Tabular Mastery / Avoidance Equivalence

My AddOns at WoWInterface · by **Digren** » Sun May 08, 2011 9:47 pm

Theck has derived the necessary formulas to compare mastery with avoidance for both maximum damage reduction and combat table coverage. I want to generate a table of equivalents for a range of avoidance values.

If you want to skip the derivations:
Tabular Mastery / Dodge Equivalence

Constant and variable definitions:

Ad = post-DR (character sheet) dodge
Ap = post-DR (character sheet) parry
Av = post-DR (character sheet) avoidance, equal to Ad + Ap + 5%
A = post-DR avoidance, either parry or dodge when unspecified
dAd, dAp, dAv = changes in post-DR dodge, parry, or avoidance

Ad' = pre-DR dodge
Ap' = pre-DR parry
A' = pre-DR avoidance, either parry or dodge when unspecified
dAd', dAp', dA' = changes in pre-DR dodge or parry

Rd = dodge rating
Rp = parry rating
R = avoidance rating, either parry or dodge rating when unspecified
dRd, dRp, dR = changes in dodge or parry rating

B = block percent
dB = change in block percent

Rm = mastery rating
dRm = change in mastery rating

For dodge: given post-DR (character sheet) dodge Ad, how much additional dodge rating is MDR-equivalent to one mastery rating? How much additional dodge rating is CTC-equivalent to one mastery rating? For parry: given post-DR (character sheet) parry Ap, how much additional parry rating is MDR-equivalent to one mastery rating? How much additional parry rating is CTC-equivalent to one parry rating?

This is based on Theck's formulas here.

The important place to start is equation (4), which defines the change in damage taken dD for a given melee swing Do based on changes in armor dAr, avoidance dAv, or block dB:

Code: Select all: dD/Do = -dAr*S*Fa/(Ar+K)*[1-Av-0.4*B] - Fa*S*[dAv+0.4*dB] (4)

Values S, Fa, and K are the Sanctuary damage reduction factor, the armor mitigation factor, and the opponent armor coefficient, all of which are constants when considering a level 85 character facing a fixed-level opponent.

dAr is a change in armor, which for the purposes of this discussion is assumed to be zero. This simplifies the above equation to:

Code: Select all: dD/Do = 0 - Fa*S*[dAv+0.4*dB] (i)

To calculate equivalence in damage reduction between a change in avoidance and a change in block, we want to find values dR and dRm such that:

Code: Select all: dAv = 0.4*dB (ii)

To calculate equivalence in combat table coverage between a change in avoidance and a change in block, we want to find values dR and dRm such that:

Code: Select all: dAv = dB (iii)

Without diminishing returns, changes in mastery rating dRm yield linear changes in block percent dB. From Theck:

theckhd wrote:dB is linear in mastery, at 2.25 percent per point of mastery, or 0.0225/Cm percent per point of mastery rating, with Cm being the mastery rating conversion factor (Cm=179.28 @ level 85). In other words, dB = 0.0225/Cm*dRm for mastery rating dRm.

Because I'm seeking an equivalence to a change in one mastery rating, dRm = 1 and thus dB = 0.0225/Cm = 0.0225/179.28 = 1/7968.

Substituting back into (ii) and (iii) yields:
MDR:

Code: Select all: dAv = 0.4 / 7968 = 1/19920 (iv)

CTC:

Code: Select all: dAv = 1/7968 (v)

Back to Theck, the diminishing returns equation is:

Code: Select all: 1/A = k/A' + 1/C (8)

where k = 0.9560 and C = 0.65631440 at level 85. (Note that I am using A' for pre-DR avoidance and A for post-DR avoidance.) Important note: for this equation, A is only the portion of post-DR avoidance subject to diminishing returns. For dodge, A is thus Ad - 3.9705%, while for parry, A is Ap - 5%.

Differentiating both sides of the equation and solving for post-DR avoidance yields:

Code: Select all: dA = -k*dA'*(A/A')^2 (9)

Solve the diminishing returns equation for (A/A') and substitute yields:

Code: Select all: dA = (dA'/k)*(1-A/C)^2 (10)

This equation is important, as it defines a change in post-DR avoidance dA (either dodge or parry) in terms of initial post-DR avoidance A (still excluding the portion not subject to diminishing returns) and a change in pre-DR avoidance dA'.

The next step is to define an equation for pre-DR avoidance in terms of avoidance rating. From Theck:

theckhd wrote:dA' is simply equal to 0.01*dR/Ca, the added avoidance rating divided by the avoidance rating conversion factor (Ca=176.7189) times 0.01 to put it in decimal notation.

Substituting into equation (10):

Code: Select all: dA = (0.01*dR/(k*Ca))*(1-A/C)^2 (vi)

Filling in some constant values:

Code: Select all: dA = (0.01*dR/(0.9560*176.7189))*(1-A/0.65631440)^2 dA = (dR/16894.3268)*(1-A/0.65631440)^2 (vii)

When changing only dodge, dA_dodge = dAv. When changing only parry, dA_parry = dAv. Thus, using equations (iv), (v), and (vii), I can now set up a table of dodge or parry rating equivalents to one mastery rating, for a given initial post-DR dodge or parry percent.

My AddOns at WoWInterface · by **Digren** » Sun May 08, 2011 9:48 pm

Columns are:
Dodge% : Character Sheet Dodge
1MDR : Dodge Rating Equivalent to One Mastery Rating for Maximum Damage Reduction
1CTC : Dodge Rating Equivalent to One Mastery Rating for Combat Table Coverage

Code: Select all: Dodge% 1MDR 1CTC -------- -------- -------- 8.00% 0.963 2.407 8.20% 0.969 2.422 8.40% 0.975 2.438 8.60% 0.982 2.454 8.80% 0.988 2.470 9.00% 0.995 2.487 9.20% 1.001 2.503 9.40% 1.008 2.520 9.60% 1.015 2.537 9.80% 1.022 2.554 10.00% 1.028 2.571 10.20% 1.035 2.588 10.40% 1.042 2.606 10.60% 1.049 2.624 10.80% 1.057 2.641 11.00% 1.064 2.659 11.20% 1.071 2.678 11.40% 1.078 2.696 11.60% 1.086 2.715 11.80% 1.093 2.734 12.00% 1.101 2.753 12.20% 1.109 2.772 12.40% 1.116 2.791 12.60% 1.124 2.811 12.80% 1.132 2.831 13.00% 1.140 2.851 13.20% 1.148 2.871 13.40% 1.157 2.891 13.60% 1.165 2.912 13.80% 1.173 2.933 14.00% 1.182 2.954 14.20% 1.190 2.976 14.40% 1.199 2.997 14.60% 1.208 3.019 14.80% 1.216 3.041 15.00% 1.225 3.063 15.20% 1.234 3.086 15.40% 1.243 3.109 15.60% 1.253 3.132 15.80% 1.262 3.155 16.00% 1.271 3.179 16.20% 1.281 3.203 16.40% 1.291 3.227 16.60% 1.300 3.251 16.80% 1.310 3.276 17.00% 1.320 3.301 17.20% 1.330 3.326 17.40% 1.341 3.352 17.60% 1.351 3.377 17.80% 1.361 3.403 18.00% 1.372 3.430

A few notes:

1. When reading your character sheet dodge percent, do so with all your regular self and group or raid buffs. The buffs will move you forward along the diminishing return curve, making dodge rating slightly less valuable than if you use your unbuffed dodge percent.

2. Once your character sheet dodge exceeds about 9.2%, one mastery rating yields a greater damage reduction than one dodge rating. The value of mastery rating continues to increase for MDR, slowly, so that one mastery rating is about 1.35 dodge rating for the best-geared characters. This means that, for MDR, pieces heavy on dodge rating are often better than pieces light on mastery rating.

3. Once your character sheet dodge exceeds the same 9.2%, it takes at least 2.5 dodge rating to yield the same combat table coverage as one mastery rating. The value of mastery rating continues to increase for CRC, so that one mastery rating is about 3.4 dodge rating for the best-geared characters. This means that, for CTC, pretty much any piece with mastery rating is better than a piece with dodge rating.

4. When considering the amount of dodge rating provided by a given piece of armor, don't forget to include 60.9% of the piece's agility as the equivalent to dodge rating. This can make pieces with agility and mastery rating great for both MDR and CTC.

My AddOns at WoWInterface · by **Digren** » Sun May 08, 2011 9:49 pm

Columns are:
Parry% : Character Sheet Parry
1MDR : Parry Rating Equivalent to One Mastery Rating for Maximum Damage Reduction
1CTC : Parry Rating Equivalent to One Mastery Rating for Combat Table Coverage

Code: Select all: Parry% 1MDR 1CTC -------- -------- -------- 8.00% 0.931 2.328 8.20% 0.937 2.343 8.40% 0.943 2.358 8.60% 0.949 2.374 8.80% 0.956 2.389 9.00% 0.962 2.404 9.20% 0.968 2.420 9.40% 0.974 2.436 9.60% 0.981 2.452 9.80% 0.987 2.468 10.00% 0.994 2.484 10.20% 1.000 2.501 10.40% 1.007 2.517 10.60% 1.014 2.534 10.80% 1.021 2.551 11.00% 1.027 2.568 11.20% 1.034 2.586 11.40% 1.041 2.603 11.60% 1.048 2.621 11.80% 1.055 2.639 12.00% 1.063 2.657 12.20% 1.070 2.675 12.40% 1.077 2.693 12.60% 1.085 2.712 12.80% 1.092 2.731 13.00% 1.100 2.750 13.20% 1.108 2.769 13.40% 1.115 2.788 13.60% 1.123 2.808 13.80% 1.131 2.828 14.00% 1.139 2.848 14.20% 1.147 2.868 14.40% 1.155 2.888 14.60% 1.164 2.909 14.80% 1.172 2.930 15.00% 1.180 2.951 15.20% 1.189 2.972 15.40% 1.198 2.994 15.60% 1.206 3.016 15.80% 1.215 3.038 16.00% 1.224 3.060 16.20% 1.233 3.083 16.40% 1.242 3.105 16.60% 1.251 3.128 16.80% 1.261 3.152 17.00% 1.270 3.175 17.20% 1.280 3.199 17.40% 1.289 3.223 17.60% 1.299 3.247 17.80% 1.309 3.272 18.00% 1.319 3.297

A few notes:

1. When reading your character sheet parry percent, do so with all your regular self and group or raid buffs. The buffs will move you forward along the diminishing return curve, making parry rating slightly less valuable than if you use your unbuffed parry percent.

2. Once your character sheet parry exceeds about 10.2%, one mastery rating yields a greater damage reduction than one dodge rating. (We knew this already; this is the data point Theck calculates in the derivations thread.) The value of mastery rating continues to increase for MDR, slowly, so that one mastery rating is about 1.3 parry rating for the best-geared characters. This means that, for MDR, pieces heavy on parry rating are often better than pieces light on mastery rating.

3. Once your character sheet dodge exceeds the same 10.2%, it takes at least 2.5 parry rating to yield the same combat table coverage as one mastery rating. The value of mastery rating continues to increase for CRC, so that one mastery rating is about 3.3 parry rating for the best-geared characters. This means that, for CTC, pretty much any piece with mastery rating is better than a piece with parry rating.

4. When considering the amount of parry rating provided by a given piece of armor, don't forget to include 26.25% of the piece's strength as parry rating. This may not be obvious when evaluating gear in isolation, though when you equip it the parry rating appears in your total.

My AddOns at WoWInterface · by **Digren** » Tue May 10, 2011 7:00 pm

The first question in response to these tables must be, "How can I use this?". Yet again here is where the tank stages concept helps. Let's make one simple assumption: that a tank has balanced dodge and parry for equal diminishing returns. Straight from the tables above, fully buffed, that means the tank has about 1% more parry than dodge.

With that in mind, look at the character models I created for each stage tank.

Stage One

Stage one survival model

A character with this gear set has:

122k health
25.4% dodge+parry+miss
42.7% block (for a total combat table coverage of 68.1%)
3.15% hit and 15 expertise including glyph (18 for a human)

This character has 20.4% dodge+parry, and, given our assumption, should thus have 9.7% dodge and 10.7% parry. Reading directly from the tables, this means that a stage one tank should consider 1.019 dodge or parry rating equal to 1 mastery rating for MDR, and should consider 2.545 dodge or parry rating equal to 1 mastery rating for CTC.

Stage Two

Stage two survival model

A character with this gear set has:

132k health
28.8% dodge+parry+miss
41.7% block (for a total combat table coverage of 70.5%)
2.35% hit and 20 expertise including glyph (23 for a human)

This character has 23.8% dodge+parry, and so should have 11.4% dodge and 12.4% parry. This means that a stage two tank should consider 1.078 dodge or parry rating equal to 1 mastery rating for MDR, and should consider 2.696 dodge or parry rating equal to 1 mastery rating for CTC.

Stage Three

Stage three survival model for a new raider

A character with this gear set has:

148k health
29.9% dodge+parry+miss
51.0% block (for a total combat table coverage of 80.8%)
2.26% hit and 15 expertise including glyph (18 for a human)

This character has 24.9% dodge+parry, and so should have 11.95% dodge and 12.95% parry. This means that a stage three tank should consider 1.101 dodge or parry rating equal to 1 mastery rating for MDR, and should consider 2.753 dodge or parry rating equal to 1 mastery rating for CTC.

Stage Four

Stage four survival model

A character with this gear set has:

156k health
30.5% dodge+parry+miss
55.1% block (for a total combat table coverage of 85.7%)
1.28% hit and 13 expertise including glyph (16 for a human)

This character has 25.5% dodge+parry, and so should have 12.25% dodge and 13.25% parry. This means that a stage four tank should consider 1.109 dodge or parry rating equal to 1 mastery rating for MDR, and should consider 2.772 dodge or parry rating equal to 1 mastery rating for CTC.

Stage Five

Stage five survival model

A character with this gear set has:

166k health
32.6% dodge+parry+miss
59.6% block (for a total combat table coverage of 92.2%)
1.27% hit and 13 expertise including glyph (16 for a human)

This character has 27.6% dodge+parry, and so should have 13.3% dodge and 14.3% parry. This means that a stage five tank should consider 1.153 dodge or parry rating equal to 1 mastery rating for MDR, and should consider 2.881 dodge or parry rating equal to 1 mastery rating for CTC.

My AddOns at WoWInterface · by **Digren** » Tue May 10, 2011 7:02 pm

Given the above, I can now provide unique weightings for mastery versus avoidance for each stage of tank.

by **Sur-Pseudo** » Mon Jun 13, 2011 3:43 pm

Any chance for a 4.2 preparatory update, with a few varied values of "uptime" on holy shield? (since damage reduction value will change)

i.e. If you use Holy shield once every 30 seconds (max), 35 seconds, 40/45/50/55/60 ? (depending on how easy it is to calculate, I would assume 30/35/40/60 would be the main numbers people would want... since there will be some 'fudging' of when exactly it is used depending on fight/play style

Theck did something on this on Sacred Duty: http://sacredduty.net/2011/06/02/math-a ... ly-shield/
But it doesn't clearly state the crossover numbers more specifically other than what you can eyeball

My AddOns at WoWInterface · by **Digren** » Mon Jun 13, 2011 4:05 pm

Digren wrote:To calculate equivalence in damage reduction between a change in avoidance and a change in block, we want to find values dR and dRm such that:
Code: Select all
dAv = 0.4*dB (ii)

To calculate equivalence in combat table coverage between a change in avoidance and a change in block, we want to find values dR and dRm such that:
Code: Select all
dAv = dB (iii)

The change in Holy Shield being tossed about for patch 4.2 has no effect on the combat table coverage numbers. In that case, the weighted value of any given type of table filler is equal once all conversions and diminishing returns have been taken into account. Only the MDR numbers will change.

For MDR, the table is generated assuming a 100% uptime of Holy Shield (but without the existing block value meta), yielding a 40% damage reduction for blocks. With the new Holy Shield, the damage reduction will vary from 30% (without HS) to 50% (with HS), with an average uptime (assuming on-cooldown use) of about 37%. This really doesn't change the table all that much in and of itself, and even if it did, almost no one uses MDR as a gearing strategy anyway.

Now any other changes they make to our mastery could have a huge effect on the tables. And the change they made to agility will have an effect as well (on the dodge table) in that the parry and dodge tables will now line up exactly. It's just too early to tell what else they plan to tweak, so there's not that much value in me spending an entire night running all the math again to show the shift in crossover for parry and dodge from 9-10% up to 12% or wherever (for the MDR column only).

by **Sur-Pseudo** » Mon Jun 13, 2011 4:20 pm

I suppose it doesn't have a huge effect, but 1MDR previously was always below what people had anyways.. With Theck's 4.2 model it appears you might need up to 16% Dodge+Parry before that changeover happens... Depending on fight mechanics for Firelands (which I have not tried yet), I don't know how often I'd expect to keep Holy Shield up, I doubt I'll be at 33% uptime... More likely 25% (every 40sec)..

I also don't expect to have CTC covered, so going into new content I was just fishing for more information so I can help decide what to do, I think at this point I'm leaning on stam-heavy gemming to help with new content, which means I'll be a bit lower on CTC, and Dodge/Parry might be slightly better damage reduction overall until I get to a point I can push CTC

by **yappo** » Mon Jun 13, 2011 5:39 pm

Digren wrote:
For MDR, the table is generated assuming a 100% uptime of Holy Shield (but without the existing block value meta), yielding a 40% damage reduction for blocks. With the new Holy Shield, the damage reduction will vary from 30% (without HS) to 50% (with HS), with an average uptime (assuming on-cooldown use) of about 37%. This really doesn't change the table all that much in and of itself, and even if it did, almost no one uses MDR as a gearing strategy anyway.

Casual raiders still benefit from an MDR based strategy. We tend to be slightly to heavily overgeared for our progression content.

In difference from what has been said in other threads healer mana is an issue simply because the raid tends to bot do more (non-fatal) bad stuff as well as producing a LOT less rdps, so fights drag out timewise.

Besides, even with an MDR based strategy a pally tank will hit 102.4 during Firelands. As an example I'm at 95% CTC raidbuffed with a grand total of one raid-drop (hate RNG), and that drop is even a loss CTC-wise as it's a preparatory replacement for my reputation agility-ring.