# Absorbative

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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). Additionally, Absorbative does not work in PvP combat.

Average damage reduction for the different ranks of the Absorbative perk. The damage reduction in parentheses correspond to placing this perk on level 20 gear.
Rank Reduction per hit Average damage reduction
1 5% 1% (1.1%)
2 10% 2% (2.2%)
3 15% 3% (3.3%)
4 20% 4% (4.4%)
Calculations
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 $\left(1-p\right)^{n}p$ .
• $d_{n,i}^{(j)}$ 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 $n$ .
• $d_{n,i}^{(0)}$ 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.
• $d_{n}^{(1)}$ is the damage taken from a single hit when Absorbative procs.
• The set of values in $d_{n}^{(j)}$ for integer $j\in [0,1]$ is the same in both the numerator and denominator of the ratios for any given $n$ .

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

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

MaterialRarityPerk ranks with X materials
Standard gizmoAncient gizmo
12345123456789
Fungal componentsRare01222–3011222–333–44
Strong componentsUncommon011–21–21–20111–21–21–21–31–31–4
Plated partsCommon0011101111111–21–2
Padded partsCommon0011100011111–21–2

## Update history

The update history project is a work-in-progress – not all updates to this topic may be covered below. See here for how to help out!
• patch 22 February 2016 (Update):
• The Absorbative perk no longer uses the 30 seconds of charge.