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.