Absorbative is an Inventionperk that gives a 20% (22% on a level 20 item) chance of reducing damage by 5% per rank. It can be created in armour gizmos.
Absorbative effectively provides a 1% damage reduction per rank. However, Absorbative does not reduce hard typeless damage (typeless damage that is unaffected by defensive abilities).
Rank
Reduction per hit
Average damage reduction
1
5%
1% (1.1%)
2
10%
2% (2.2%)
3
15%
3% (3.3%)
All numbers in parentheses refer to level 20 gear.
Calculations
The average ratio of damage taken, $ r_{avg} $, from Absorbative to that of without Absorbative is
The enemy is dealing damage with anything that is not hard typeless.
$ R $ is the rank of the Absorbative perk.
$ p $ is the proc chance of Absorbative to activate (.2 normally, .22 if the Absorbative perk is on level 20 gear).
$ \textstyle\sum_{n=0}^{\infty}\left(1-p\right)^{n}p = 1 $ when $ 0 \leq p < 1 $ or $ \left|1 - p\right| < 1 $. This represents summing over all possibilities where integer $ n \in [0,\infty) $ represents the amount of hits prior to the proc of Absorbative. The probability of Absorbative proccing on hit $ {n+1} $ is therefore $ \left(1-p\right)^{n}p $.
$ d^{(j)}_{n,i} $ is the $ i^{th} $random value uniformly sampled between the enemy's minimum hit and maximum hit. The $ j $ describes different sets of hits. The sets are regenerated for every new value of $ n $.
$ d^{(0)}_{n,i} $ has $ n $ elements with integer $ i \in [1,n] $. This is the damage taken before the perk procs.
Clarification : This does mean that for $ n=0 $ that there are no elements in this set.
$ d^{(1)}_{n} $ is the damage taken from a single hit when Absorbative procs.
The set of values in $ d^{(j)}_{n} $ for integer $ j \in [0,1] $ is the same in both the numerator and denominator of the ratios for any given $ n $.
Simplifications
This can be simplified if the assumption is that every value $ d_{n,i}^{(0)} $$ \forall $ integer $ i \in [1,n] $, $ d_{n}^{(1)} $$ \forall $ integer $ n \in [0,\infty) $ is taken to be the same $ \left(d_{n,i}^{(0)} = d_{n}^{(1)} \rightarrow d\right) $. In this scenario, there is no random element and the above $ r_{avg} $ is then only dependent on the proc chance. This simplification is increasingly accurate in the limit of large $ d $. A table is provided at the top of the page.
Using these simplifications, the damage reduction reduces to
