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Stat preference wrt overall damage taken

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Stat preference wrt overall damage taken

Postby Koatanga » Mon Jan 24, 2011 2:01 pm

I am looking at putting together a rudimentary stat-value guide for myself. The basics for this stemmed from the post about which trinket is beter, the 346 Finger or a 333 mastery trinket. One has a ton of parry, the other has a lesser ton of mastery. The net result for the poster was a 1% drop in avoidance + mastery. Another example was the Iceborne Breastplate versus the blue JP item.

I thought it was an interesting question - how much additional pure avoidance makes up for the loss of 1% combat table coverage when trading block for parry/dodge?

I came up with a basic formula for damage taken, being:
boss chance to hit - (dodge% + parry% + block% * .4) = % of potential damage that actually lands.

So if I have 11% dodge + 12% parry + 50% block, I will actually be hit by 54.4% of incoming damage. Increasing parry by 1% decreases damage taken to 53.4%, which is a 1.8% decrease in damage taken. The more overall avoidance I have, the more valuable the additional 1% avoidance becomes.

Increasing block by 1% gives me 54%, which is a decrease in damage taken of 0.7%.

However, block% itemisation is much cheaper, so you can get more block% for the same item-cost. The trick is in finding the tipping point, which is pretty much what this model is about. I want to plug in before and after numbers to see if damage taken goes up or down.

My questions are around the current damage model, and the influence of armour.

With the current damage model, is it relevant to look at a reduction in overall damage taken, or are we still looking at burst-scenarios where mitigating a greater number of hits (thus reducing the chance of 3 consecutive full hits, for example) is more important than the overall amount of damage taken?

As for armour, I am ignoring it for the purpose of weighting block, parry, and dodge. However, I wonder if that is correct, since the more pure avoidance I have, the less armour influences the overall reduction in damage taken, whereas the more I lean toward block%, the greater influence armour has. Armour only plays a role in blocked or full hits, since a dodged or parried hit does no damage anyway.

Part of the idea behind this is also to look at the chance of 3 consecutive full hits (being a potential death scenario). With my 11%/12%/50% example above, there is a 24.4% chance that I will take a full hit, a 5.95% chance I will take two in a row, and a 1.45% chance of taking 3 full hits in a row.

If I consider that to be an acceptable risk level, then I can also look at that value as well when assessing various combinations. While I want to reduce the overall damage taken, I don't want to run into the situation where burst survival becomes jeopardised. Block% has a much greater influence on burst scenario than parry or dodge because I can get more block% for the same item budget.

In the case of something like the Iceborne Breastplate, it has a stat (hit) that I would like to have more of. So I would like to see just how much I really lose from my JP chest in terms of table coverage and in terms of overall damage taken to see if I can justify adding a nice offensive stat (that will become more important once I have a 10-sec interrupt).
Retired. Koatanga, Shapely, Sultry, Doominatrix of Greenstone - Dath'Remar
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Re: Stat preference wrt overall damage taken

Postby theckhd » Tue Jan 25, 2011 7:20 am

This post might be of interest to you, since it has all of the formulas worked out already.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of Grehn|Skipjack.
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Re: Stat preference wrt overall damage taken

Postby Koatanga » Tue Jan 25, 2011 12:43 pm

theckhd wrote:This post might be of interest to you, since it has all of the formulas worked out already.

With due respect for the work you have done, I haven't been to a math class in over 20 years and don't work in an industry where I use ordered pairs and differentiation on a regular basis.

Your work is detailed and thorough and well thought out, but you lose me with the calcs and it's completely incomprehensible to me.

What I glean from reading that thread is that mastery > all on a point-for-point basis above certain levels of dodge and parry. What I need to know is by how much is mastery > all with my current numbers, so that I can determine if a piece with 206 dodge/parry rating beats a piece with 182 mastery (for instance), where the mastery piece represents greater combat table coverage but the piece with more pure avoidance may or may not offer better overall damage reduction.

That takes me back into your calcs, where I just get lost in your math. I read dB and while it's supposed to be about block, my brains insists it is a measure of sound pressure. Something about teaching old dogs new tricks, I guess.

I don't think I am alone in this, because I am seeing more and more threads about "is X piece better than Y piece" with this same scenario - one of the pieces has less mastery rating than the other piece has avoidance rating.
Retired. Koatanga, Shapely, Sultry, Doominatrix of Greenstone - Dath'Remar
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Re: Stat preference wrt overall damage taken

Postby theckhd » Tue Jan 25, 2011 4:35 pm

The first two equations outline the way damage intake is calculated, and involve no calculus at all.

Furthermore, you don't need any calculus to use the results of my derivation, provided you trust that I've done the math correctly. Equation (4) is all you need to do the calculations you want, along with equation (10) for avoidance DR.

If your mental block is preventing you from seeing past differential notation, here it is with a slightly different notation:


Code: Select all
F = K/(Ar+K)                                    (2)
W/Do = -X*F/(Ar+K)*[1-Av-0.4*B] - F*[Y+0.4*Z]   (4)
Yi = (yi/k)*(1-Ai/C)^2                          (10)


F is the armor reduction factor
K=32573 is the armor constant at level 85
Ar is your Armor

W is the absolute change in damage taken (i.e. 10 DPS or 100 damage, you can choose either units as long as Do matches)
Do is the boss' raw damage output (i.e. 40k DPS or 100k damage)
W/Do is the relative reduction in damage taken. Generally you won't need to explicitly define W or Do, you'll just solve for W/Do.
Av is your total post-diminishing returns avoidance
B is your total block percentage

Yi is the post-DR amount of avoidance granted by yi pre-DR avoidance, given that you have Ai post-DR avoidance of that type.
k=0.9560 and C=0.65631440 are the constants in the avoidance diminishing returns equation.

X is the amount of armor added
Y is the amount of avoidance added (in decimal notation, so 5% is 0.05)
Z is the amount of block added (in decimal notation)

This formulation is completely algebra-based from here on out, no calculus necessary.

As an example of how to use this, let's say you want to compare 50 dodge rating to 100 mastery rating. First, calculate the constants you need:

X=0 (we're not changing armor)
Z=100*2.25/Cm, where Cm is the mastery rating -> mastery conversion factor (Cm~179)
Y has to be calculated from equation (10). We add 100 rating, so yi=50/(100*Cd), where Cd is the dodge rating -> dodge % conversion factor. Note that we divide by 100 so that yi is in decimal notation. Cd is ~176. If we have 15% dodge fully raid-buffed, then Ai=0.15, and we can calculate Yi. This is what we plug in for Y; if you had more than one different type of avoidance rating, you would calculate each Yi separately and sum them to get Y.

The rest of your stats are pretty straightforward, calculate F by plugging your armor Ar into equation (2), and plug that, your total post-DR avoidance Av, total block chance B, and the appropriate constants into equation (4).

To compare the stats, first plug X=0, Y=0, and Z=(whatever it works out to) into that equation and find W/Do, the relative reduction in damage taken. Then repeat with X=0, Z=0, and Y=(whatever it works out to). The stat that gives you the larger number is the one that reduces damage taken the most.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of Grehn|Skipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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