Absorbative

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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.

Calculations

• The average ratio of damage taken, $r_{avg}$, from Absorbative to that of without Absorbative is

$r_{avg}={\frac {\sum \limits _{n=0}^{\infty }\left(1-p\right)^{n}p\left[\left(\sum \limits _{i=1}^{n}d_{n,i}^{(0)}\right)+\lfloor {\left(1-.05\times R\right)\times d_{n}^{(1)}}\rfloor \right]}{\sum \limits _{n=0}^{\infty }\left(1-p\right)^{n}p\left[\left(\sum \limits _{i=1}^{n}d_{n,i}^{(0)}\right)+d_{n}^{(1)}\right]}}$

• The average damage reduction is then, after some rearranging,

$1-r_{avg}={\frac {\sum \limits _{n=0}^{\infty }\left(1-p\right)^{n}p\left[d_{n}^{(1)}-\lfloor {\left(1-.05\times R\right)\times d_{n}^{(1)}}\rfloor \right]}{\sum \limits _{n=0}^{\infty }\left(1-p\right)^{n}p\left[\left(\sum \limits _{i=1}^{n}d_{n,i}^{(0)}\right)+d_{n}^{(1)}\right]}}$

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 $d^{(0)}_{n,i}$ $\forall$ integer $i \in [1,n]$, $d^{(1)}_{n}$ $\forall$ 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

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

Sources

Material		Rarity	Perk ranks with X materials
			1	2	3	4	5
	Fungal components	Rare	0	1	2	2	2–3
	Strong components	Uncommon	0	1	1–2	1–2	1–2
	Plated parts	Common	0	0	1	1	1
	Padded parts	Common	0	0	1	1	1

Suggested gizmos

Gizmo layout	Possible perks
	Absorbative 2–3
	Absorbative 2 Venomblood Other possible perks: Efficient Cautious Committed Turtling
	Absorbative 2 Mobile (rare) Other possible perks: Demon Bait Crystal Shield
	Absorbative 2 Mobile (rare) Other possible perks: Dragon Bait Reflexes