Blog · Derived

One formula for a tank: block, DEF and DMG RES

21 September 2026, rewritten 23 September · 7 min read

The expected damage of one hit as a single expression, the derivative of each stat read off it, and sliders to put your own numbers in.

The formula Fact

Expected damage of one hit, \(D\), as a share of an unmitigated hit, and effective HP \(H\). Everything below is read from the client’s Damage(); the skill percentage, the two fixed PvP rank divisors and the elemental ratio multiply every option the same way and are dropped.

$$ D \;=\; \underbrace{\frac{A}{A+\mathrm{DEF}}}_{\text{DEF}}\;\cdot\; \underbrace{\frac{1+\beta}{1+\rho}}_{\text{DMG RES}}\;\cdot\; \Big[\,(1-b)\,\underbrace{\big(1+c\,(m-1)\big)}_{\text{crit}}\;+\;b\,\underbrace{\frac{1-f}{v}}_{\text{block}}\,\Big], \qquad H \;=\; \frac{\mathrm{HP}}{D} $$ $$ b=\operatorname{clip}_{[0,1]}(B-\alpha),\qquad v=\max\!\big(1.5,\;1+E-\alpha\big),\qquad f=\min\!\Big(0.9,\;F\,\tfrac{A+\mathrm{DEF}}{A^{2}}\Big), $$ $$ c=\operatorname{clip}_{[0,1]}(0.05+\chi-r),\qquad m=\max\!\big(1.3,\;1+\mu-r\big). $$

Three facts of the engine sit inside it: a blocked hit cannot crit, so the crit factor multiplies only the \((1-b)\) share; Accuracy is subtracted twice, from \(b\) and from \(v\); and the flat value \(F\) is removed from the base before anything multiplies, so it appears as a share \(f\) of the hit rather than a percentage of itself.

Why each stat works Derived

Take the logarithmic derivative of \(H\): each line is “one more point of this stat gives this fraction more effective HP”.

$$ \frac{\partial \ln H}{\partial\,\mathrm{HP}}=\frac{1}{\mathrm{HP}},\qquad \frac{\partial \ln H}{\partial\,\mathrm{DEF}}=\frac{1}{A+\mathrm{DEF}},\qquad \frac{\partial \ln H}{\partial \rho}=\frac{1}{1+\rho} $$ $$ \frac{\partial \ln H}{\partial B}=\frac{X-Y}{(1-b)\,X+b\,Y}\quad(\alpha \lt B \lt 1+\alpha,\ \text{else }0), \qquad X=1+c\,(m-1),\quad Y=\frac{1-f}{v} $$ $$ \frac{\partial \ln H}{\partial E}=\frac{b\,Y/v}{(1-b)\,X+b\,Y}\quad(v \gt 1.5),\qquad \frac{\partial \ln H}{\partial F}=\frac{b\,\tfrac{A+\mathrm{DEF}}{A^{2}\,v}}{(1-b)\,X+b\,Y}\quad(f \lt 0.9),\qquad \frac{\partial \ln H}{\partial r}=\frac{(1-b)\,\big(c+m-1\big)}{(1-b)\,X+b\,Y} $$

(DEF also sits inside \(f\); with \(F \gt 0\) its derivative gains a second term, \( \tfrac{b\,F/(A^{2}v)}{(1-b)X+bY} \), which the sliders include.)

Read them: HP and DMG RES never diminish to zero; DEF diminishes as \(1/(A+\mathrm{DEF})\); Block Rate is a constant slope inside a window and zero outside it; both Block Efficiencies and Crit RES are scaled by the share of hits they touch, \(b\) or \(1-b\).

What follows Derived

Put one gear roll into each derivative. At level 113 a Gold roll is 1,676 DEF, 8,382 HP, 4% Block Rate or 4% Crit RES; DMG RES and Block Efficiency cannot roll and come from relics, sets and Charms.

1. Inside the window, a Block Rate roll beats an HP roll for any sheet. \( X-Y \ge 1-\tfrac{1}{1.5}=\tfrac13 \) because \(Y\le 1/v\le\tfrac{2}{3}\) and \(X\ge 1\); and \((1-b)X+bY\le X\le 1+\mu\). So a 4% roll is worth at least \( \tfrac{0.04}{3\,(1+\mu)} \), which is 0.83% at \(\mu=0.6\) and still 0.67% at \(\mu=1\), while the HP roll is \( \tfrac{8{,}382}{\mathrm{HP}} \), 0.67% at 1.25M HP and less above it. Outside the window the Block roll is worth exactly zero.
2. A flat DEF roll beats an HP roll only if \(\mathrm{HP} \gt 5\,(A+\mathrm{DEF})\). From \( \tfrac{1{,}676}{A+\mathrm{DEF}} \gt \tfrac{8{,}382}{\mathrm{HP}} \). At Champion, HP is about 2.5 times \(A+\mathrm{DEF}\), so HP wins and DEF halves in value again every time DEF doubles.
3. A point of DMG RES beats a point of Block Efficiency unless \(E-\alpha \lt \rho\). At full block the two derivatives are \( \tfrac{1}{1+\rho} \) and \( \tfrac{1}{v}=\tfrac{1}{1+E-\alpha} \). With the default \(E=1\) that needs their Accuracy above \(1-\rho\), about 75%, which nobody carries. Block Efficiency still matters because it arrives in 5–15% pieces and DMG RES in 1–5% pieces.
4. Flat Block Efficiency is the largest term once blocks land. \( f = F\,\tfrac{A+\mathrm{DEF}}{A^{2}} \): Block Mastery at rank 24 (\(F=33{,}889\)) against \(A=\mathrm{DEF}=250{,}000\) gives \(f=0.27\), a \( \tfrac{1}{1-f} \) = 1.37× multiplier on every blocked hit, before the divisor. It falls as \(1/A\) when their ATK grows.
5. Crit RES only pays on the \((1-b)\) share. Its derivative carries the factor \((1-b)\); at full block it is zero, and a block already deletes the crit.

Put your numbers in Derived

Every number below is the formula above with the sliders substituted. Block Rate is the in-combat value: add Block Awareness (+22% at rank 16, +54% at rank 24 at level 113) and Luminous Shield (+54% / +63% while it is up) to your sheet. Block Mastery gives \(F\) = 14,014 at rank 16 and 33,889 at rank 24.

The last column is the derivative times the size of one roll or one point; the middle column is the exact change from recomputing \(D\), which is what you would see. They differ where a floor or the window edge is crossed.

Not in the formula Fact

Shields and healing (they scale with HP and DEF, not with block), taunt (more hits, same ratios), true damage, later hits of multi-hit skills, Fantomon, and the PvP governor that scales both sides. The Charms’ block values are not on the Character screen or in the captured sheets; they are applied in the fight, which is why \(B\) and \(F\) here are in-combat values. No captured fight has a Block Mastery user being hit, so the \(F\) term is the formula’s word, not an observed one.

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