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Some Blessing of Sanctuary Math

Warning: Theorycraft inside.

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Some Blessing of Sanctuary Math

Postby jere » Wed Aug 01, 2007 2:56 pm

I want to start this off by saying I am not trying to comment so much on how good/better/worse BoSanc is, but more show some interesting trends in BoSanc that come out in the math. I used excel to do some calculations to see what impact BoSanc had on armor and incoming damage. Here is the sheet I came up with

http://spreadsheets.google.com/pub?key= ... mXLDZ0N2XA

Incase you want more info on what the columns are:
A -- Various Armor Values
B -- The calculated Damage Reduction against a lvl 73 mob
C -- The multiplier you use along with incoming unmitigated damage (1-DR)
D -- The amount of damage BoSanc actually reduces damage by for that AC

F -- Damage you took after armor without BoSanc
G -- Damage you took after armor with BoSanc
H -- The "effective" (1-DR) mulitiplier if you account for BoSanc
I -- The "effective" DR value if you account for BoSanc
J -- The "effective" AC if you account for the damage reduction of BoSanc
K -- The AC multiplier to get from AC to "effective" AC from BoSanc
L -- The damage reduction achieved from BoSanc
M -- The multiplier used to get the damage reduction in column L

Anyway, so some trends:

Higher AC ==> Less damage reduced by BoSanc (independent of incoming damage)
Higher AC ==> More "effective" armor added from BoSanc (declines in % though)
Higher incoming damage ==> less damage reduction from BoSanc (independent of AC)

The thing I found interesting was, no matter what your armor value (AC) is, BoSanc reduces damage by the same percent given the same incoming unmitigated damage.

If an enemy hits for 10000 damage, then BoSanc reduces that damage by 0.8% (a multiplier of 0.992) regardless of AC

If an enemy hits for 20000 damage, then BoSanc reduces that damage by 0.4% (a multiplier of 0.996) regardless of AC.

It looks like the DR of BoSanc is defined by the equation:

80/unmitigated_dmg

And the multiplier for this is:

1-80/unmitigated_dmg

Where 80 is the BoSanc value of reduction (highest rank so far)

Anyways, I didn't post all of this to prove any points, but just found the math behind it interesting.
Last edited by jere on Wed Aug 01, 2007 10:27 pm, edited 1 time in total.
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Postby Fridmarr » Wed Aug 01, 2007 4:15 pm

In other words, thank God it produces some threat to justify the cost of the reagent?
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Postby jere » Wed Aug 01, 2007 8:08 pm

Fridmarr wrote:In other words, thank God it produces some threat to justify the cost of the reagent?


LoL

yep.
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Postby Joanadark » Wed Aug 01, 2007 9:01 pm

nice, thoughtful work you've done here.

would you mind if I added some of your observations to the section of Mysterious Ways discussing BoSanc, and possibly link your spreadsheet?

You'd be properly credited of course.
(p.s. in order to credit you, what server are you on and is your character's name Jere, or is that a shortened username?)
Arkham's Razor: a theory which states the simplest explaination tends to lead to Cthulu.
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Postby Baelor » Wed Aug 01, 2007 9:21 pm

Joanadark wrote:nice, thoughtful work you've done here.

would you mind if I added some of your observations to the section of Mysterious Ways discussing BoSanc, and possibly link your spreadsheet?

You'd be properly credited of course.
(p.s. in order to credit you, what server are you on and is your character's name Jere, or is that a shortened username?)

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Postby jere » Wed Aug 01, 2007 10:25 pm

Joanadark wrote:nice, thoughtful work you've done here.

would you mind if I added some of your observations to the section of Mysterious Ways discussing BoSanc, and possibly link your spreadsheet?

You'd be properly credited of course.
(p.s. in order to credit you, what server are you on and is your character's name Jere, or is that a shortened username?)


yeah, that is fine. I don't mind at all.

As stated before, I am Jere on the Llane server (or llame server as the pvp'ers like to call it)

If you have any questions about what equations I used, just ask. I took it for granted that Google Docs would let yall see the equations for each cell, but now looking at it, I am not sure it did. Most of it is pretty straight forward though.
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Postby Garwin » Thu Aug 02, 2007 4:39 am

Considering the general hitpoint/mitigation short fall paladin tanks contend with. Do you think that changing this blessing so that it's effects took place after armour mitigation rather than before would go some way to making this a more viable prot pally tool.

And perhaps also changing it so that it was a "self buff" only akin to rightious fury.

Thus it would become purely a paladin perk and acually used as well as the kings blessing.
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Postby Base » Thu Aug 02, 2007 4:48 am

I think a self buff would be nice - I always use kings for tanking (well for kara at least) - the damage mitigation on BoS is a joke at higher levels and threat is not really something I'm short of. Now if it reduced the damage by a percent - that would be a talent :)
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Postby Lore » Thu Aug 02, 2007 7:18 am

I use BoSanc purely because we usually have 4 paladins in our raids, and it's that or Salv.
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Postby jere » Thu Aug 02, 2007 11:34 am

Garwin wrote:Considering the general hitpoint/mitigation short fall paladin tanks contend with. Do you think that changing this blessing so that it's effects took place after armour mitigation rather than before would go some way to making this a more viable prot pally tool.

And perhaps also changing it so that it was a "self buff" only akin to rightious fury.

Thus it would become purely a paladin perk and acually used as well as the kings blessing.


If it worked after armor then the following would be true:
Higher AC ==> Higher effective Damage Mitigation %
Higher incoming damage ==? lower effective damage mitigation %

And the DR equation would be DR = 80/mitigated damage

mitigated damage is less than unmitigated damage, so the DR would go up

It would be a decent buff in that if you look at the following scenarios:

10000 unmitigated hit with 15000 AC ==> 0.982 DR multiplier (1.8%)
10000 unmitigated hit with 20000 AC ==> 0.979 DR multiplier (2.1%)
20000 unmitigated hit with 15000 AC ==> 0.991 DR multiplier (0.9%)
20000 unmitigated hit with 20000 AC ==> 0.989 DR multiplier (1.1%)

In terms of effective armor:
10000 unmitigated hit with 15000 AC ==> 15496 effective AC
10000 unmitigated hit with 20000 AC ==> 20681 effective AC
20000 unmitigated hit with 15000 AC ==> 15246 effective AC
20000 unmitigated hit with 20000 AC ==> 20355 effective AC

So it would be a definite buff and would increase in power as we gathered more AC. It would still decrease in effectiveness as we fight harder bosses, but the difference isn't too bad.
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