Invulnerability, Fortresses and math
This thread will contain Math. If that triggers, frightens or irritates you, consider yourself warned.
First, a couple of Basic knowledge:
- Several of your stats are written as percentages but in general, those are used differently in formulas. To properly use them, they are transformed into a float-representation by dividing them by hundred - eg. 101% would be transformed into 1.01 and 49% would be transformed into 0.49
- Percentages have "caps" meaning the result of a certain portion of the formula can never be higher than 100% and never be lower than 0%. Some however only have 1 limit, meaning that they can be higher than 100% but not lower than 0%
In general, damage in Fortresses is based on the power of the actor - be it you during your phase or the enemy during theirs. That power depends on the base stats but can be enhanced by passive abilities (like Magizooligists
BECOME THE BEAST or Professors
IDEAL EXCHANGE ). Additional situational power can come from Buffs like Magizoologists "Bravery Charm".
Proficiency and Deficiency
If you're proficient against your enemy, that number then is multiplied by subtraction of your "Proficiency Power" (already including Buffs like professor's "Proficiency Charm") and your enemies "Deficiency Power".
ProficiencyFactor = 1 + MAX(0, ProficiencyPower-EnemyDeficiencyDefence)
(that means that it will never be lower than 1 but might be higher than 2. Also this factor will be 1 if there is no proficiency-pairing between you and your enemy)
If you're not proficient against your enemy that factor looks like this:
ProficiencyFactor = 1
Defence and Defence Breach
That is the multiplied by the Subtraction of your Defence and your enemies Deficiency Defence.
DefenceFactor = 1 - CAP(0, 1, EnemyDefence-DefenceBreach)
(that means that this factor can be zero or one or anything in between. For example, if your enemy has 125% defence and you only have 5% defence breach, your enemy is effectively invulnerable)
Crit is interesting as it contains of 2 parts:
- Determining whether a crit happened
- Determining how much more damage your spell did
This post will not look at the first part.
If a Crit happened, then the previously computed value is then multiplied by your Critical Power:
CritFactor = CriticalPower
If you didn't score a Crit, that factor would just be 1.
Putting all of that together then looks something like this
Damage = Power * ProficiencyFactor * DefenceFactor * CritFactor
Now for the interesting part (and that teaser of invulnerability):
If any of those are ZERO, the damage done would be Zero too. And it so happens that one of those factors CAN actually be zero for the damage-computation of your enemy: the Defence-Factor.
IF you managed to Increase your own defence to above 100% AND make sure that your enemy does NOT have sufficient Defence-Breach, then your defence would be 100% (due to the capping). That would result in the DefenceFactor of your enemy to look like this:
DefenceFactor = 1 - CAP(0, 1, 1.01-0) = 1 - 1 = 0
Which then reduces the Damage of your Enemy to Zero.
Now let's look at it practicly:
Magizoologists can raise their Defence to 71% (50% from base stats, +6% when at or above 50% Stamina, +15% when at or above 5 Focus):
0.5 + 0.06 + 0.15 = 0.71
Protection Charm can increase that by an additional 30% - which is ADDED and not multiplied, resulting in 101%:
0.71 + 0.3 = 1.01
Confusion Hex can reduce the Enemies Defence Breach by up to 60% (which AFAIK is more than any Enemy currently in the game)