Effective Health In GW2 (Math / Theorycrafting heavy thread)

Effective Health In GW2 (Math / Theorycrafting heavy thread)

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Posted by: Khift.4706

Khift.4706

Effective Health (henceforth EHP) is a measurement of how much raw, unmitigated damage you can receive before dying. It is an important stat to know and keep in mind when deciding how to gear your character. How it is calculated varies from game to game, but at its simplest it is Health * (1 – %Mitigation) = EHP. Being an old theorycraft buff from a game which shall not be named, the moment I saw how simple GW2’s damage formula was I simply had to get my fingers in there and figure out exactly which ratio of toughness to vitality yields the most EHP possible.

After some work at it, here is the formula I ended up with:

V = (10D + 10S – B) / 20

  • V is the optimum amount of ADDITIONAL vitality you should itemize for out of S stats.
  • D is your base defense from gear and traits (with level 80 exotics that is 920 for light, 1064 for medium, and 1211 for heavy armor. Add 61 if you use a shield.)
  • B is your base health BEFORE vitality is factored into — being again, health from traits plus base health (1545 for elementalists, guardians and thieves, 5922 for mesmers, engineers and rangers and 9212 for warriors and necromancers.)
  • S is the amount of stats you’re willing to put toward EHP. This amount is set by you, the user of the formula. If you want to use 1k stats for EHP, then put 1k in for S.

Some notes about the formula:

  • This is just a measure of EHP. This doesn’t factor healing or Healing Power in at all. However, you can put it in there if you want — take a rough guesstimate of how much healing you expect to get throughout a fight and add it to B. Let’s say, as a mesmer, I expect to use Ether Feast twice in a fight, I’d just take double what my Ether Feast heals for and add it to B.
  • This formula gives you the ideal mix of vitality and toughness that grants you the highest possible EHP. The formula, however, outputs in terms of V, so if you need to get toughness, just take the output and subtract it from S, which is the amount of stat points you’re spending on both toughness and vitality.
  • For low quantities of S you will usually get a V which is larger than S. This is okay; all this means is that if it were possible the ideal spread of vitality and toughness actually involves dropping below the base toughness amount, which clearly isn’t possible. The opposite is true if you get a negative V somehow — that means the ideal amount of stats involves so much toughness it’d be best to below minimum V. In either of these cases, just go full toughness or vitality.

So how about some practical results and examples?

Let’s say I’m playing my mesmer, which is almost always true. Let’s say I’m in WvW, running a build with 20 inspiration (vitality and healing power) so I can get that delicious Warden’s Feedback trait as well as 20 points in Chaos (toughness) to get the 20% faster staff skill recharge. Let’s say I expect to cast Ether Feast once before dying, but don’t expect to get any benefit from the additional illusions because those guys have the lifespan of a microbe in WvW. (Also assume no healing power on gear, for simplicity’s sake.) And finally, let’s say that I’m going to itemize my gear so that I’ve put 500 stat points into toughness and vitality — I don’t want to to an undying juggernaut, but I’d like to not explode when someone looks at me either.

So let’s get into the formula. My D is going to be 920 (full cloth exotics) + 200 (from 20 points in Chaos), or 1120. My S is 500, as I set it in the last sentence. My B is going to be 5922 (mesmer base health), plus 2000 (vitality from the Inspiration trait line), plus 5760 (the value of one cast of Ether Feast), or 13682. Now put it together:

V = ( [10 * 1120] + [10 * 500] – 13682) / 20
V = 125.9

Of my 500 stat points, I should make 126 of them vitality and the other 374 points toughness so I have maximum EHP under this scenario. Important — and good to know.

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Posted by: Khift.4706

Khift.4706

How practical is it? Hard to say. It doesn’t take a genius to figure out that necromancers prefer toughness over vitality, nor that guardians want the opposite. Necromancers have the highest base health in the game, tied with warriors, but the lowest defense from armor because they wear light armor; guardians are the opposite, with the highest base defense and the lowest health. Given the concept of EHP it isn’t a big surprise that necros would prefer toughness and guardians would prefer vitality. And really, that same concept of gearing to cover your weakness continues on with other classes and builds – as a general rule, wear the gear that gives you the greatest balance between health and armor. But if you want to know specifically how to accomplish that? Drop it in the formula. Neat things come out.

For anyone who cares about the math (Warning: Includes calculus):

  • The damage formula is pretty simple: Damage = (stuff)/Armor
  • Health is simply damage you can take before dying, so set Health – Damage = 0
  • Solve for (stuff), (stuff)=Armor * Health
  • This is EHP. (stuff) is just damage before considering armor, aka unmitigated damage, so EHP = Armor * Health. Easy.
  • Now for the fun part. Armor is actually defense (D) from gear + toughness (T), and also at level 80 you start with 916 toughness, so Armor = 916 + D + T
  • The same with Health. Health is actually Base Health (B) + 10 * vitality, and again you start with 916 vitality before gear at level 80. So Health = 9160 + B + 10V
  • Now expanded we have EHP = (916 + D + T)(9160 +B + 10V)
  • That’s a lot of letters, yes, but only three variables (T, V and EHP). All the others are just constants defined by your class. We still can’t do much with a three variable equation, though, but thankfully T and V have another relationship.
  • There are only so many stats you’re willing to put towards increasing your EHP — we’ll call this Stats (S). So, S = T + V. Again, three letters but only two variables — S is a constant set by you. Solve for one variable, let’s do T, T = S – V.
  • Drop that into the first equation and you get EHP=(916 + D + S – V)(9160 + B + 10V)
  • Now to find the maximum — first take the derivative with respect to V.
  • DEHP/DV = (-1)(9160 + B + 10V) + (10)(916 + D + S – V), simplifying to DEHP/DV = -20V – B + 10D + 10S
  • Set that equal to 0 and solve for V, yielding:
  • V = (10D + 10S – B )/20

(edited by Khift.4706)

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Posted by: Iason Evan.3806

Iason Evan.3806

I liked Money Ball as much as the next guy. Too bad I am not like the dude in the front office that makes those decisions based on equations. I go with my gut and instinct. Cool stuff you compiled there though and I am glad that type of play works for some people.

Tiger Woods turns golf into a science while Arnold Palmer just went out there and played. I am more the Arnold Palmer or Bubba Watson as opposed to the Tiger Woods or Vijay Singh.

Leader of The Guernsey Milking Coalition [MiLk] Sanctum of Rall

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Posted by: CrazyGoNuts.9536

CrazyGoNuts.9536

Maybe I’m not familiar enough with this games mechanics, but about this:

“B is your base health BEFORE vitality is factored into — being again, health from traits plus base health (1545 for elementalists, guardians and thieves, 5922 for mesmers, engineers and rangers and 9212 for warriors and necromancers.)”

Are you saying without itemizing or traiting for health a thief will only have 1545 health? That doesn’t seem correct.

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Posted by: Johnson.3874

Johnson.3874

Are you saying without itemizing or traiting for health a thief will only have 1545 health? That doesn’t seem correct.

I think he meant base health without taking in account the “base” vitality of your character. So, if a thief had 0 vitality, he would indeed have 1545 HP. Fortunately, when you play your thief, even without his equipment, you have to add his vitality to get his “real” health.

Or at least that’s how I understand it ^^

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Posted by: Khift.4706

Khift.4706

Are you saying without itemizing or traiting for health a thief will only have 1545 health? That doesn’t seem correct.

I think he meant base health without taking in account the “base” vitality of your character. So, if a thief had 0 vitality, he would indeed have 1545 HP. Fortunately, when you play your thief, even without his equipment, you have to add his vitality to get his “real” health.

Or at least that’s how I understand it ^^

Yep, that’s it. Everyone has 916 vitality when naked at level 80. Minus that, each class also has a different base health value — 1545 for thieves.

Don’t worry about the base vitality, it actually fell out of the equation when it cleaned up at the end, same as the base toughness did. Just worry about the base health value.

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Posted by: Red Falcon.8257

Red Falcon.8257

I don’t believe in Vitality.
2800-3000 armor does all I need on all my classes; this and a good build is all I need.

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Posted by: Johnson.3874

Johnson.3874

I’ve tried to give some thoughts about your formula, and I’m wondering in which case it can be applied.
For example, I thought about using it for my warrior (shout specs), but since I’m quite limited with the stuff I can use (nothing except Power/Toughness/Healing Power, otherwise it’s not interesting to go for that build), I was wondering if there were situations where your formula can be used, and other cases where it’s not worth it ?

Or am I just lazy here, because it’s quite a challenge at this time of the night to calculate how much healing I’m gonna receive during a fight before dying
Anyhow, I have this feeling that your formula must be more useful for some builds than others, but I’m not sure which ones.

I mean, somebody playing glasscanon is not gonna wonder how much toughness compared to vitality he has to put on his gear. Nor someone like me going for +healing. Or am I missing a point somewhere ?

In any case, thanks for the thread, it’s quite interesting

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Posted by: Khift.4706

Khift.4706

Unfortunately for us, Johnson, they didn’t really include even a fraction of the possible stat combinations on gear, yeah. Which is unfortunate; I would kill for a Power/Precision/Vitality alternative to Knight’s gear. And of course of the stat combos that are present almost half of them aren’t even available in PvP — your character, for example, could use the Healing Power / Vitality / Precision stat combo in the Ascalonian / Nightmare / Svanir gear sets.

That said, this is most useful for classes who cannot heal very often. If you’re getting a ton of healing like your build does then toughness is definitely going to outweigh vitality. Fight length also matters; long, drawn out battles like in WvW tend to involve tons of healing so again, toughness reigns supreme. But a relatively quick 1v1 or 2v2 in sPvP? That’s where this would matter.

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Posted by: CrazyGoNuts.9536

CrazyGoNuts.9536

Depending on your build you should be able to convert healing to equivalent vitality – obviously you would need to make a few assumptions on a per build basis, but at the end you could get some good approximation of how much vit each point of healing power is.

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Posted by: Leiloni.7951

Leiloni.7951

There’s a similar thread posted on GW2Guru from back in September, based partly on some Reddit post they link in the OP: http://www.guildwars2guru.com/topic/60838-math-damage-reduction-toughness-and-vitality/

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Posted by: Corian.4068

Corian.4068

Good read, thanks for putting it together.

Hit level eighty
Priorities, what to do?
Spend hours with dye

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Posted by: Eveningstar.6940

Eveningstar.6940

Khift,

Thank you so much for this. I gave it a good read, let it percolate in my mind and didn’t come back to it until I’d had a sudden “aha” moment. I’m pretty terrible at math, but I got the gist of what you’re saying, and this totally transforms the way I’m looking at mitigation and healing on my Guardian (a profession which offers an interesting anomaly, being a high armor low health profession with access to constant low-level healing). This really gives me a much more sophisticated justification for Guardian health pools.

Elegant work. Thanks!

Valerie Cross: Roleplayer, Writer, Tarnished Coast

A Beginner’s Guide to Guardians