Hoarfrost and +MaxHP powers

[oedipus_tex]

Hi all,

 

I'm hoping someone can walk me through the math on Hoarfrost. I'm pretty familiar with Resistance powers, but +Max HP is a bit murkier to me.

 

If I remember right, Arcanaville used to say that +Max HP has the same effect as Resistance. However I can't quite seem to get that result when I puzzle through the math;

 

• If you have 1000 HP and 0 Resistance and take 500 points of damage, you now have 500 HP
  • If you have 1500 HP (50% increase) and 0 Resistance and take 500 points of damage, you now have 1000 HP
  • If you have 1000 HP and 50% Resistance and take 500 points of damage, 500 reduces to 250, and you now have 750 HP

 

 

So, I'm not getting the result I expect, which means I'm either doing the math wrong or  misunderstood Arcanaville's point. How does it work in real life?

Edited September 4, 2020 by oedipus_tex

[Hopestar]

Your math is correct and is how it works ingame, I don't think it was meant that it was the same as resistance but more that it just added to eHP. Or there's the fact Hoarfrost gives toxin resist?

[Mezmera]

I think the intent from Arcanaville was to illustrate that building in more hp is almost as important as having high resists.  Coupled together you get quite a meaty toon.  

 

The allure of Hoarfrost is that it is both a heal when you need it and also that it buffs your hp.  There's a few problems with the power though.  First it's a base 6 minute recharge so it's quite unreliable as a heal when most times it's not available when you'll need the heal so you'll still find yourself popping green inspirations.  The other issue is that Dominators hp cap is 1600 and a well built dom with their accolades is typically already in the 1400-1500 range so you're only benefiting on maybe a 150 hp buff.  

 

If I took the Ice APP I'd take hoarfrost but there are these caveats.  

[CaptainLupis]

I don't think Arcana said it was the same as resistance, more that it is equivalent to it in that it is a buffer to your health, however in certain circumstances it is better in that it doesn't care what damage type you are taking, so adding extra HP will benefit you against all damage types, where most resistance bonuses are typed.

[Bopper]

Got a link to their math?

 

Personally I would not say they're synonymous, afterall if you added 100% resistance versus adding 100% HP, the 100% resistance would lead you to being immortal whereas +100% HP would let you take twice as much damage (if we ignore regeneration). I have a guide for my Survivability Tool that details all the various math involved with seeing impacts of adding resistance, defense, HP, and regeneration if you'd like to check out various formulas.

 

As for the relationship between resistance and added HP, its actually an inverse relationship. Adding resistance increases survival by 1/(1 - Resistance%), while adding HP increases survival by a factor of (1 + HP%). So to truly compare the relationship, we can do some algebra.

 

1 + HP = 1/(1 - Res)

HP = 1/(1 - Res) - 1

HP = 1/(1-Res) - (1-Res)/(1-Res)

HP = Res/(1-Res)

 

So having 20% resistance is equivalent to

HP = 0.2/0.8 = +25% max hitpoints

 

Edit: For completeness, I should show the relationship for equivalent resistance.

 

1-Res = 1/(1 + HP)

Res = 1 - 1/(1+HP)

Res = HP/(1 + HP)

 

So adding 50% HP is equivalent to having

Res = 0.5/1.5 = 33.3% resistance

Edited September 4, 2020 by Bopper

[mbre2006]

I use hoarfrost as following:

 

Five resist procs can go in there.

 

Use it alongside Unrelenting and Unleash potential. 

 

Hoarfrost has a 120 minute duration and with my build a 186 recharge. So mine is down for like 26 secs which I can reduce even further with incarnates. I really guess how your play style is. Those three powers and I can tank alpha strikes with ease. 

[DreadShinobi]

6 slot preventive medicine set is a beautiful thing in hoarfrost, providing 8.75% recharge which doesn't compete with similar set bonuses, and an incredibly good absorb proc. The reason for it's being though is really just that it is in the same ancillary pool that offers dominators Sleet, a debuff that alone transforms the archetype's role on teams.

[kelika2]

All this means giving up fire shield, fireball and rise of the phoenix.

[carroto]

On 9/4/2020 at 11:46 AM, Bopper said:

the relationship between resistance and added HP

Are you also taking into account the increased HP regen from higher max HP?  Your math seems to be apply for a situation in which a chunk of damage comes in all at once, how much will it take to defeat a toon.  But in prolonged battles the increased regen will play a role as well, increasing the value of +HP more than that shows.  I suspect that was also a factor in Arcanaville's statement.

[Bopper]

15 minutes ago, carroto said:

Are you also taking into account the increased HP regen from higher max HP?  Your math seems to be apply for a situation in which a chunk of damage comes in all at once, how much will it take to defeat a toon.  But in prolonged battles the increased regen will play a role as well, increasing the value of +HP more than that shows.  I suspect that was also a factor in Arcanaville's statement.

I most certainly am not. Regeneration is a frequency metric, and to apply it in such a case would require a time interval. That greatly over-complicates the analysis, especially in this situation where we're just looking for a relationship between Resistance added and Max HP added. If you would like to see that type of math factored in, I recommend my Survivability Tool. You can apply your HP, Regen, Defense, Resistance, To-Hit Debuffs, and Damage Debuffs, and my tool will output metrics for the builds projected survivability (I do not factor in debuffs that could be applied on you, that would require turning a simple spreadsheet into a full-on simulator program).

[Bopper]

11 hours ago, carroto said:

Are you also taking into account the increased HP regen from higher max HP? 

I thought about this more this morning. Although it's true, I was not considering it, but now that I am I don't think there's a difference. Regeneration translates to HP/sec as so:

 

HP/sec = (MaxHP / 240) x Regen%

HP added = HP/sec x Time

 

So if we looked at our health pools over time, we would have the following:

 

MaxHP + HP/sec x Time = MaxHP + (MaxHP / 240) x Regen% x Time = MaxHP x (1 + Time x Regen% / 240)

 

If I use one of my examples from earlier (+25% HP is equivalent to 20% Resistance), and assume both builds have the same Regen% and we analyze for the same amount of time, then there is no difference to the analysis. It scales as it would before.

 

Scenario A: +25% HP, 0% Resistance

Total HP = MaxHP x (1 + Time x Regen%/240) = 1.25 x BaseHP x (1 + Time x Regen% / 240)

Damage to kill = Total HP / (1 - Res) = Total HP / (1 - 0%) = 1.25 BaseHP x (1 + Time x Regen% / 240)

 

Scenario B: +0% HP, 20% Resistance

Total HP = BaseHP x (1 + Time x Regen% / 240)

Damage to kill = Total HP / (1 - Res) = Total HP / (1 - 0.20) = 1.25 x BaseHP x (1 + Time x Regen% / 240)

 

As you can see, this remains the same, and always should.

[kiramon]

3 minutes ago, Bopper said:

I thought about this more this morning. Although it's true, I was not considering it, but now that I am I don't think there's a difference. Regeneration translates to HP/sec as so:

 

HP/sec = (MaxHP / 240) x Regen%

HP added = HP/sec x Time

 

So if we looked at our health pools over time, we would have the following:

 

MaxHP + HP/sec x Time = MaxHP + (MaxHP / 240) x Regen% x Time = MaxHP x (1 + Time x Regen% / 240)

 

If I use one of my examples from earlier (+25% HP is equivalent to 20% Resistance), and assume both builds have the same Regen% and we analyze for the same amount of time, then there is no difference to the analysis. It scales as it would before.

 

Scenario A: +25% HP, 0% Resistance

Total HP = MaxHP x (1 + Time x Regen%/240) = 1.25 x BaseHP x (1 + Time x Regen% / 240)

Damage to kill = Total HP / (1 - Res) = Total HP / (1 - 0%) = 1.25 BaseHP x (1 + Time x Regen% / 240)

 

Scenario B: +0% HP, 20% Resistance

Total HP = BaseHP x (1 + Time x Regen% / 240)

Damage to kill = Total HP / (1 - Res) = Total HP / (1 - 0.20) = 1.25 x BaseHP x (1 + Time x Regen% / 240)

 

As you can see, this remains the same, and always should.

Which makes perfect sense that it would scale in such a way.

[HelBlaiz]

Extra max HP is like resists in that they both increase the amount of damage that needs to hit you to reduce you to zero. 50% resist doubles your time to die just as well as 100% bonus hp. In a game like CoH that doesnt really work in percent max hp damage, that will always be true. The only thing that would ignore max hp buffs are one hit ko hax in incarnate trials. Those also ignore resists, and I imagine are auto hit if you don't run away hard enough, so they ignore defense too. Max hp buffs are damage type agnostic though, so act as resistance to all damage types, but are often not as strong as the type specific resist bonuses you can get in return. Im fairly certain the 75% resist cap for most ATs is also more effective when the specific damage type applies than the hp cap to continue the trend.

 

Like previousy mentioned above, building for both can make you extra durable.