Guild Wars 2

TL;DR

In some cases, it is better to take Sigil of Life than Sigil of Benevolence for allied healing based on your healing power and the abilities you are using.

If you have moderate to high healing power, you should be safe using the Sigil of Benevolence for maximizing allied healing, and don’t have to worry about Sigil of Life.

Sigil of Life will be useful if you still want to benefit your own healing (i.e. for solo play).

Preface

I wanted to create a quick and easy way to know if Sigil of life or Sigil of Benevolence would be better for a particular build looking to maximize allied healing only without having to do extensive calculations each time. I also wanted to make sure that Sigil of Benevolence was not a “trick” sigil that was causing people to mistakenly think it was helping them out when Sigil of Life would actually do the job better.

As such, I developed an easy formula that lets you know which one will be better based on what abilities you are using and how much healing power you have. It does not directly tell you how much better one sigil or the other will be, only that a certain one is better (though you can perhaps make a judgement based on the relative values). You will have to do manual calculations if you want to know the exact amount.

Someone please correct me if I’m wrong in my analysis. I wasn’t able to find another thread dedicated to this topic (admittedly I didn’t look very hard). Most of the values I used were obtained off the wiki, and I haven’t tested much of this in game. This is simply a mathematical analysis of how the system should work.

Note that I assume that the outgoing healing benefit mechanic is a global multiplier that effectively multiplies the entire healing value. If this is not how this mechanic actually operates, the results here will not be accurate.

I am not sure if this mechanic applies to the regeneration boon and regeneration-like effects, although the formula should still work on it if it does.

Background Info

Sigil of Life will give up to 250 healing power, whereas Sigil of Benevolence will provide up to +12.5% healing effectiveness to allies.

Since both of these sigils cannot be taken together, one has to decide which is more beneficial to them. In the case of someone playing solo, the Sigil of Life is clearly the better choice since the Sigil of Benevolence applies no self benefit.

In a group scenario, it’s a bit more difficult to decide which one is better. Naturally, one would assume that the Sigil of Benevolence would be better due to the fact that it provides a benefit to allies and not to oneself, whereas the Sigil of Life provides a benefit to allies and oneself.

However, the only way I see this being true is if the benefit provided by Sigil of Benevolence actually provides more healing potency than the Sigil of Life. Thus we need to determine when this is true.

Determining Sigil Benefits

Since Sigil of Life provides extra healing through improving healing power, it is subject to the particular scaling coefficient of the ability. However, Sigil of Benevolence appears to just apply a flat percentage increase to overall healing without worrying about the scaling factor of the ability used. This also means that Sigil of Benevolence will benefit from a character’s base healing power.

Thus, for a character with healing power HP using ability with a base heal B, scaling factor S:

Benefit from Sigil of Life: B + ((250 + HP) * S)
Benefit from Sigil of Benevolence: 1.125 * (B + (HP * S))

We assume that the character has sigil benefits of 25 stacks in these cases.

Since we are interested in the point at which both sigils provide equal benefit, we equate and manipulate the equations to arrive at the following:

0.125 = (250 * S) / (B + (HP * S))

What this means is that, for a given ability, if the S, B, and HP values are such that the result of the equation is 0.125, the sigils will provide equal benefit. Since each ability will have a fixed S and B value, we are interested in isolating the healing power, HP, since this will vary on a character’s build. As such, we obtain the following formula:

HP = 2000 – (B / S)

What this means is that, for any given healing ability, the equilibrium healing power value can be determined. By “equilibrium”, this means the healing power at which both Sigil of Life and Sigil of Benevolence will provide equivalent outgoing healing (the equilibrium value should be rounded down when necessary).

If the healing ability occurs over a number of pulses, one of two things can be done. The healing value per pulse should be considered B with the scaling value for each pulse used for S. Alternatively, the total healing across all pulses can be used as B, with the scaling value S being equal to the scaling value for one pulse multiplied by the number of pulses in the ability. For instance, Geyser (3 pulse heal) can be calculated with B = 808 and S = 0.25, or B = 2424 and S = 0.75.

Applications and Examples

Since we now know the healing power for which a particular ability benefits equally from both sigils, we can make two stipulations:

1. Healing power values greater than the equilibrium healing power value will benefit more from Sigil of Benevolence.

2. Healing power values less than the equilibrium healing power value will benefit more from Sigil of Life.

This is important when a person is deciding whether to use a Sigil of Life or a Sigil of Benevolence. Based on their healing power and abilities available to them, they can determine which one is best for overall outgoing healing.

For instance, let’s take the elementalist ability Water Blast (staff water auto attack). This has a base heal of 370 and a scaling coefficient of 0.25 for healing power. As such, the equilibrium healing power value is given by:

HP = 2000 – (B / S) = 2000 – (370 / 0.25) = 2000 – 1480 = 520

This means that, to maximize the allied healing of Water Blast, an elementalist with less than 520 healing power would want to use Sigil of Life, whereas an elementalist with more than 520 healing power would want to use Sigil of Benevolence. If they had exactly 520 healing power, it would would be irrelevant which one they chose (at least at maximum stacks).

For another example, take the Elixir-Infused Bombs trait available to engineers which lets their bombs heal others with a base heal of 145 and a scaling of 0.15.

HP = 2000 – (145 / 0.15) = 1033 (rounded down)

Thus, an engineer with less than 1033 should use Sigil of Life if they want to maximize the healing to allies from the bombs, whereas an engineer with more than 1033 healing power should use Sigil of Benevolence.

Lastly, let us consider the Merciful Intervention ability for guardians, which has a base healing of 1960 and scaling of 0.6.

HP = 2000 – (1960 / 0.6) = -1266

Note that this is a negative value. Since healing power cannot go below zero, this means there is no situation in which Sigil of Life will be the most beneficial. As such, Sigil of Benevolence should always be used to maximize the allied healing of this ability.

Conclusions

Any person can now calculate whether or not Sigil of Life or Sigil of Benevolence will be better for their outgoing healing based on their builds.

In general, high healing power builds should default to Sigil of Benevolence, since this sigil will be more beneficial if a character’s healing power is greater than the equilibrium value. The only real situation in which Sigil of Life will be better for allied healing is when a character’s healing power is low, or the primary ability for which they are looking to heal with has a low base heal (i.e. Elixir-Infused Bombs).

This also does not consider by how much better a given sigil is. Thus, it may be possible that Sigil of Benevolence will be better according to the formula, but it may only be by a small fraction (this will have to be determined manually). As such, one may not deem it worthwhile since the Sigil of Life also benefits self healing in addition to allied healing, whereas Sigil of Benevolence does not.

For instance, with 1200 healing power, it is better to take Sigil of Benevolence for allied healing with Elixir-Infused Bombs since the equilibrium healing power value is 1033. However, the actual healing per bomb will be 365.625, whereas using Sigil of Life with the same healing power would give 362.5. As such, it may be more worthwhile for the engineer to use Sigil of Life to benefit self healing instead of obtaining an extra 3 HP on each heal for allies.

In any case, this can be useful if you are simply not sure what sigil will be better for you, or if you want to know how much healing power you will need in order for Sigil of Benevolence to be a stronger choice for allied healing than Sigil of Life. I wouldn’t expect most low healing power builds will want to focus on allied healing anyways though, so defaulting to Sigil of Benevolence will likely be safe in most cases.

Notable Values

I made a short table of some abilities that had notable equilibrium healing values. That is, they actually pose a question as to whether or not to take Sigil of Life or Sigil of Benevolence.

Guardian:

Selfless Daring: 1871

Given the low base heal and high healing coefficient, this results in requiring 1871 healing power in order for Sigil of Benevolence to provide more benefit to allies instead of Sigil of Life. Since this is also a convenient way to heal yourself, it is probably better using Sigil of Life if Selfless Daring is the primary group healing ability a guardian uses. If they use other abilities it still might be worthwhile to use Sigil of Benevolence.

Battle Presence (via applying Virtue of Resolve): 600

I haven’t tested if “outgoing healing” apply to this, although if they do then you should use Sigil of Life for maximizing party healing if your healing power is less than 600.

Engineer:

Elixir-Infused Bombs: 1033

Bomb healer builds will only want to take Sigil of Benevolence if they have over 1033 healing power. Obviously, any sort of bunker build using this will use Sigil of Life to maximize self healing.

Necromancer:

Transfusion (using Life Transfer): 540

I imagine most healing necromancers have more than 540 healing power, but if not then Sigil of Life will be better than Sigil of Benevolence.

Warrior:

Vigorous Shouts: 355

It will almost always be better to take Sigil of Benevolence for party healing since the equilibrium value is very low. However, if the warrior only has a minor or no investment in healing power, Sigil of Life should be taken if they want to maximize the healing from this trait.

EDIT: If this mechanic affects regeneration boons you apply, the equilibrium healing power value will be 960. Water blast finishers give a negative number, so Sigil of Benevolence will be better for them if the mechanic applies to them. I haven’t tested if the Sigil of Benevolence applies to either of these healing methods.

I’d like to nominate this as the post of the patch. Really excellent analysis. Thanks so much.

I feel like sigils of benevolence needs an additional effect, like x% of self heals affect allies, in order to be competitive.

Really good post man! Props.

Thanks so much, now I know to run sigil of life on my necromancer thanks.

So I tested it out and it works but could you explain how you derived that equation?

thank you for having good math skillz

Shaogin.2679:

So I tested it out and it works but could you explain how you derived that equation?

Sorry for the late reply on this. Sorry for the bump as well, I just didn’t want to leave a question unanswered.

Healing abilities all have a base healing amount, and then they receive an extra amount based on your healing power and a certain scaling factor that varies per skill. The scaling factor is determined by testing how much the heal improves per unit of healing power, and most of the skills have documented values on the wiki.

So a healing skill normally heals it’s base heal plus your healing power multiplied by the scaling factor for that ability (i.e. B + (HP * S)).

With sigil of life, your healing power is improved by 250, and sigil of benevolence should cause the overall healing to increase by 12.5%, which leads us to the initial two “benefit from” equations. From there, we equate the equations, and then it’s just a matter of manipulating the equations to isolate healing power.

I skipped over most of the steps for sake of brevity, but if you’re interested, it goes something like this:

1. Equate equations: B + ((250 + HP) * S) = 1.125 * (B + (HP * S))
2. Expand multiplied terms: B + 250S + (HP * S) = 1.125B + 1.125(HP * S)
3. Subtract (B + (HP * S)) from both sides: 250S = 0.125B + 0.125(HP * S)
4. Divide both sides by 0.125: 2000S = B + (HP * S)
5. Divide both sides by S: 2000 = (B + (HP * S)) / S
6. Split divided term: 2000 = (B / S) + ((HP * S)/ S)
7. S cancels out on last term: 2000 = (B / S) + HP
8. Solve for HP: HP = 2000 – (B / S)

Hopefully that clears anything up if you were still wondering.

Also, I’m glad some people found this useful. I guess boredom can produce helpful things now and again.