Revenge

Revenge

Release date	20 November 2012 (Update)
Members	No
Skill	Defence
Level	15
Type	Threshold
Adrenaline	−15%
Equipment	Shield
Cooldown	45 seconds
Description
Enact revenge upon your foes, causing any attacks you receive to increase your max hit by 10%, stacking up to 100%. Lasts 20 seconds.
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Revenge is a threshold Defence ability. When activated, any attacks the user receives increases the user's own max hit by 10% of the normalised damage range up to a maximum of 100% stacked. This ability lasts 20 seconds.

Revenge will increase max hit by only 5% per stack if activated with a defender.

Removing the shield while Revenge is still active will remove all stacks immediately.

This ability is particularly potent in PvP when used in conjunction with the Dark bow special attack.

If revenge is used with Raids armour and a defensive reset occurs, and revenge is activated again before the duration of the first has ended, the revenge stacks will be reset back to zero.

Calculations

The following calculations assume the use of a shield and no Raids armour.

Average hit formula for abilities

• Without Revenge :

$a = \frac{M + m}{2}$

• With Revenge :

$A = \frac{M \cdot (100$

• Average hit increase formula:

$\frac{A - a}{a} = a_{increase}$

Notes

• $m$ = Minimum ability damage
• $M$ = Maximum ability damage
• $s$ = number of revenge stacks
• $a_{increase}$ = Average hit increase
• $a$ = Average hit without revenge
• $A$ = Average hit with revenge

Examples

• Average hit increase for Slice (damage range 30–120%) with 10 Revenge stacks:

$a={\frac {120\%+30\%}{2}}=75\%$

$A={\frac {120\%\cdot (100\%+10\%\cdot {\frac {120\%-30\%}{120\%}}\cdot 10)+30\%}{2}}=120\%$

$a_{increase}={\frac {129\%-75\%}{75\%}}=60\%$

Comparison with 2 handed or dual wield weapons

The downside of revenge is that you need to wear a shield to use it, this means you ability damage will be reduced to 2/3 of the ability damage of 2 handed or dual wield. So we need a minimum average hit increase to be on par or better than 2 handed or dual wield. This minimum can be calculated as follows:

$\frac{2}{3} \cdot (a + a \cdot a_{increase}^{min}) \geq a$

$\Rightarrow \frac{2}{3} \cdot (1 + a_{increase}^{min}) \geq 1$

$\Rightarrow a_{increase}^{min}\geq {\frac {3}{2}}-1=50\%$

Now we can use this to calculate the average damage increase compared to 2 handed or dual wield. We can calculate this as follows:

$a_{increase}^{2H}={\frac {2}{3}}\cdot (a_{increase}^{Revenge}-50\%)$

Analysis

The following tables assume the use of a shield and no Raids armour.

Typically, abilities have ability damage ranges from 20% to 100%; this can be represented as a ratio 1:5. As an example, Havoc's ability damage range is 31.4–157%; this can be calculated as 20–100%, as the percentage range ratio is 1:5.

As such, Revenge increases the ability damage of abilities with a 1:5 ratio as follows:

# Stacks	Increase	Avg hit	Avg hit increase	Avg hit increase compared to 2H or dual wield
0	0%	60%	0%	-33,33%
1	10%	64%	6,67%	-28,89%
2	20%	68%	13,33%	-24,44%
3	30%	72%	20%	-20%
4	40%	76%	26,67%	-15,56%
5	50%	80%	33,33%	-11,11%
6	60%	84%	40%	-6,67%
7	70%	88%	46,67%	-2,22%
8	80%	92%	53,33%	2,22%
9	90%	96%	60%	6,67%
10	100%	100%	66,67%	11,11%

Notes

• The table above applies to most abilities, with the exception of abilities with bleed effects.

For abilities with an ability damage ratio of 1:4 such as Slice (30–120%), the average hit increase of Revenge varies. The table below lists the average hit increase of these abilities:

Analysis table
Skill	Ability	Min hit	Max hit (Normal)	Max hit (w/ 10 stacks)	Average hit (Normal)	Average hit (w/ 10 stacks)	Average hit increase	Avg hit increase compared to 2H or dual wield
Attack
	Slice	30%	120%	210%	75%	120%	60%	6,67%
	Slice (Stun)	80%	146%	212%	113%	146%	29%	-13,86%
	Overpower	200%	400%	600%	300%	400%	33%	-11,11%
Strength
	Hurricane	84%	161%	238%	123%	161%	31%	-12,38%
	Hurricane (Adjacent)	66%	219%	372%	143%	219%	54%	2,46%
	Meteor Strike	250%	350%	450%	300%	350%	17%	-22,22%
	Pulverise	250%	350%	450%	300%	350%	17%	-22,22%
	Frenzy (Hit #1)	80%	180%	280%	130%	180%	38%	-7,69%
	Frenzy (Hit #2)	90%	200%	310%	145%	200%	38%	-8,05%
	Frenzy (Hit #3)	100%	220%	340%	160%	220%	38%	-8,33%
	Frenzy (Hit #4)	110%	240%	370%	175%	240%	37%	-8,57%
Ranged
	Snap Shot (Hit #1)	100%	120%	140%	110%	120%	9%	-27,27%
	Snap Shot (Hit #2)	100%	210%	320%	155%	210%	35%	-9,68%
	Snipe	125%	219%	313%	172%	219%	27%	-15,12%
	Incendiary Shot	250%	350%	450%	300%	350%	17%	-22,22%
	Shadow Tendrils (Self)	33%	250%	467%	142%	250%	77%	17,79%
	Shadow Tendrils (Enemy)	66%	500%	934%	283%	500%	77%	17,79%
Magic
	Omnipower	200%	400%	600%	300%	400%	33%	-11,11%
	Detonate	100%	350%	600%	225%	350%	56%	3,70%
	Tsunami	200%	300%	400%	250%	300%	20%	-20,00%
Constitution
	Storm Shards & Shatter (1 stack)	75%	95%	115%	85%	95%	12%	-25,49%
	Onslaught (Hit #1)	33%	150%	267%	92%	150%	64%	9,29%
	Onslaught (Hit #2)	44%	183%	322%	114%	183%	61%	7,49%
	Onslaught (Hit #3)	55%	216%	377%	136%	216%	59%	6,27%
	Onslaught (Hit #4)	66%	249%	432%	158%	249%	58%	5,40%
	Onslaught (Hit #5)	77%	282%	487%	180%	282%	57%	4,74%
	Onslaught (Hit #6)	88%	315%	542%	202%	315%	56%	4,22%
	Onslaught (Hit #7)	99%	348%	597%	224%	348%	56%	3,80%
	Onslaught (Hit #8)	110%	381%	652%	246%	381%	55%	3,46%
	Onslaught (Hit #9)	121%	414%	707%	268%	414%	55%	3,18%
	Onslaught (Hit #10)	132%	447%	762%	290%	447%	54%	2,94%
	Onslaught (Hit #11)	143%	480%	817%	312%	480%	54%	2,73%
	Onslaught (Hit #12)	154%	513%	872%	334%	513%	54%	2,55%