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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).

• All numbers in parentheses refer to level 20 gear.

Calculations

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

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

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

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

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.
• ${\displaystyle R}$ is the rank of the Absorbative perk.
• ${\displaystyle p}$ is the proc chance of Absorbative to activate (.2 normally, .22 if the Absorbative perk is on level 20 gear).
• ${\displaystyle \textstyle\sum_{n=0}^{\infty}\left(1-p\right)^{n}p = 1}$ when ${\displaystyle 0 \leq p < 1}$ or ${\displaystyle \left|1 - p\right| < 1}$. This represents summing over all possibilities where integer ${\displaystyle n \in [0,\infty)}$ represents the amount of hits prior to the proc of Absorbative. The probability of Absorbative proccing on hit ${\displaystyle {n+1}}$ is therefore ${\displaystyle \left(1-p\right)^{n}p}$.
• ${\displaystyle d^{(j)}_{n,i}}$ is the ${\displaystyle i^{th}}$ random value uniformly sampled between the enemy's minimum hit and maximum hit. The ${\displaystyle j}$ describes different sets of hits. The sets are regenerated for every new value of ${\displaystyle n}$.
  • ${\displaystyle d^{(0)}_{n,i}}$ has ${\displaystyle n}$ elements with integer ${\displaystyle i \in [1,n]}$. This is the damage taken before the perk procs.
    • Clarification : This does mean that for ${\displaystyle n=0}$ that there are no elements in this set.
  • ${\displaystyle d^{(1)}_{n}}$ is the damage taken from a single hit when Absorbative procs.
  • The set of values in ${\displaystyle d^{(j)}_{n}}$ for integer ${\displaystyle j \in [0,1]}$ is the same in both the numerator and denominator of the ratios for any given ${\displaystyle n}$.

Simplifications

• This can be simplified if the assumption is that every value ${\displaystyle d^{(0)}_{n,i}}$ ${\displaystyle \forall}$ integer ${\displaystyle i \in [1,n]}$, ${\displaystyle d^{(1)}_{n}}$ ${\displaystyle \forall}$ integer ${\displaystyle n \in [0,\infty)}$ is taken to be the same ${\displaystyle \left(d_{n,i}^{(0)} = d_{n}^{(1)} \rightarrow d\right)}$. In this scenario, there is no random element and the above ${\displaystyle r_{avg}}$ is then only dependent on the proc chance. This simplification is increasingly accurate in the limit of large ${\displaystyle d}$. A table is provided at the top of the page.

Using these simplifications, the damage reduction reduces to

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

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

v • d • e Invention perks
Abilities	Brief Respite Bulwark Caroming Clear Headed Energising Lunging Mobile Planted Feet Preparation Reflexes Shield Bashing Turtling Ultimatums Taunting
Damage/Accuracy modifying	Aftershock Biting Blunted Crackling Demon Bait Demon Slayer Dragon Bait Dragon Slayer Equilibrium Flanking Genocidal Inaccurate Mediocrity Precise Spendthrift Undead Bait Undead Slayer
Damage reduction	Absorbative Crystal Shield Devoted Enhanced Devoted Lucky Venomblood
Adrenaline	Fatiguing Invigorating Impatient
Prayer	Antitheism Profane Hoarding
Additional items	Brassican Looting Scavenging
Experience	Enlightened Tinker Wise
Skilling	Butterfingers Breakdown Charitable Cheapskate Confused Furnace Honed Imp Souled Polishing Pyromaniac Rapid Refined
Miscellaneous	Cautious Committed Efficient Enhanced Efficient Glow Worm Hallucinogenic Junk Food Mysterious Prosper Talking Trophy-taker's