Devoted is an Inventionperk that has a chance each hit of replicating the Devotion ability for 3 seconds. This effect does not put the ability itself on cooldown. Devoted has an effective level requirement of 74 as the materials required can only be unlocked at that level; however, enhanced devoted can be utilised at any Invention level for the cost of 2 perk slots. It can be created in armour gizmos.
Any type of damage, including typeless damage and self-inflicting damage, can activate the perk. The hit that activates Devoted will also be affected by the perk's effect. Devoted will play the same animation as Devotion whenever it activates, but uses its own icon in the buffs/debuffs interface. In player-versus-player situations the icon does not appear.
Devoted will be superseded by enhanced devoted if both are active.
Activation chance
Rank
Chance (level 20)
1
3% (3.3%)
2
6% (6.6%)
3
9% (9.9%)
Calculations
For PvM:
The average ratio of damage taken, , from Devoted to that of without Devoted is
The average damage reduction is then, after some rearranging,
For PvP :
The average ratio of damage taken, , from Devoted to that of without Devoted is
The average damage reduction is then, after some rearranging,
Notes
A calculator for this is at the top of this page.
Assumptions :
The enemy is always attacking with the same style that matches the protect prayer (deflect curse) used.
The enemy is always attacking at the same attack speed.
is the rank of the Devoted perk.
is the proc chance of Devoted to activate (if the perk is on level 20 gear, then this value is multiplied by 1.1).
when or . This represents summing over all possibilities where integer represents the amount of hits prior to the proc of Devoted. The probability of Devoted proccing on hit is therefore .
is the time that Devoted is active. This is taken to be 5 game ticks.
is the attack speed of the enemy in game ticks.
is the random value uniformly sampled between the enemy's minimum hit and maximum hit. The describes different sets of hits. The sets are regenerated for every new value of .
has elements with integer . This is the damage taken before the perk procs.
Clarification : This does mean that for that there are no elements in this set.
has elements with integer . This is the damage taken during the time where Devoted procced.
The set of values in for integer is the same in both the numerator and denominator of the ratios for any given .
Simplifications
This can be simplified if the assumption is that every value of integer , integer , integer , is taken to be the same . In this scenario, there is no random element and the above is then only dependent on the proc chance and the attack speed of the enemy. This simplification is increasingly accurate in the limit of large . Three examples are provided in total. Two examples, simultaneously provided, look at normal proc chance per rank (non-level 20 gear) and a value of that could be either 4 (a common boss attack speed) or 3 in a PvM situation. One more example looks the normal proc chance per rank (non-level 20 gear) in a PvP situation where is set to 3. All three examples are using large enough values of such that the values should not change to the first decimal place in percent.
Using these simplifications, along with , the damage reduction reduces to