Multiple Stoneskin procs

Icefire · 06-03-2008, 11:59 AM

First of all I'm not on PvP so don't flame me for that, at least.

From what I understand and gathered from this post by Fyreflyte, multiple procs are calculated by the following, where a is the proc chance of item A, b is the proc chance of item b etc:

a + (b*[1-{a/100}]) + (c*[1-{a/100}]*[1-{c/100}])+...

So for example if you had 2 items with 10% stoneskin, and 1 item with 3%, you would have:

3 + (10*[1-0.03]) + (10*[1-0.03]*[1-0.10]) = 21.43% chance of a stoneskin proc when hit.

Alternatively you could have ordered it differently, using:

10 + (10*[1-0.10]) + (3*[1-0.10]*[1-0.10]) = 21.43, in case you didn't believe that was right :P

Yeah I know the brackets aren't really needed in some cases, but it makes it easier to read.

My question is how to calculate the chance of one of the Displacement items, i.e. Soulshattering Band or Robe of Dark Power, which proc two triggers of stoneskin rather than just the one. It can't be a simple as multiplying the brackets by 2 for those items, because it works out differently depending which ones you use...

If you don't account for the two triggers then mages can get up to 68.2% stoneskin with a Dirge and Templar, 71.7% with the Runed Guard of Sel'nok up :D

FYI I'm bored camping Philosophers on an alt for Claymore :/

Pinski · 06-03-2008, 12:21 PM

Basically let's assume you have the following gear:

Robe of Dark Power
Shoulders of Dispersion
Bracers of Dispersion
Belt of Dispersion
Earring of Templar's Dispersion
Soulshattering Band

You have, 3 Dispersion procs, 1 Templar's Dispersion, and 2 Displacements. So you have the following chance to proc a stoneskin for the next hit:
1-(.9*.9*.9*.9*.9*.97)=~.427, or 42.7% chance for a stoneskin on the next hit.

So, now we know about the next hit. When you have Displacement up, you can still proc it again on a stone-skinned hit. Now we know that if we only have a 19% chance for Displacement to trigger, well that means 81% of hits will not have Displacement for the next 2 hits.

What we also know now is that 44.5% of all stoneskins will have a 2nd trigger. So where does that put us? It puts us an additional 19% chance to have a 2nd trigger on stoneskin, which means we add in .9*.9 again to the formula above, and we end up getting:
53.6% chance to stoneskin.

If we add in a Mystic we get(1-.87*.87*.87*.87*.87*.94*.87*.87):
64.5% chance

Templar+Dirge we get(1-.86*.86*.86*.86*.86*.958*.86*.86):
66.7% chance

Templar+Dirge+Mystic we get(1-.83*.83*.83*.83*.83*.94*.83*.83):
74.5% chance

Templar+Dirge+Mystic+Book we get(1-.805*.805*.805*.805*.805*.94*.805*.805):
79.4% chance

Also, I'm confused by your math on how you get 68.2% with just Templar+Dirge, and 71.7% with the Book as well, because I'm getting the following:
1-.86*.86*.86*.86*.86*.958=54.9% Templar+Dirge makes 14% and 4.2%
1-.835*.835*.835*.835*.835*.9505=61.4% Templar+Dirge+Book makes 16.5% and 4.95%

Your initial math is correct, as seen by 1-.9*.9*.97=21.43%, just I think you've got some wrong math on Proc Buffs going on there.

Icefire · 06-03-2008, 12:34 PM

Heh was hoping you'd post Cal. I think the mistake I made on Templar and Dirge was getting the %'s wrong, for some reason I thought that with Blessings and LotD they were 18% and 15% respectively.

Looks like my way was a ridiculously complicated method lol. I was way off on the Displacement procs too, thanks for clarifying that. Would a warlock also increase Unyielding Benediction and Percussion of Stone? Either way, almost 80% stoneskin is pretty powerful, even if you do need a group stacked around you to have it.

dakkota · 06-03-2008, 12:36 PM

Avatar of Math strikes again

Pinski · 06-03-2008, 01:35 PM

Quote:

Originally Posted by Icefire

Heh was hoping you'd post Cal. I think the mistake I made on Templar and Dirge was getting the %'s wrong, for some reason I thought that with Blessings and LotD they were 18% and 15% respectively.

Looks like my way was a ridiculously complicated method lol. I was way off on the Displacement procs too, thanks for clarifying that. Would a warlock also increase Unyielding Benediction and Percussion of Stone? Either way, almost 80% stoneskin is pretty powerful, even if you do need a group stacked around you to have it.

Yes, a warlock would increase both. If you want to tank raid mobs as a Mage, you should be either a Wizard or a Warlock. As a wizard with Templar Stoneskin(20.4%, because of the way Templar Stoneskin works it acts like the caster is casting it, so you go from 17.4% to 20.4% with Ancestry), and PoS(16.8%) will be added, along with a 17% Displacement proc. Giving you the following:
1-.83*.83*.83*.83*.83*.83*.94*.796*.832*.83*.83*.83 = 88.4%, without the book!
Add in the book and you get:
1-.805*.805*.805*.805*.805*.805*.94*.78*.832*.805*.8 05*.805 = 91.3% with the book.

If you are a Warlock instead, you will get the following, 22% from Templar Stoneskin, 20.8% from PoS and thus have:
1-.83*.83*.83*.83*.83*.94*.78*.792*.83*.83 = 84.2% without
1-.805*.805*.805*.805*.805*.94*.78*.792*.805*.805 = 87.3% with.

So basically, Wizards get 88.4% static Stoneskin, lol, basically making the best group for a raid tanking Sorceror to be:
Sorceror, Dirge, Guardian, Templar, Mystic, Illusionist.

Yah, that'd be a pretty stellar group for them. Of course, having all that gear is another question. If only I was a Wizard, then I would have all that gear

, I just don't have the 2-set, boo.

Dehah · 06-03-2008, 03:25 PM

Quote:

Originally Posted by Pinski

You have, 3 Dispersion procs, 1 Templar's Dispersion, and 2 Displacements. So you have the following chance to proc a stoneskin for the next hit:
1-(.9*.9*.9*.9*.9*.97)=~.427, or 42.7% chance for a stoneskin on the next hit.
So, now we know about the next hit. When you have Displacement up, you can still proc it again on a stone-skinned hit. Now we know that if we only have a 19% chance for Displacement to trigger, well that means 81% of hits will not have Displacement for the next 2 hits.

What we also know now is that 44.5% of all stoneskins will have a 2nd trigger. So where does that put us? It puts us an additional 19% chance to have a 2nd trigger on stoneskin, which means we add in .9*.9 again to the formula above, and we end up getting:
53.6% chance to stoneskin.

You're not accounting for the fact that a stoneskin'd hit can proc Dispersion and Displacement again. You acknowledge that it can, but your numbers don't reflect it.

The Math involved in calculating an avoidance percentage due to these stoneskin procs is quite involved as you have to consider the several different states the player can be in:

1. None
2. Dispersion
3. Dispersion - Displacement (2 triggers remaining)
4. Displacement (2 Triggers remaining)
5. Displacement (1 Trigger remaining)
6. Displacement (2 Triggers remaining) - Dispersion
7. Displacement (1 Trigger remaining) - Dispersion

This is one of those situations where a simple simulation can be created much more quickly than actually hammering out the exact probabilities.

Using the numbers from your example 3 (10% Dispersion), 1 (3% Dispersion), and 2 (10% Displacement), I get 57.48% avoidance after 100,000 simulated hits.

Some assumptions I used for the model:

1) You can only have one Dispersion proc active on yourself at one time, otherwise you get a "Won't Take Effect" message.
2) You can only have one Displacement proc active on yourself at one time, otherwise you get a "Won't Take Effect" message. This means that if you have 1 trigger remaining, it will not refresh and become 2.
3) The buff is removed before the check to proc it occurs. This means that in the case of Dispersion, if the hit is absorbed by Dispersion, then it is possible that it can proc and go back on you.

I can simulate other gear / buff combinations if anyone wants.

Arlen Bouldersmi · 06-03-2008, 06:20 PM

my head hurts

Homegrown · 06-03-2008, 11:59 PM

yah im with arlen, this post made my head explode...

Ramone · 06-04-2008, 12:38 AM

That's ok Home, mine just melted!

But good shit none the less.

Elvbryn · 06-04-2008, 03:13 PM

i was good up till dehah's post