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The effects of block on effective health

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The effects of block on effective health

Postby jere » Fri Aug 17, 2007 1:16 pm

Just as a precurser:

Effective Health, as I understand it, is the amount of unmitigated damage you can take before you die. It is based upon armor and health pool and given by:

EH = HP/(1-DR)

Where DR=AC/(AC+11960), for lvl 73 mobs

I was toying around with it and was trying to see what relationship block played into EH as the above equation only assumes full hits (not blocked). The problem with trying to find out the relationship block has to EH is that it requires additional information. I am not saying this fully characterizes all the benefit of blocking for EH, but wanted to share some of the stuff I found.


*********This section contains errors. The equations were fixed in my next post************

First of all, I checked to see what gain in life I got from blocking. Basically, whether you block or not, some enemy is going to try to hit you for some amount on average, so that is a pretty constant number (in the averaged frame of reference).

If I have 15000 life and the enemy is hitting me for 3500, it will take him 15000/3500 = 4.2857 hits to kill me.

If I block each attack by 500 (I wish), then it will take 15000/(3500-500) = 5 hits to kill me.

In both situations the enemy is trying to hit me for the same value, but because of block, it took more hits to kill me.

The increase of hits it took to kill me was 5/4.2857 = 1.167 more hits (multiplicative). In case you are wondering, the damage before block divided by the damage after block also equals this number (3500/3000), so the multiplier is defined by d/(d-b), which can be shown through algebra as well if anyone is interested.

In the unmitigated frame, the equation for number of hits is :

#hits = EH/unmitigated_damage

Since the unmitigated_damage the boss is trying to do to me doesn't change whether I block or not, the increase in the number of hits it takes to kill me directly translates into an increase in EH.

So EH really becomes EH*d/(d-b), if you want to consider block.

So if you have an EH of 30000 and you fight an enemy that hits for 3500 but you block 500, then your EH raises to 35000. I am not saying this is your true effective health. That is still 30000, but the enemy has to hit you for 35000 because you block all of his hits for 500.

One thing that is pretty intuitive is that blocking tends to give higher effective EH for enemies that hit for less (more # of hits).

Also, if you have two gear setups, one with higher block, but less base EH than another set, you can compare them by using the equation, EH*d/(d-b), for each (filling out the EH and b values), setting the two equations equal and solving for d.

This value for d is the damage a mob hits you for on average that will give you the same effective EH for both sets. If the mob hits less than that value, the set with higher block will give slightly more effective EH. If the mob hits more than the value, then the set with less block but more base EH will give slightly more effective EH.

In summary:

Effective_EH = EH*d/(d-b), where d is the mitigated damage before block.

d = (EH_1*b_2 - EH_2*b_1)/(EH_1 - EH_2), where d is the incoming mitigated damage (before block) done by a mob that nets the same Effective_EH for both sets of gear.

Anyways, found it interesting at least to play with the math some.

EDIT: The bottom half of this post had a bad error in that I didn't account for separate armor values when calculating d. That is fixed in my next post.
Last edited by jere on Sun Aug 19, 2007 1:36 pm, edited 3 times in total.
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Postby Joanadark » Sun Aug 19, 2007 12:20 am

The problem with trying to find out the relationship block has to EH is that it requires additional information.


Why not this:

EH = (HP+BV) / (1-DR)

?
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Postby jere » Sun Aug 19, 2007 1:29 pm

Joanadark wrote:
The problem with trying to find out the relationship block has to EH is that it requires additional information.


Why not this:

EH = (HP+BV) / (1-DR)

?


Because that only accounts for 1 block. Unless the enemy is going to one shot you, that won't tell you much, and you might as well use just plain old EH = HP/(1-DR).

On top of that, you want to use the full value of block, not just BV, as what little strength you do have will increase that value slightly.

You have to look at how many times you get hit as that will tell you how many blocks and the amount of damage blocked. However, to figure that out, you need to determine first, how many times the enemy needed to hit you to kill you if you weren't blocking and then how many times the enemy need to hit you if you were blocking. The percentage increase in that number of hits will directly change the base EH.

On a side note, I made one mistake in my equations for the block ones. I made the mistake of using the same alpha for both sets of armor. The correct equations are actually:

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Postby Joanadark » Sun Aug 19, 2007 3:46 pm

Because that only accounts for 1 block. Unless the enemy is going to one shot you, that won't tell you much


but thats what Effective Health represents. the size of a single hit that would one-shot you.
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Postby jere » Sun Aug 19, 2007 4:11 pm

Joanadark wrote:
Because that only accounts for 1 block. Unless the enemy is going to one shot you, that won't tell you much


but thats what Effective Health represents. the size of a single hit that would one-shot you.


I guess I view it more as the amount of unmitigated damage you can take before dying. It's a small difference, but in my definition, a mob can hit you multiple times before you die. I don't look only at one shots, but the worst case scenario of a string of hits as well.

Effective Health is your hit points divided by your damage reduction multiplier. Whether all of that is done in one hit or multiple hits, the number stays the same (if you don't look at block).
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Postby Dunkan » Sun Aug 19, 2007 6:58 pm

The answer here is not a static answer, but a value on a scale form a 1HP hit all the way to {max_EH}+1HP.

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Postby jere » Fri Sep 07, 2007 3:35 pm

Joanadark wrote:
Because that only accounts for 1 block. Unless the enemy is going to one shot you, that won't tell you much


but thats what Effective Health represents. the size of a single hit that would one-shot you.


Alrighty, I know we disagree on this a bit, so let me take a step back on this and maybe try a different approach.

What do you think of the idea of me figuring out the amount of "effective AC" a particular amount of block equals, and use that in the effective health equation. Would that be a more desireable or acceptable way of characterizing the effects of block on effective health?

Anyways, I hope this discussion doesn't offend you at all, I never meant to step on anyone's toes with it, I just like math is all.
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Postby Joanadark » Fri Sep 07, 2007 6:11 pm

lol if you can come up with some brilliant way of interpriting things, more power to you.

I'm just not sure I follow the concept youre expressing.

You're going for solving the problem of "how much block value reduces Total Damage In"?
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Postby Lore » Fri Sep 07, 2007 8:05 pm

It seems like you're both correct, you just have different definitions of "Effective Health."

Joana, you define it as "How much a single hit has to do to 1-shot you." With that definition, your formula is correct. It's only one hit, so there's only one block... just add your block value to your health pool.

Jere defines effective health as "How much damage can be taken before dying." Similar, but with no restriction on number of hits. It could just as easily be 1 hit for, say, 30k damage, as it could be 30,000 hits for 1 damage. In order to create a formula for that definition, however, you have to take the number of incoming hits into consideration.
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Postby jere » Fri Sep 07, 2007 10:00 pm

I am sorry, I wasn't meaning any disrespect towards you Joanadark. I apologize if it came across that way.

The problem I was trying to solve was:

We know that the current effective health equation tells us how much unmitigated damage we can take before dying. It may be that the current theory only allows us to look at the one-shot scenario, but I feel at some point you reach a level of effective health where a boss doesn't one shot you (I am sure there are obvious exceptions to that, but talking in general). So instead of one-shot, it might take most bosses 2-4 hits to knock you down to zero (assuming no heals/dodges/parries/etc).

I was trying to see how much BV improved that. Can X amount of block value make it so it now takes 3-5 hits to kill you rather than 2-4. And if it does indeed improve that scenario, how much "extra" unmitigated damage is that that the BV accounted for.

Just for example, say your EH is 35000 and a boss hits for 10000 unmitigated. It would take 3.5 hits to kill you in that scenario. If you then looked at the fact that you will most likely block all of your incoming attacks (holy shield is up) and say you block for 500. That might boost you up to having to take 4 full hits before dying. Obviously in this example, there is no practical difference in 3.5 versus 4, but I was curious to see how much extra EH did that BV net us (how much more damage did the boss have to do to kill ya). In this example, it might be somewhere on the order of 5000 extra unmitigated damage the enemy had to do (if say you had 16000ish armor).

Anyways, that was the thing I was trying to look at, how much does BV extend our life, but I was applying it to the EH frame of reference. Maybe that was a bad idea, but so far I have found it somewhat of something interesting for me to play with.

But I wasn't trying to cause any kind of problems or anything, so I am sorry I caused a disagreement.
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Postby Joanadark » Fri Sep 07, 2007 10:42 pm

dont be worried about offending me. If i'm offended by something, I'll say so.
Besides, it's not like Effective Health is somehow "my theory how dare you mess with it".


I'm certainly in no way put off by such good thinking and contribution to the theorycraft community. Don't ever be afraid of contradicting the popular perception if you think youre on to something.

Besides, I have no problem being wrong. I have thick skin, I'm a tankadin.

I may just quote you in my blog or maybe mysterious ways.
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Heh

Postby Mavrix » Sat Sep 08, 2007 10:16 am

I think more along the lines of the other thread someone made about "effective lifespan". "Effective Lifespan" (similar to but not equal to "tankpoints" mod totals) does seem to be more important (at least to my mind) compared to "effectively not being one shotted".
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Re: Heh

Postby jere » Sat Sep 08, 2007 11:46 am

Mavrix wrote:I think more along the lines of the other thread someone made about "effective lifespan". "Effective Lifespan" (similar to but not equal to "tankpoints" mod totals) does seem to be more important (at least to my mind) compared to "effectively not being one shotted".


I think in general you can look at our 3 views in different ways:




1. Joanadark's EH: Worst case scenario of getting one shotted. Will you have enough EH to survive the boss's worst attack(s)

2. My EH with blocking: Next-to-worst case scenario where you aren't one shotted, but you receive no heals and do not dodge/parry/miss the incoming attacks until you die. How much damage will you be able to take before you finally die based purely on your HP, AC, and block versus the incoming damage?

3. Corc's lifespan calculations: Your average lifespan given you get no heals, but are able to dodge, parry, or be missed.





It's kind of like a set of steps. You start at the top and then start adding in conditions that may extend your life:

1 shot --> mulitple shots --> able to dodge/parry/miss the incoming attack

Each has their own merit in my opinion. The next step would be to factor in HPS you are receiving, which goes back to the time to live equation in its expanded form.
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Postby Fridmarr » Sat Sep 08, 2007 12:04 pm

Well it's all about context. Effective health can fluctuate a good bit between different encounters. Which is why we are good AoE and fast hit tankers, our effective health against those mobs tends to go up a bit because of lots of blocks and Ardent Defender. It would be nice to have an effective health calculator where we can enter attack parameters as well. For instance, perhaps on a certain set of mobs, the Autoblocker would give much more effective health than say Darkmoon card trinket with 51 stam.

Although, some of the tanking sims that are out there can give you a pretty good representation, of effective health if you study the numbers.
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Postby jere » Sat Sep 08, 2007 12:13 pm

Fridmarr wrote:It would be nice to have an effective health calculator where we can enter attack parameters as well. For instance, perhaps on a certain set of mobs, the Autoblocker would give much more effective health than say Darkmoon card trinket with 51 stam.

Although, some of the tanking sims that are out there can give you a pretty good representation, of effective health if you study the numbers.


The bottom right equation in my equations picture covers that idea somewhat.

You take your delta_HP (-540 for the loss of the darkmoon fair) and your delta_block (+76 if you have shield spec 3/3) and plug them into the equations.

Since armor doesn't change, delta_alpha = 0
You have to calculate your delta_EH using the equation there too, but what you end up with using that bottom right equation is the amount of unmitigated damage an enemy must do where they provide the same amount of Effective health. If the enemy hits less than that, then the auto blocker is better. If the enemy hits harder than that, the stamina trinket will give you more mileage.

Granted, it is a complicated equation, but that is the intended use of it, to see where the breaking point is between say stamina and block value

Take my stats for example. I have the DMF card equipped and have:

12897 HP
15489 AC
block for 315

So:

alpha = 2.4416
EH = 31488.8060

swapping trinkets means:

delta_AC = 0
delta_HP = -540
delta_block = +76

delta_EH = ((0-540*15489)/11960 - 540)/0.94 = -1318.4427

unmit_dmg = 2.4416*315-(31488.8060/-1318.4427)*2.4416*76
unmit_dmg = 5202.45

So if a mob is hitting for less than 5202.45 unmitigated (2130.75 mitigated and before block), then the auto blocker would extend my life farther than the DMF card would if I endured a string of hits (blocks) with no incoming heals....so basically AoE situations.

However, in my equation, it only addresses the situation where you get no heals and don't dodge, parry, or are missed. When you factor those in, then you might see the auto blocker being better for mobs that hit harder than that. And of course, if you already have enough HP's anyway, the auto blocker is the better choice.
Last edited by jere on Sat Sep 08, 2007 3:36 pm, edited 2 times in total.
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