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Tabular Mastery / Avoidance Equivalence

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Tabular Mastery / Avoidance Equivalence

Postby 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.
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Tabular Mastery / Dodge Equivalence

Postby 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.
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Tabular Mastery / Parry Equivalence

Postby 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.
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Tabular Mastery / Avoidance Equivalence

Postby 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.
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Re: Tabular Mastery / Avoidance Equivalence

Postby 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.
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Re: Tabular Mastery / Avoidance Equivalence

Postby 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
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Re: Tabular Mastery / Avoidance Equivalence

Postby 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).
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Re: Tabular Mastery / Avoidance Equivalence

Postby 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
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Re: Tabular Mastery / Avoidance Equivalence

Postby 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.
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