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Absorbative
Absorbative
Description?
20% chance to reduce an attack by 5% per rank.
Release date 25 January 2016 (Update)
Gizmo type Armour
Maximum rank 3

Absorbative is an Invention perk 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.

CalculationsEdit

  • The average ratio of damage taken, $ r_{avg} $, from Absorbative to that of without Absorbative is
$ r_{avg} = \frac{\sum\limits_{n=0}^{\infty}\left(1-p\right)^{n}p\left[\left(\sum\limits_{i=1}^{n}d^{(0)}_{n,i}\right) + \lfloor{\left(1 - .05 \times R \right)\times d^{(1)}_{n}}\rfloor\right]}{\sum\limits_{n=0}^{\infty}\left(1-p\right)^{n}p\left[\left(\sum\limits_{i=1}^{n}d^{(0)}_{n,i}\right) + d^{(1)}_{n} \right]} $
  • The average damage reduction is then, after some rearranging,
$ 1-r_{avg} = \frac{\sum\limits_{n=0}^{\infty}\left(1-p\right)^{n}p\left[d^{(1)}_{n} - \lfloor{\left(1 - .05 \times R \right)\times d^{(1)}_{n}}\rfloor\right]}{\sum\limits_{n=0}^{\infty}\left(1-p\right)^{n}p\left[\left(\sum\limits_{i=1}^{n}d^{(0)}_{n,i}\right) + d^{(1)}_{n} \right]} $
Notes
  • A calculator for this is at the top of this page.
  • Assumption :
    • 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

$ 1 - r_{avg} = \frac{pR}{20} $

SourcesEdit

MaterialRarityPerk ranks with X materials
12345
Fungal components
Fungal componentsRare01222–3
Strong components
Strong componentsUncommon011–21–21–2
Plated parts
Plated partsCommon00111
Padded parts
Padded partsCommon00111

Suggested gizmosEdit

Gizmo layout Possible perks
Fungal components
Fungal componentsFungal componentsFungal components
Fungal components
  • Absorbative Absorbative 2–3
Evasive components
Fungal componentsHealthy componentsFungal components
Fungal components
  • Other possible perks:
Subtle components
Fungal componentsFungal componentsFungal components
Fungal components
  • Other possible perks:
Dextrous components
Fungal componentsFungal componentsFungal components
Fungal components
  • Other possible perks: