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an effective (health) wall of text

March 6, 2009

Oh god he’s doing that thing again! No, not the animated ‘dot’ gifs. That’s next week. I’m pulling out my pocket protector and spreadsheet again. Oh yeah, I’m going there. My old friends have probably been in shock for some time now wondering why I haven’t posted about effective health yet. Well guess what kiddies, it’s that time! Get out your center-taped square rim glasses, calculators and pocket protectors, this should be fun.

Effective Health is your health pool as modified by your defenses. The importance of this is it gives a measure of how long you can survive while unhealed. In some games this is as simple as multiplying out your armor and health. In others, like WoW it’s horribly complicated and involves diminishing returns on armor, flat rate reductions from shield block, avoidance percentages and… okay most people just go to Tankspot and use their calculator. I’m actually not entirely interested in providing a comprehensive calculation of effective health for WAR as I am dispelling some rather silly speculations. So, here’s my agenda:

1.) Provide a rough analysis of effective health without avoidance.
2.) Compare toughness and wounds.
3.) Reflect on EH in WAR.

Hey, only three things to go over, my day is looking up. Now all we have to do is find a rough formula for effective, oh crap yeah that sucks. Well, maybe not so much. What we need to find is how each stat alters the damage income. That isn’t so bad at all! Our defensive stats, since we’re not dealing with avoidance are resistances, armor and toughness. Since resistances and armor don’t apply to the same things, that means we need two similar formulas. However, since toughness reduces incoming damage by a flat DPS decrease it means we have to work that in as well. Bother.

First let’s go for armor. I’ve mentioned it before, but this is a fairly straightforward formula: Armor / ( Level * 44 ) * 40. We’d need to extend that a bit so it can be used without translation. That’s not too bad. What we need is the remaining percentage, for instance 3300 armor is a capped 75% reduction. So it’s easiest to modify to say that you take 25% damage. We can change the formula around pretty quickly so that all we need to do is multiply by .25. So we have the first part of our equation:

1 – ( Armor / ( Level * 44 ) * .4 ) = Percent damage taken.

Now all we need to do is work in toughness. Toughness reduces DPS by 1 for every 5 points. So that’s very easy: DPS – Toughness / 5 = Reduced DPS. The next step is to thread the two together into a single formula that computes both. That comes out like this:

( DPS – Toughness / 5 ) * ( 1 – ( Armor / (Level * 44 ) * .4 ) ) = Reduced DPS.

This takes your incoming damage, reduces it from our toughness, then runs it through an armor check. Now all we need to do is work in your wounds as that also effects your health. That again is a very simple matter, as wounds simply increases health by 10 per point: Wounds * 10 = HP. How do we add it to the formula though? Well, we need to find out how the incoming damage divides up our health. So, we just divide it.

Wounds * 10 / ( ( DPS – Toughness / 5 ) * ( 1 – ( Armor / (Level * 44 ) * .4 ) ) ) = Survival time in seconds.

We’re starting to get somewhere at this point, but this really doesn’t give a true sense of how much effective health you have. It’s really only missing one step though. We have to take this survival time in seconds and apply it to the original unmodified damage. This would then convert out survival time into an effective health number and give a grasp of how much damage is being reduced. That gives us this formula, which while not at all absolute, is a very good baseline idea of WAR effective health:

Wounds * 10 / ( ( DPS – Toughness / 5 ) * ( 1 – ( Armor / (Level * 44 ) * .4 ) ) ) * DPS = Effective Health

Now this of course is for physical damage and we need another formula for resistances. Sadly, I actually don’t know the formula for resistances. I should really look into it. What I do know is that we can use the percentage rate to modify our physical EH equation into a magic EH calculation. All you have to do is replace the armor modifier with your resistance number as a decimal (ie: 50% = .5, 28% = .28). That would be done like so:

Wounds * 10 / ( ( DPS – Toughness / 5 ) * ( 1 – Resistance ) * DPS = Magic Effective Health

So the next step would be to throw in some numbers. Let’s go with physical for now, since it’s really the same formula and this will give a better sense of what’s going on. This is when I look up someone randomly on realm war for stats. We’ll call him Timmy, for personal reasons. Timmy is a rank 34 Blackguard, he has 2229 armor, 633 wounds and 390 toughness. Thanks for playing Timmy! So we punch in Timmy’s number and it looks like this:

633 * 10 / ( ( DPS – 390 / 5 ) * ( 1 – ( 2229 / ( 34 * 44 ) * .4 ) ) ) * DPS = Timmy!

So we’re missing something. We need to apply some damage to little Timmy! What you’ll find is because toughness reduces DPS at a flat rate, the more damage we put into Timmy, the less effective health he’ll have. Poor Timmy. Let’s go with a nice solid 1,000 base DPS. How much punishment will Timmy be able to take?

633 * 10 / ( ( 1000 – 390 / 5 ) * ( 1 – ( 2229 / ( 34 * 44 ) * .4 ) ) ) * 1000 = 16,993 EH

Hey, little Timmy aint so bad! He can absorb almost 17,000 health when taking 1,000 DPS before mitigation. Hey, let’s do one better and get his friend Jimmy instead though. Jimmy is a rank 40 Black Orc with 3,530 armor, 402 toughness and 790 wounds. Jimmy is a big boy. Sadly, since Jimmy is over the armor cap, we must treat him as if he has 3,300 armor, the full 75% reduction. Poor Jimmy. Let’s pick on him some more and make him take 2,000 DPS instead! Trying to cheat with all that armor and all, he deserves it:

790 * 10 / ( ( 2000 – 402 / 5 ) * ( 1 – ( 3300 / ( 40 * 44 ) * .4 ) ) ) * 2000 = 32,923 EH

Holy crap, Jimmy really is a big boy! Jimmy can actually absorb just under 33,000 base damage before dying. You can throw anyone into this and, while it’s not absolutely correct in every possible situation ever, it’s a good guideline and a solid way to work out just how much of a pounding you can take. You can do the same with resistances, but it’s really the same formula with a different type of ‘armor’ so I’d rather not keep spying on people with realm war.

Instead of mindlessly filling out a spreadsheet with random characters, I’d like to talk about something which has gotten a good deal of debate. That is Toughness versus Wounds. There are two reasons I’d like to talk about it, first because I find the debate over it rather silly in light of the role of toughness in effective health, but also because I think toughness is a very misunderstood stat.

First let me explain why I think the debate isn’t entirely needed. Toughness contribution to effective health diminishes greatly when dealing with higher DPS. If you’d like to see this for yourself, take my example of Timmy and bump the damage up to 5000. You’ll see a drop of 800 effective health. Now take the toughness and reduce it to 221, the base toughness of a Black Orc . You’ll notice your effective health only drops by about 300 at 5000 DPS. Now check at 221 and 402 with 2000 DPS, you’ll notice that EH drops by about 500 instead. You’ll find the lower the damage you’re taking the more meaning Toughness has.

Now, since we’re discussing Toughness versus Wounds, why don’t you play a game with me. Try subtracting Wounds instead of Toughness. We know that at 2000 DPS, dropping 181 Toughness reduced EH by 500. If you return Toughness to 402 and instead reduce Wounds by 181 (from 790 to 609) you’ll find that your EH drops from nearly 33,000, to about 25,400. A loss of right around 7,600 effective health. This means that your 181 wounds is worth over 15 times as much as 181 toughness would be.

So, if the disparity is that big and wounds really is that much better than toughness, why is there even debate over this? Well, there seems to be a large group of people who like to use toughness as if toughness were armor. The reality is that armor is light-years ahead of toughness in worth. Remember taking away 181 wounds? Let’s go from Jimmy’s Sentinel helm at 676 armor to a crappy green one at 542 armor. Now we’re ignoring that Jimmy is over the cap and this would actually not impact him. Let’s say this drops him from 3300 armor (cap) to 3166 armor. Doesn’t seem like a big loss, right? 134 armor? The loss of 134 armor would reduce Jimmy’s EH from right around 33k to 29.3k. That’s a loss of 3,700 EH. That loss of 134 armor is more substantial than if Jimmy had his Toughness reduced to 0, which still results in a respectable 31,600 EH. This is even worse if you use a higher DPS.

So, we really can’t compare Toughness to Armor. Wound is 15 times better at this level. What the hell is toughness anyway, useless juice? Nope. Toughness is, for those of you who played WoW, shield block value. These stats function in the exact same way. They reduce a static amount of damage and the more damage you take, the less they mean. It also means the reverse is true though. When dealing with very low incoming DPS, Toughness, like block value before it, becomes exceptionally good. Try this, go back to Jimmy and reduce the incoming DPS to 300. You’ll notice that suddenly his EH spikes up to 43,169. Now, to put the point home, reduce the toughness back to 0. You’ll see that he drops right back to 31,600 EH. That’s means you’re gaining 11,569 EH from your Toughness. Amazing, huh?

This makes Toughness much more valuable than it appears in RVR because you’re much more apt to be taking a lot of small DPS sources. So the same reason Toughness actually sucks in hardcore PVE, it’s quite good in RVR. Is it as good as wounds? Well, no not really. Try taking away 402 wounds and see what happens (hint: losing 22,000 EH isn’t a great idea). Still, let’s give Toughness some credit here. Wounds is roughly twice as good and Toughness absolutely sucks if you’re taking massive damage, but just like shield block it has its place.

So, how can I really reflect on EH theory in WAR? Well, you really have to understand how avoidance factors in and things to really get a grasp of it. I haven’t been able to run a test on WARs combat table, so I really can’t contribute in the way of avoidance. If WAR does use a single roll, which I hope that it does, avoidance rather than having a diminishing effect has a stacking effect. The more avoidance you build up in a single roll system the more each percentage of avoidance will be worth. The best way I can explain is this, if you are being hit for 15,000 damage every half a second a character with 99% avoidance would live for about 50 seconds on average, avoiding 49 swings before exploding when finally hit. By adding 1% more avoidance your character can now live an infinite amount of time as long as your avoidance is maintained. This is at the very extreme end of course, but this actually starts all the way down at a thousandth of one percent of avoidance.

What is pretty straightforward though is how our primary defensive stats work together. The game really is a lot like WoW in many ways, although armor doesn’t suffer diminishing returns and shield block value has been renamed toughness, the idea is very similar. You might be wondering about something I said at the beginning though that this is how much damage you can take without being healed. That’s vital to why EH works. You’ll see a lot of people talking about it and bringing up healing, but as soon as you do you’ve actually missed the entire point. That point is that a character with higher effective health can sustain more damage than one with lower effective health. If you can sustain higher damage, then it means you can receive more healing. At lower effective health you begin to reach a situation where heals become useless. This situation occurs when incoming damage exceeds effective health and the target is killed in either a single hit, or a string of hits so quickly that healing is physically impossible.

Just like WoW, when a level of effective health is achieved that allows you to be comfortably healed by the group size, avoidance becomes more important than effective health. Yup, you heard me, effective health is not the end-all be-all of tanking numbers. Effective health is used to literally power through encounters which you should not be able to complete. It’s a very easy game-plan to go to, but once you’re at that minimum, avoidance is better as you will be reducing healer strain more than you would be by increasing effective health. This is one of the reasons I find certain stats to be undervalued, particularly Weapon Skill in PVE where you’re almost assured to be taking a lot of melee damage.

It’s kind of amusing really, for defensive purposes in WAR, parry is WoW’s dodge. Block is WAR’s version of WoW parry. You can’t gain some extra block by stacking stats, just like parry was its own value. Parry in WAR however can be increased, just like agility increased dodge. Sadly the conversion rate to parry is rather low at 50:1. Still, for hard encounters 50 WS is going to reduce more damage than 50 Toughness would. I guess the reason really is the low ratio and the lack of use in PVP , but still it does go right back to these strange debates. I suppose since armor is so easy to cap it’s hard to really try and compare the only stat that stands up and shouts that it’s a defensive stat.

In any case, here’s to you, Toughness stat. If only there were a ‘Toughness Slam’ ability, perhaps I would love you as much as I loved my shield block value. I’ll miss you, most of all, Gnomeregan Auto-Blocker 6000. I’ll miss you most of all.

pancakez

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10 Comments leave one →
  1. mjukis permalink
    March 6, 2009 8:30 pm

    I’m not sure what the question was but Parry and Block are two separate rolls as far I know. Otherwise I’d be sitting at like 85% physical avoidance when buffed minimum (not counting ironbreaker or banners) and from my experience thats not the case. Not sure if that was the question but yeah.

  2. pancakez permalink*
    March 6, 2009 9:56 pm

    That’s one of the questions, I suppose, but since attacker strength reduces your chance to block and parry relying merely on the sum total doesn’t work. You would need to test to see if one of the stats was rolled before the other. You’d be looking for one of your avoidance stats being reduced proportionally to the other. So if you have 50 block and 35 parry you’d be looking for either block rates around 32.5% on average, or parry rates around 17.5% on average. If there’s some other ratio then it’s quite possible that the attackers strength is the cause.

  3. Light permalink
    March 9, 2009 4:26 pm

    Nice read, but I have two gripes:

    1. You assumed that toughness is calculated before armor/resistance. If it was proven otherwise then my apologies 🙂 But otherwise we should at least consider formula that goes like this:
    Wounds * 10 /( ( DPS * ( 1 – ( Armor / (Level * 44 ) * .4 ) ) ) – Toughness/5) * DPS = Effective Health

    2. The hard part about calculating the usefulness of toughness is that it ‘spreads’. It’ll be best to explain in an example: Let’s say you have 20% elemental resistance, and a 100dps toughness reduction. A Bright Wizard sees you and decides that you shall be a great target for his 500DPS DOT. (I’m going to use your damage reducing formula) The damage would be reduced to (500-100) * (1-0.2) = 320 DPS. Unsatisfied with the results, he decides to cast another 500DPS DOT, which goes thorugh the same damage reduction formula. Now we are being hit for 640 total DPS. Ouch. However, his high level buddy decides it’s not enough, and casts a 1000DPS DOT. Let’s run the numbers again: (1000-100) * (1-0.2) = 720 DPS
    720 DPS > 640 DPS
    Now, I know that my toughness factor was high for damage dealt, but I wanted to show that when calculating the usefulness of toughness stat 500DPS + 500DPS is not equal 1000DPS

  4. pancakez permalink*
    March 9, 2009 5:44 pm

    Toughness is accepted to be first in line on mitigation. The easiest way to test this is to find some gear with no toughness on it and let a monster hit you for a while. Then find another monster of the same type (including level) and let that one hit you and compare damage. My Disciple has no +toughness on his gear and 45% armor. When I do this swap I go from taking hits for ~100 to hits for ~220. He has 97 toughness, which is -19.4 DPS. If Toughness were first, I should be taking around 80 damage, or less if attacks come slower than once per second with my armor on, not 100. Considering the monsters I was testing with were attacking about every two seconds, I should have been hit for more like 60 damage with my armor on. It’s not a difficult thing to figure out. You can also test by keeping an armor buff up one fight, then not keeping up the next fight, but the numbers become harder to read.

    As far as multiple damage sources, the issue of toughness ‘spreading’ isn’t really the issue. As long as the damage source is greater than your toughness / 5, toughness will reduce the same amount of damage. What the issue becomes is that the ‘time to live’ formula must also be divided by the number of incoming attacks. Your effective health actually remains the same and the amount of damage reduced by toughness is the same, it’s just that the amount of damage reduced now comes at a faster pace. So while your toughness reduction is really toughness / 5 * sources, your effective health in unchanged by that fact. Your toughness’ worth is based on incoming attacks, yes, but it goes both ways. So for instance if you have 500 toughness and are being attacked by 5 targets, four of which are doing 200 DPS and one which is doing 600 DPS, your effective health is the same as it would be if you were being attacked by one target dealing 280 DPS. However, your life expectancy with 500 wounds would be 3.5 seconds, instead of 17.8 seconds. The amount of damage mitigated and by extension your effective health is actually the same.

  5. Light permalink
    March 9, 2009 9:02 pm

    Hi, thanks for a quick reply 🙂
    1. This part is really confusing… you start by saying that toughness is considered to be first in line of mitigation, and then you seem to prove that it’s not. So um… what the..?

    2. I can’t really see the argument you’re giving here. How exactly does it go ‘both ways’? Could you please provide an example?

    PS Please don’t bash me 🙂 I’m not here to nitpick your work, I’m just trying to understand some of the details. Also, I’m not arguing wheter wounds, armor, or any other stat is better or worse then toughness.

  6. pancakez permalink*
    March 9, 2009 9:54 pm

    Don’t misunderstand. I actually have no problem with people nitpicking. 🙂

    As far as the testing of if Toughness, or Armor comes first this is how it works. First I went with all my gear on, which as I said is 97 toughness and 45% armor. I was hit for about 100 damage. Then I took off anything that added armor, so I was at 97 toughness and 0% armor. I was hit for about 220 damage. I was being attacked around once every 2 seconds, which means the base damage on those attacks was about 260. If Armor was first, it should have reduced the damage to just under 80. If Toughness was first, it would reduce damage first to 220, then armor would reduce it to 100, which is the actual result.

    For the second part, I may have been a bit vague. I’ll go with your example of having two sources dealing 500 DPS, versus one doing 1,000 DPS against a 20% resistance. You didn’t supply a wounds number, so I’m going to wing it at 500 wounds. Against 500 DPS your effective health would be at 7,812. Against 1000 DPS your effective health would be at 6,944. No matter how many sources you add in it would take 7,812 damage to drop you against 500 DPS, while against 1,000 DPS you would always take 6,944 damage. There could be ten sources of 500 DPS, but you would still take 7,812 damage prior to mitigation. The difference is the survival time, not the effective health.

    To find your survival time you take your effective health and divide it by the sum of all incoming DPS. So if your effective health is 7,812 and you’re taking damage from two 500 DPS sources you would live for 12.2 seconds. Against one 500 DPS source you’d live twice as long at 24.4 seconds.

    I was probably a bit vague in my wording that Toughness worked both ways. What I meant is that Toughness works in my effective health formula for one target, or many targets. The issue is how you have to figure out that incoming DPS, which is to average it. So for two 500 DPS sources, your effective health is based on taking 500 DPS. For a 200 DPS source, a 350 DPS source, two 300 DPS sources and a 700 DPS source you would use 370 DPS to find effective health, not 1,850 DPS.

  7. Light permalink
    March 10, 2009 3:48 am

    Hi again 🙂 Thanks a lot for elaborating, especially on the second part, it was a bit confusing 🙂 It would be great if you added that explanation to the main body of the article, because I think a lot of people would just add up the DPS 🙂
    But for the first part… My calc doesn’t agree with you 😛
    We know that while armored you were taking 220 damage, and while unarmored you were taking 100 damage. Your armor was 45%, and if toughness was first you should be taking 1 – 0.45 = 0.55 or 55% of 220. That’s ~120 not ~100. But I’m going to assume that you actually have 55% armor and made a mistake out of rush 🙂

    Thanks again for patience 🙂

    PS I would test it myself but all my higher level characters are tanks and it’s pretty frustrating getting some gear without toughness for a tank 😛

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