAW's attrition model resembles the maximum attacker mechanism in DC, which reduces the attacker's strength after multiple attacks within a single combat round. This can be represented as a piecewise function with both linear and logarithmic components:
loss ratio = k * attacker's fire value (linear if the threshold is not reached)
loss ratio = k * thresholded attacker's fire value + k2 * log(extra attacker's fire value)
Regarding defense values, consider the effect of bombardment. Doubling the strength results in approximately a 2 * 1/sqrt(2) = sqrt(2) ~=1.41 losses increase, assuming no stacking limit penalties apply (in PZC, a linear relationship would prevent such a increase (2 * 1/2 = 1)). It looks that TOAW just assumes the target units are uniformly distributed within the combat zone and that artillery fire strikes randomly across the area.