# Thread: Optimizing physical damage mitigation

1. ## Optimizing physical damage mitigation

I've been asked many questions about whether it's better to invest in dodge, PRR, or AC. Here's a simple technique to calculate what benefits you more.

If we consider mitigation only due to dodge, PRR, and AC, the time-averaged fraction of physical damage taken f is:

f = (1 - .01*d) * (1 - .65*(1-.99^p)) * Min[(b+10.5)/(2*a),1]

for dodge d (in percent), PRR p (in points), AC a (in points), and monster attack bonus b.

f ranges from 0 to 1, where 1 means you take full damage. If (b+10.5)/(2*a) >= 1, the next point of AC added gives no benefit (monster to-hit too high). I'll call this the AC threshold.

We can take new values for d, p, and a and calculate f(d1,p1,a1,b)/f(d0,p0,a0,b) to get the relative proportion of damage taken versus the old values. This proportion is constant in b unless the AC threshold falls within the range {a0,a1}.

As an example, say I have 10% dodge, 50 PRR, and 80 AC, and have a feat to spend on damage mitigation. I'm debating between mobility, shield mastery (large shield), or bulwark of defense. Calculating the 3 cases:

f(12,50,80,b)/f(10,50,80,b)
f(10,55,80,b)/f(10,50,80,b)
f(10,50,84,b)/f(10,50,80,b)

shows that the +4 AC from bulwark is better by about double unless b > 149 (some epic elites). Second best would be the 5 PRR from shield mastery.

Note that this is a time average. PRR mitigation has a variance of 0, but both dodge and AC are subject to chance. Squishier toons may value the consistency of PRR.

If you have multiple feats, enhancements, gear slots, or destiny points to spend, you should be able to sequentially apply this process since f and its gradient are monotonic.

Concealment and incorporeality work the same way as dodge, so you can multiply on another factor for each one.

2. Nice post Scoob, thanks for that. Have you looked at creating optimized party function/role profiles? In other words, someone wants to combine together the three defense variables in a way that is optimized for their desired role. An Epic Elite raid tank may want 150AC, 100PRR, and 20%, dodge given reasonable consideration of available factors. An Epic Hard pugger who often ends up with boss focus may find 80AC, 30PRR, 10% is reasonable. Just to give general guidelines on the 3 variable "dial settings", starting points.

3. Oh and I forgot to ask, how does the old school DR factor into all of this now? Like Docent of Defiance used to be DR20 when it proc'd, haven't checked in today's game.

4. Originally Posted by Humperdink
Nice post Scoob, thanks for that. Have you looked at creating optimized party function/role profiles? In other words, someone wants to combine together the three defense variables in a way that is optimized for their desired role. An Epic Elite raid tank may want 150AC, 100PRR, and 20%, dodge given reasonable consideration of available factors. An Epic Hard pugger who often ends up with boss focus may find 80AC, 30PRR, 10% is reasonable. Just to give general guidelines on the 3 variable "dial settings", starting points.
There is no absolute optimum, only relative to how much DPS and/or utility you want to sacrifice for the sake of physical mitigation. Higher numbers are better is the only rule. The relative optimum would be (first multiplying on a factor that looks just like dodge but for incorporeality) a point where swapping something that causes any of the parameters to change increases the value of the function f. It isn't correct to equate the gradients because the parameters rarely increment/decrement by intervals of 1. The whole point of the first post is just to help decide what feat/enhancement/destiny/gear gives the best benefit, given only limited number of feats/slots you want to devote to defense.

It's hard to treat DR in this calculation because it is additive, which presents 2 problems:
1. Order of operations: it's unclear whether DR applies before or after multiplicative bonuses
2. Its benefit depends on the absolute damage number of hits instead of a proportion of DPS

5. ## I like the part

where you said simple technique.

6. Originally Posted by Mindos
where you said simple technique.
I was hoping for calculus! But +1 all the same.

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