Some math on Seal of Vengeance ( SoV )

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Some math on Seal of Vengeance ( SoV )

Postby jere » Tue Aug 14, 2007 5:45 pm

Seal of Vengeance is always a hot topic amongst paladins both horde and alliance. People argue over whether it is viable as a tank seal, a dps seal, and whether or not the horde should have it.

The basics of this seal is that on any given swing that does damage, there is some chance that it will proc Holy Vengeance, a 12 second DoT. Holy Vengeance stacks up to 5 times and each time it is applied, it refreshes the 12 second timer. Some things to note:

1. Holy Vengeance is not a judgement (CS does not refresh it), it is a DoT applied by a seal.
2. Holy Vengeance has a chance to fall off if it is not applied in 12 seconds, so this seal relies on chance.
3. It is affected by spell hit and melee hit (indirectly) as well as an internal proc chance (20 procs per minute on average)
4. Both partially blocked hits and glancing blows have a chance to proc holy vengeance (from my combat log parses)
5. The application of Holy Vengeance is a binary chance to be resisted, but the dot itself can be partially resisted.

So what is the possibility that you will successfully proc Holy Vengeance on a given hit?

Well some knowns:

1. The probability that you will proc Holy Vengeance if a melee hit does damage is 20 ppm or weapon_speed/3 (weapon_speed is capped at 3.0 for this equation).

2. The chance that if you try to proc Holy Vengeance, that it will be resisted is 17% against a lvl 73 boss. So the chance to actually land the proc when it tries to be applied is 83%.

3. The chance to do a damage against a lvl 73 boss is 80.8%. This comes from 8% chance to miss, 5.6% chance to be dodged, and 5.6% chance to be parried.

Now into the math. Lets declare some events:

S = [Holy Vengeance is applied (not resisted)]
A = [Holy Vengeance tries to proc]
M = [A damaging melee attack was successful]

We know from Kalgan that P[A|M] = 20 ppm = weapon_speed/3
We also know that for the spell portion: P[S|A] = 0.83
Finally we know that for a melee hit: P[M] = 0.808

In the end we want P[S].

From basic probability laws we know P[S] = P[S|A]*P[A]/P[A|S]

The P[A|S] is 1 because the probability that Holy Vengeance tried to proc given that it was resisted is 1.

So P[S] = P[S|A]*P[A]

Likewise P[A] = P[A|M]*P[M]/P[M|A]

The P[M|A] is 1 because the probability that a successful melee attack occured given that Holy Vengeance tried to proc is 1.

So P[A] = P[A|M]*P[M]

This gives: P[S] = P[S|A]*P[A|M]*P[M]

So P[S] = 0.83*(weapon_speed/3)*0.808 = 0.67063*weapon_speed/3

So to look at how the different weapon speeds affect it's chance to successfully proc:

Code: Select all
Weapon Speed     P[S]
------------     -----
1.5              33.5320%
1.6              35.7675%
1.8              40.2384%
2.7              60.3576%
3.0+             67.0640%


Those percentages apply to each time you swing. So each time you swing your merciless gladiator's gavel (1.6 speed), you will have a 35.8% chance to apply holy vengeance.

Now lets look at the probability that a stack will fall off. For that to happen all swings in 12s will have to miss. So lets declare the event:

F = [Holy Vengeance stack falls off]

and so

P[F] = (1-P[S])^(12/weapon_speed).

Here is a table for the results:
Code: Select all
Weapon Speed     P[F]
------------     -----
1.5              3.8098%
1.6              3.6154%
1.8              3.2321%
2.7              1.6370%
3.0              1.1767%  <--- sweet spot
3.3              1.7623%
3.6              2.4674%


If you are wondering why the percentage to fall off increases after 3.0 speed weapons, remember that for P[S], weapon speed was capped at 3 for the purposes of the PPM system of SoV (you can't have greater than 100% chance to proc). However, when figuring out the chance the stack would fall off you have to calculate the average number of hits in 12 seconds, so the weapon speed is not capped at 3 for that part of the equation.

If you are curious how the increase to 15sec duration will affect P[F]:
Code: Select all
Weapon Speed     P[F]
------------     -----
1.5              1.6832%
1.6              1.5765%
1.8              1.3704%
2.7              0.5855%
3.0              0.3876%  <--- sweet spot
3.3              0.6421%
3.6              0.9779%


DISCLAIMER: All these calculations are based upon averages and probabilities. Even with a low chance, bad luck happens and the stack can still fall off. AKA: Mileage may vary.
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Postby Swiffer » Wed Aug 15, 2007 2:23 am

nice stuff there :)
you seem to be a bit of a math buff. I was wondering, after reading a post by Suba claiming he was using weapon expertise instead of reckoning, what the break even point for avoidance was where weapon expertise becomes as good as reckoning to keep up SoV stacks.

I could do the maths myself , but I'm not really that good at it =\ and I have no clue how weapon expertise affects the chance to hit.

would be much appreciated :D
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Re: Some math on Seal of Vengeance ( SoV )

Postby Girard » Wed Aug 15, 2007 3:57 am

Since I haven't found any 3.0s +dmg weapons in game.. this proves that my personal belief that the Gavel of Unearthed Secrets is the best tanking weapon in game for us who use SoV. 2.7s and 24 sta, GO-GO!


Don't suppose we know what the +dmg coefficent is, do we?
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Re: Some math on Seal of Vengeance ( SoV )

Postby jere » Wed Aug 15, 2007 8:15 am

Swiffer wrote:nice stuff there :)
you seem to be a bit of a math buff. I was wondering, after reading a post by Suba claiming he was using weapon expertise instead of reckoning, what the break even point for avoidance was where weapon expertise becomes as good as reckoning to keep up SoV stacks.

I could do the maths myself , but I'm not really that good at it =\ and I have no clue how weapon expertise affects the chance to hit.

would be much appreciated :D


There are two problems with doing the math:

1. Reckoning procs based off when you are attacked so it has a lot of variables to consider.
2. So far know one seems to know the real effect of weapon expertise. Even the post made by the blue on the forums seems to be incorrect given testing.

Things to consider though: Weapon expertise is probably more reliable (I go with precision honestly since I know it gives 3% hit for sure), but reckoning does have the nice effect of fast stack building (along with other nice benefits).

Personally, I took reckoning for utility purposes not related to SoV. One day I might drop it for weapon expertise, but right now, I find it useful for soloing/aoe purposes.

If you are interested in how they would affect the math..well:
IF you knew the effects of weapon expertise, you would use those to adjust P[M] to the appropriate number (it would increase).
IF reckoning was indeed easy to quantify, you would determine the average number of extra swings in a 12 (or 15) second duration, given your weapon speed, and the final equation would look like:

P[F] = (1 - P[S])^(12/weapon_speed + avg_reck_swings)

Girard wrote:Since I haven't found any 3.0s +dmg weapons in game.. this proves that my personal belief that the Gavel of Unearthed Secrets is the best tanking weapon in game for us who use SoV. 2.7s and 24 sta, GO-GO!


Don't suppose we know what the +dmg coefficent is, do we?


SoV gets 3.4% spell dmg per stack per tick (17% per tick for a 5 stack).
JoV gets 42.9% spell dmg straight up.
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