Calculator:Combat/Combined Enhanced Devoted and Devoted

Having Devoted and Enhanced Devoted on one's gear has a benefit.^[1] Enhanced Devoted takes priority over Devoted. However, as Enhanced Devoted is unable to proc while it is currently active, this allows for a small window of time for Devoted to proc. Both Devoted and Enhanced Devoted, on their own, last 5 game ticks (3 seconds). This also means that it is possible (though unlikely) to have continuous procs of Enhanced Devoted and Devoted. The chance of continuous procs occurring is highly dependent on the attack rate of the enemy.^{[note 1]}

Damage reduction

Average damage reduction in PvM for Devoted 4, Enhanced Devoted 4, and the combination of Enhanced Devoted 4 with Devoted 4. The attack rate, $t_{AR}$ , of the enemy (given in game ticks) has an effect on the damage reduction. The damage reduction in parentheses correspond to placing this perk on level 20 gear (For the combination, both perks are placed on level 20 gear.).
Perk(s)	PvM Average Damage Reduction
Perk(s)	$t_{AR}=1$	$t_{AR}=2$	$t_{AR}=3$ or $4$	$t_{AR}=5+$ ^{[note 2]}
	40.54% (43.19%)	29.03% (31.33%)	21.43% (23.32%)	12.00% (13.20%)
	52.33% (55.25%)	39.71% (42.55%)	30.51% (33.06%)	18.00% (19.80%)
	59.01% (62.53%)	43.08% (46.37%)	32.01% (34.80%)	18.00% (19.80%)

Average damage reduction in PvP for Devoted 4, Enhanced Devoted 4, and the combination of Enhanced Devoted 4 with Devoted 4. The attack rate, $t_{AR}$ , of the enemy (given in game ticks) has an effect on the damage reduction. The damage reduction in parentheses correspond to placing this perk on level 20 gear (For the combination, both perks are placed on level 20 gear.).
Perk(s)	PvP Average Damage Reduction
Perk(s)	$t_{AR}=1$	$t_{AR}=2$	$t_{AR}=3$ or $4$	$t_{AR}=5+$ ^{[note 2]}
	20.27% (21.60%)	14.52% (15.66%)	10.71% (11.66%)	6.00% (6.60%)
	26.16% (27.62%)	19.85% (21.28%)	15.25% (16.53%)	9.00% (9.90%)
	29.49% (31.25%)	21.53% (23.20%)	16.00% (17.41%)	9.00% (9.90%)

Continuous procs

When both are active, an icon for both Enhanced devoted and Devoted will be on the buff bar. Enhanced Devoted and Devoted cannot proc on the same tick and Devoted can only proc when Enhanced Devoted is active. This means there are at most 4 ticks for Devoted to proc because the internal cooldown of Enhanced Devoted is 5 ticks (the internal cooldown for Devoted is also 5 ticks). Furthermore, as Enhanced Devoted is unable to proc again until it is no longer active, the biggest benefit one could get is to have the next proc of either perk occur toward the end of duration of the most recent proc; this would give the longest possible duration of continuous procs (this is not controllable, however). For example, consider a case of three in a row procs against an enemy that attacks every tick (an attack rate of 1):

An example of Enhanced Devoted and Devoted proccing together to increase damage reduction.

In this scenario, the first proc of Enhanced Devoted occurs and the hit that caused the proc and the next 4 subsequent hits will be reduced by the perk (five total hits)
Now, within these next 4 hits, Devoted can proc.
- If Devoted were to proc on the first opportunity (the second hit in the five hit sequence), then Enhanced Devoted is unable to proc again until three more ticks pass.
- If Devoted were to proc on the second opportunity (the third hit in the five hit sequence), then Enhanced Devoted is unable to proc again until two more ticks pass.
- Etc.
- Likewise, once Devoted procs, it is also unable to proc again for five ticks.
After the fifth hit, Enhanced Devoted can once again proc (meaning the earliest is on attack six).
All possibilities should be taken into consideration for calculating the damage reduction. However, this can quickly become complicated and so another way to do this is to use a simulator that follows the way the perks work (and also work together).

Calculator

This dynamic calculator requires JavaScript.

This page takes user input via JavaScript and may use changing prices from the Grand Exchange Market Watch.

Templates used

Calculator:Template/Combat/Combined Enhanced Devoted and Devoted

One can use the simulator to compare to the values in the table above as well as find the damage reduction for all other Enhanced Devoted and Devoted combinations.

The simulator assumes:

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 rate.

template  = Calculator:Template/Combat/Combined Enhanced Devoted and Devoted
form      = combinedDevoEnhancedDevoCalcForm
result    = combinedDevoEnhancedDevoCalcResult
param     = pvmorpvp| PvM or PvP?|PvM|buttonselect|PvM,PvP
param     = edevRank|Enhanced Devoted perk rank|4|int|0-4
param     = level20edev| Is Enhanced Devoted on level 20 gear?|No|check|Yes,No
param     = devRank|Devoted perk rank|4|int|0-4
param     = level20dev| Is Devoted on level 20 gear?|No|check|Yes,No
param     = t_AR|Enemy attack rate|3 or 4|buttonselect|1,2,3 or 4,5+
param     = runSpeed|Select speed of simulator|Moderate|buttonselect|Slow (higher precision),Moderate,Fast (lower precision)

This text will disappear if the form is loaded properly.

This text will disappear if the form is submitted.

Template documentation

This documentation is transcluded from Calculator:Combat/Combined Enhanced Devoted and Devoted/doc. [edit] [history] [purge]

Description

This calculator is a simulator that uniformally samples a random number between 0 and 1 each time a comparison is made to the Enhanced Devoted proc chance or Devoted proc chance. Because of this, the results will vary.

PvM or PvP?

Choce of either PvM or PvP.

Enhanced Devoted perk rank

Rank of Enhanced Devoted perk.

Is Enhanced Devoted on level 20 gear?

If checked, the proc rate of the Enhanced Devoted perk is multiplied by 1.1 for choice of rank. If unchecked, the proc rate of the Enhanced Devoted perk is the normal value for choice of rank.

Devoted perk rank

Rank of Devoted perk.

Is Devoted on level 20 gear?

If checked, the proc rate of the Devoted perk is multiplied by 1.1 for choice of rank. If unchecked, the proc rate of the Devoted perk is the normal value for choice of rank.

Enemy attack rate

Attack rate of enemy in ticks.

Note : For PvP, the normal attack rate of the player is 3 game ticks (not including legacy combat).

Select speed of simulator

Slow (higher precision) runs over $10^{7}$ hits.
Moderate runs over $10^{6}$ hits.
Fast (lower precision) runs over $10^{5}$ hits.

Notes

^ To be more precise, it is really the frequency of ticks that the player is taking damage and not really the attack rate that determines the increased chance of continuous procs. However, in the simplest case, this is the attack rate of the enemy. As an example, take 4 enemies, each with an attack rate of 4, attacking the player with their hits offset by one tick from each other (enemy A attacks tick 1, enemy B attacks tick 2, ...). In this example, this is effectively the same as an attack rate of 1 to the player. This means that as long as the player is taking at least one hit every tick, regardless of the number of enemies attacking, the effective attack rate is 1. Conversely, if these same enemies, each with an attack rate of 4, are attacking the player on the same tick (enemy A attacks tick 1, enemy B attacks tick 1, ...), then the effective attack rate is 4. In general, more enemies attacking the player leads to a higher frequency of ticks that the player is taking hits, increasing the chance of continuous procs and therefore increasing the damage reduction.
^ ^a ^b For enemies that attack once every 5 ticks or slower, Devoted will never go off if both Enhanced Devoted and Devoted are on one's gear. Therefore, this value of damage reduction for the combination match that of a standalone Enhanced Devoted 4.

References

^ Mod Pi. Devoted and enhanced devoted stack. 20 November 2018. (Archived from the original on 13 January 2021.)

[proc-2] To be more precise, it is really the frequency of ticks that the player is taking damage and not really the attack rate that determines the increased chance of continuous procs. However, in the simplest case, this is the attack rate of the enemy. As an example, take 4 enemies, each with an attack rate of 4, attacking the player with their hits offset by one tick from each other (enemy A attacks tick 1, enemy B attacks tick 2, ...). In this example, this is effectively the same as an attack rate of 1 to the player. This means that as long as the player is taking at least one hit every tick, regardless of the number of enemies attacking, the effective attack rate is 1. Conversely, if these same enemies, each with an attack rate of 4, are attacking the player on the same tick (enemy A attacks tick 1, enemy B attacks tick 1, ...), then the effective attack rate is 4. In general, more enemies attacking the player leads to a higher frequency of ticks that the player is taking hits, increasing the chance of continuous procs and therefore increasing the damage reduction.

[tAR-3] For enemies that attack once every 5 ticks or slower, Devoted will never go off if both Enhanced Devoted and Devoted are on one's gear. Therefore, this value of damage reduction for the combination match that of a standalone Enhanced Devoted 4.

[DevotedAndEnhancedDevotedWorkTogether-1] Mod Pi. Devoted and enhanced devoted stack. 20 November 2018. (Archived from the original on 13 January 2021.)

[1]

[note 1]

[note 2]

Calculator:Combat/Combined Enhanced Devoted and Devoted

Contents

Damage reduction

Continuous procs