# Thread: Theorycrafting PRR and HP

1. ## Theorycrafting PRR and HP

So I decided to do some calculations and see what I came up with, and my results are rather surprising.

Assumptions:
% Damage mitigated from PRR (as a decimal) is 1-100/(100+PRR Rating). From the Wiki.
So, effective HP is HP/(portion of damage NOT mitigated from PRR). So if only 1/3 of the damage gets through, you have 3x the effective hit points.

From now on when I say "PRR" mean the actual PRR rating shown on the character sheet.

This means that Effective HP = (HP*(100+PRR))/100. Or in image form:

So far this has been basic algebra.

This is now calculus.

I wanted to find the point at which 1 point of HP gave the same benefit of 1 point of PRR.
To do this I set the partial derivative of Effective HP with respect to PRR equal to the partial derivative of Effective HP with respect to HP:

Translation: I set the increase in Effective HP when I added 1 point of PRR equal to the increase when I added 1 point of HP.

Solving this gave me HP = 100+PRR. OR: 1 point of PRR gives the same benefit as one point of HP when your HP is equal to your PRR plus 100. This means that PRR is almost always better than HP, in equal amounts.

This means:
If your HP is less than 100+PRR, HP with give you a larger benefit than PRR.
If your HP is greater than 100+PRR, PRR will give you a larger benefit than HP.

To show this visually:

The horizontal Axis is HP and goes from 0 to 3000. The vertical Axis is PRR, and goes from 0 to 400.

The Black Line is where HP = 100+PRR. If you put a point where your HP and PRR are, if that point is to the right of the line, PRR will give you more benefit point for point. If you are to the left of the line, HP will give you more benefit.

Of course, this does not mean a feat that gives you 2 PRR is better than a feat that gives you 30 HP if you have 2000 HP and 40 PRR. To find that out:
• Plug your PRR and HP values into the forumla for Effective HP.
• Add 30 to HP without changing PRR.
• Record Effective HP.
• Remove the 30 aditional HP.
• Record Effective HP.

When you are gaining varing amounts of PRR and HP, use the formula

Delta PRR is the amount of PRR from the feat/enhancement/whatever. Delta HP is the amount of HP from the feat/enhancement/whatever. HP naught is how much HP would would have without the feat/enhancement/whatever, same for PRR naught.

If this value is greater than 1, then the PRR is better. If it is less than 1, the HP is better. If it is equal to 1, they are the same.

Example:
Build with 1000 HP and 200 PRR.
They can trade Toughness (32 HP) for Heavy Armor Combatant (6 PRR)

Calculations go as follows:

is equal to 6*1000/(32*(100+200)) or 0.625, which is less than 1. This means that Toughness is the better feat to take.

2. In general, for every type of damage mitigation (Dodge, AC, PRR, MRR, Elemental Resistances):

3. Originally Posted by Ligraph
I'm fairly sure there is a more elegant way of doing this using the HP=100+PRR formula, but I'm to tired to think of it right now.
Thanks for laying this all out.

Here's a quick little worksheet to plug in changes to HP and PRR/MRR and see if the effective HP is better or worse. Hopefully I didn't mess up the sharing permissions.

4. yep this is very fancy! especially the prr/hp diagramm. i always wondered about that issue, thanks for doing all that fancy math!

5. Originally Posted by Ligraph
In general, for every type of damage mitigation (Dodge, AC, PRR, MRR, Elemental Resistances):
Others may have a different opinion them me on this but, EHP is a bad tool to use for evaluation of Dodge, AC and any other kind of avoidance.

EHP when looking at mitigation tells you how much damage you can take before you die its a concrete number, when your EHP is 5000 and a mob is doing 500 dps you know you have 10 seconds before you will die this is a concrete number and 100% consistent, further if a mob does 4999 damage in one hit and you are at 100% health you will live.

Avoidance when converted to EHP dose not create a concrete number if an aEHP says you can take 5000 damage and a mob does 4999 in one hit you will die unlike with mitigation further if a mob is doing 500 dps you may live a lot longer then 10 seconds or a lot less. Avoidance is not predictable enough to use EHP as a useful metric.

6. Originally Posted by Glenalth
Thanks for laying this all out.

Here's a quick little worksheet to plug in changes to HP and PRR/MRR and see if the effective HP is better or worse. Hopefully I didn't mess up the sharing permissions.
Nice! It wanted me to make a copy of it so I could edit it, worked fine.

Originally Posted by Grailhawk
Others may have a different opinion them me on this but, EHP is a bad tool to use for evaluation of Dodge, AC and any other kind of avoidance.

EHP when looking at mitigation tells you how much damage you can take before you die its a concrete number, when your EHP is 5000 and a mob is doing 500 dps you know you have 10 seconds before you will die this is a concrete number and 100% consistent, further if a mob does 4999 damage in one hit and you are at 100% health you will live.

Avoidance when converted to EHP dose not create a concrete number if an aEHP says you can take 5000 damage and a mob does 4999 in one hit you will die unlike with mitigation further if a mob is doing 500 dps you may live a lot longer then 10 seconds or a lot less. Avoidance is not predictable enough to use EHP as a useful metric.
Yeah, I agree. It's the only statistic I found where I could easily combine Mitigation and Dodge chances.

Although it's still an accurate average.

7. Did a little more work, wanted to find a formula to determine whether X amount of PRR will be better than X amount oh HP:

Delta PRR and Delta HP are the potential changes in PRR/HP. HP and PRR naught are the initial values.

If this value is greater than 1, the PRR will be better than the HP. Otherwise, HP will be better.

Edit: forgot a closing parentheses!!!! I am not retaking that image!

8. Would need an expected range or average of incoming damage amounts to get it just right for dodge and similar.

9. PRR makes HP better. This post basically says to me to get as much PRR as possible/practical within your build theme. It is also probably a good idea to reach critical levels of whatever else your build does. Do you need a certain no fail reflex save? Do you have a no fail intimidate? Is your dodge(dodge/AC/conceal/incorp/etc) potential maxed? Do you have a way to reach max BAB? DPS output goals met? Usually I can find that I can meet all/most my goals with proper gear planning. So looking at the PRR graph and HP graph one may say don't worry about HP but it is still very important and shouldn't be ignored.

10. Originally Posted by Warbler
PRR makes HP better. This post basically says to me to get as much PRR as possible/practical within your build theme. It is also probably a good idea to reach critical levels of whatever else your build does. Do you need a certain no fail reflex save? Do you have a no fail intimidate? Is your dodge(dodge/AC/conceal/incorp/etc) potential maxed? Do you have a way to reach max BAB? DPS output goals met? Usually I can find that I can meet all/most my goals with proper gear planning. So looking at the PRR graph and HP graph one may say don't worry about HP but it is still very important and shouldn't be ignored.
Yeah. This is just from a pure math standpoint. Also, the graph is for 1 point of PRR vs 1 point of HP. Since you usually get more HP that PRR, you need to use this formula:

If it is greater than 1, then the PRR feat/enhancement/whatever will be better, if it's less than 1, the HP is better.

Of course, this assumes that your build does what you want it to do.

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