
This article has a calculator here.

Enhanced Devoted is an improved version of the Devoted Invention perk that has a chance on each hit of replicating the Devotion ability for 3 seconds, which causes protection and deflection prayers to reduce damage from the appropriate style to 1. The perk does not put the ability itself on cooldown. This perk takes up two slots in a gizmo, meaning that it cannot be paired with any other perk in the same gizmo. It is created in armour gizmos.
Any type of damage, including typeless damage and selfinflicted damage can activate the perk. The opponent's hit that activates Enhanced Devoted is also affected by the perk. Enhanced Devoted will play the same animation as Devotion whenever it activates, but has an icon of its own in the buffs/debuffs interface.
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 speed of the enemy. Further information about the combination can be found here.
Activation chance
Rank

Chance

1 
4.5% (4.95%)

2 
9.0% (9.90%)

3 
13.5% (14.85%)

PvM average damage reduction
Rank

$t_{AS}=1$

$t_{AS}=2$

$t_{AS}=3$ or $4$

$t_{AS}=5+$

1

19.07% (20.66%)

12.39% (13.51%)

8.61% (9.43%)

4.50% (4.95%)

2

33.09% (35.46%)

22.88% (24.79%)

16.51% (18.02%)

9.00% (9.90%)

3

43.83% (46.58%)

31.89% (34.35%)

23.79% (25.86%)

13.50% (14.85%)

PvP average damage reduction
Rank

$t_{AS}=1$

$t_{AS}=2$

$t_{AS}=3$ or $4$

$t_{AS}=5+$

1

9.53% (10.33%)

6.19% (6.76%)

4.31% (4.72%)

2.25% (2.48%)

2

16.54% (17.73%)

11.44% (12.40%)

8.26% (9.01%)

4.50% (4.95%)

3

21.92% (23.29%)

15.94% (17.17%)

11.89% (12.93%)

6.75% (7.43%)

 $t_{AS}$ is the attack speed of the enemy in game ticks.
 All numbers in parentheses refer to level 20 gear.
For PvM :
 The average ratio of damage taken, $r_{avg}$, from Enhanced Devoted to that of without Enhanced Devoted is
 $r_{avg}={\frac {\sum \limits _{n=0}^{\infty }\left(1p_{R}\right)^{n}p_{R}\left[\left(\sum \limits _{i=1}^{n}d_{n,i}^{(0)}\right)+\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil \right]}{\sum \limits _{n=0}^{\infty }\left(1p_{R}\right)^{n}p_{R}\left[\sum \limits _{i=1}^{n}d_{n,i}^{(0)}+\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }d_{n,i}^{(1)}\right]}}$
 The average damage reduction is then, after some rearranging,
 $1r_{avg}={\frac {\sum \limits _{n=0}^{\infty }\left(1p_{R}\right)^{n}p_{R}\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }\left(d_{n,i}^{(1)}1\right)}{\sum \limits _{n=0}^{\infty }\left(1p_{R}\right)^{n}p_{R}\left[\sum \limits _{i=1}^{n}d_{n,i}^{(0)}+\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }d_{n,i}^{(1)}\right]}}$
For PvP :
 The average ratio of damage taken, $r_{avg}$, from Enhanced Devoted to that of without Enhanced Devoted is
 $r_{avg}={\frac {\sum \limits _{n=0}^{\infty }\left(1p_{R}\right)^{n}p_{R}\left[\sum \limits _{i=1}^{n}d_{n,i}^{(0)}+\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }\left\lfloor {.5\times d_{n,i}^{(1)}}\right\rfloor \right]}{\sum \limits _{n=0}^{\infty }\left(1p_{R}\right)^{n}p_{R}\left[\sum \limits _{i=1}^{n}d_{n,i}^{(0)}+\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }d_{n,i}^{(1)}\right]}}$
 The average damage reduction is then, after some rearranging,
 $1r_{avg}={\frac {\sum \limits _{n=0}^{\infty }\left(1p_{R}\right)^{n}p_{R}\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }\left(d_{n,i}^{(1)}\left\lfloor {.5\times d_{n,i}^{(1)}}\right\rfloor \right)}{\sum \limits _{n=0}^{\infty }\left(1p_{R}\right)^{n}p_{R}\left[\sum \limits _{i=1}^{n}d_{n,i}^{(0)}+\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }d_{n,i}^{(1)}\right]}}$
 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.
 $R$ is the rank of the Enhanced Devoted perk.
 $p_{R}$ is the proc chance of Enhanced Devoted to activate (if the perk is on level 20 gear, then this value is multiplied by 1.1).
 $\textstyle \sum _{n=0}^{\infty }\left(1p\right)^{n}p=1$ when $0\leq p<1$ or $\left1p\right<1$. This represents summing over all possibilities where integer $n\in [0,\infty )$ represents the amount of hits prior to the proc of Enhanced Devoted. The probability of Enhanced Devoted proccing on hit ${n+1}$ is therefore $\left(1p\right)^{n}p$.
 $t_{ed}$ is the time that Enhanced Devoted is active. This is taken to be 5 game ticks.
 $t_{AS}$ is the attack speed of the enemy in game ticks.
 $d_{n,i}^{(j)}$ 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.
 $d_{n,i}^{(1)}$ has $\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil$ elements with integer $i\in \left[1,\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil \right]$. This is the damage taken during the time Enhanced Devoted procced.
 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 $n$.
 Simplifications
 This can be simplified if the assumption is that every value of $d_{n,i}^{(j)}$ $\forall$ integer $i\in [1,n]$, integer $n\in [0,\infty )$, integer $j\in [0,1]$, is taken to be the same $\left(d_{n,i}^{(j)}\rightarrow d\right)$. In this scenario, there is no random element and the above $r_{avg}$ 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 $d$. All examples are using large enough values of $d$ such that the values should not change to the first two decimal places in percent. Two tables are provided at the top of the page. The first covers all values of $t_{AS}$ for PvM situations. The second table is for PvP for all values of $t_{AS}$ (normal attack speed of player is $t_{AS}=3$ in nonlegacy mode , but all values of $t_{AS}$ have been provided to account for proccing on damageovertime abilities, 4 tick auto attack, etc., as well as the varied attack speeds of weapons if using legacy combat).
Using these simplifications, the damage reduction reduces to
For PvM :
 $1r_{avg}={\frac {\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil p_{R}}{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil p_{R}+\left(1p_{R}\right)}}$
For PvP :
 $1r_{avg}={\frac {.5\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil p_{R}}{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil p_{R}+\left(1p_{R}\right)}}$
Gizmo layout 
Possible perks 




Abilities 

Damage/Accuracy modifying 

Damage reduction 

Adrenaline 

Prayer 

Additional items 

Experience 

Skilling 

Miscellaneous 

Navbox JSON: {"groups":[{"title":"Abilities","contents":[{"text":"Brief Respite","image":"Brief Respite.png","link":"Brief Respite"},{"text":"Bulwark","image":"Bulwark.png","link":"Bulwark"},{"text":"Caroming","image":"Caroming.png","link":"Caroming"},{"text":"Clear Headed","image":"Clear Headed.png","link":"Clear Headed"},{"text":"Energising","image":"Energising.png","link":"Energising"},{"text":"Lunging","image":"Lunging.png","link":"Lunging"},{"text":"Mobile","image":"Mobile.png","link":"Mobile"},{"text":"Planted Feet","image":"Planted Feet.png","link":"Planted Feet"},{"text":"Preparation ","image":"Preparation (perk).png","link":"Preparation (perk)"},{"text":"Reflexes","image":"Reflexes.png","link":"Reflexes"},{"text":"Shield Bashing","image":"Shield Bashing.png","link":"Shield Bashing"},{"text":"Turtling","image":"Turtling.png","link":"Turtling"},{"text":"Ultimatums","image":"Ultimatums.png","link":"Ultimatums"},{"text":"Taunting","image":"Taunting.png","link":"Taunting"}]},{"title":"Damage/Accuracy modifying","contents":[{"text":"Aftershock","image":"Aftershock.png","link":"Aftershock"},{"text":"Biting","image":"Biting.png","link":"Biting"},{"text":"Blunted","image":"Blunted.png","link":"Blunted"},{"text":"Crackling","image":"Crackling.png","link":"Crackling"},{"text":"Demon Bait","image":"Demon Bait.png","link":"Demon Bait"},{"text":"Demon Slayer ","image":"Demon Slayer (perk).png","link":"Demon Slayer (perk)"},{"text":"Dragon Bait","image":"Dragon Bait.png","link":"Dragon Bait"},{"text":"Dragon Slayer ","image":"Dragon Slayer (perk).png","link":"Dragon Slayer (perk)"},{"text":"Equilibrium","image":"Equilibrium.png","link":"Equilibrium"},{"text":"Flanking","image":"Flanking.png","link":"Flanking"},{"text":"Genocidal","image":"Genocidal.png","link":"Genocidal"},{"text":"Inaccurate","image":"Inaccurate.png","link":"Inaccurate"},{"text":"Mediocrity","image":"Mediocrity.png","link":"Mediocrity"},{"text":"Precise","image":"Precise.png","link":"Precise"},{"text":"Spendthrift","image":"Spendthrift.png","link":"Spendthrift"},{"text":"Undead Bait","image":"Undead Bait.png","link":"Undead Bait"},{"text":"Undead Slayer","image":"Undead Slayer.png","link":"Undead Slayer"}]},{"title":"Damage reduction","contents":[{"text":"Absorbative","image":"Absorbative.png","link":"Absorbative"},{"text":"Crystal Shield","image":"Crystal Shield.png","link":"Crystal Shield"},{"text":"Devoted","image":"Devoted.png","link":"Devoted"},{"text":"Enhanced Devoted","image":"Enhanced Devoted.png","link":"Enhanced Devoted"},{"text":"Lucky","image":"Lucky.png","link":"Lucky"},{"text":"Venomblood","image":"Venomblood.png","link":"Venomblood"}]},{"title":"Adrenaline","contents":[{"text":"Fatiguing","image":"Fatiguing.png","link":"Fatiguing"},{"text":"Invigorating","image":"Invigorating.png","link":"Invigorating"},{"text":"Impatient","image":"Impatient.png","link":"Impatient"}]},{"title":"Prayer","contents":[{"text":"Antitheism","image":"Antitheism.png","link":"Antitheism"},{"text":"Profane","image":"Profane.png","link":"Profane"},{"text":"Hoarding","image":"Hoarding.png","link":"Hoarding"}]},{"title":"Additional items","contents":[{"text":"Brassican","image":"Brassican.png","link":"Brassican"},{"text":"Looting","image":"Looting.png","link":"Looting"},{"text":"Scavenging","image":"Scavenging.png","link":"Scavenging"}]},{"title":"Experience","contents":[{"text":"Enlightened","image":"Enlightened.png","link":"Enlightened"},{"text":"Tinker","image":"Tinker.png","link":"Tinker"},{"text":"Wise","image":"Wise.png","link":"Wise"}]},{"title":"Skilling","contents":[{"text":"Butterfingers","image":"Butterfingers.png","link":"Butterfingers"},{"text":"Breakdown","image":"Breakdown.png","link":"Breakdown"},{"text":"Charitable","image":"Charitable.png","link":"Charitable"},{"text":"Cheapskate","image":"Cheapskate.png","link":"Cheapskate"},{"text":"Confused","image":"Confused.png","link":"Confused"},{"text":"Furnace ","image":"Furnace (perk).png","link":"Furnace (perk)"},{"text":"Honed","image":"Honed.png","link":"Honed"},{"text":"Imp Souled","image":"Imp Souled.png","link":"Imp Souled"},{"text":"Polishing","image":"Polishing.png","link":"Polishing"},{"text":"Pyromaniac","image":"Pyromaniac.png","link":"Pyromaniac"},{"text":"Rapid","image":"Rapid.png","link":"Rapid"},{"text":"Refined","image":"Refined.png","link":"Refined"}]},{"title":"Miscellaneous","contents":[{"text":"Cautious","image":"Cautious.png","link":"Cautious"},{"text":"Committed","image":"Committed.png","link":"Committed"},{"text":"Efficient","image":"Efficient.png","link":"Efficient"},{"text":"Enhanced Efficient","image":"Enhanced Efficient.png","link":"Enhanced Efficient"},{"text":"Glow Worm","image":"Glow Worm.png","link":"Glow Worm"},{"text":"Hallucinogenic","image":"Hallucinogenic.png","link":"Hallucinogenic"},{"text":"Junk Food","image":"Junk Food.png","link":"Junk Food"},{"text":"Mysterious","image":"Mysterious.png","link":"Mysterious"},{"text":"Prosper","image":"Prosper.png","link":"Prosper"},{"text":"Talking","image":"Talking.png","link":"Talking"},{"text":"Trophytaker's","image":"Trophytaker's.png","link":"Trophytaker's"}]}],"name":"Perks","title":"[[PerksInvention perks]]"}