I’ve been commenting on several threads that have been asking about support builds, and whether to choose banners or shouts as a source of Healing. However I’ve been challenged on one particular statement lately. I believe Shouts are a better source of healing than Banners. I’ve detailed a number of reasons why in the other thread. Shouts, I believe, give you more healing for your Healing Power, than Banners do, but I am being challenged on that (and rightly so might I add), so in this thread I am going to detail some Numerical Proof for my theory. This thread is purely to compare the Healing Support builds, so the Control build is not discussed here.
Firstly, here are some opening statements to set the scene.
Banners provide you a large heal over the duration you are under their effects and the talent that makes this so is called Inspiring Battle Standard (or IBS). The other talent usually coupled with this is Inspiring Banners (IB) which reduces Banner cooldown by 20%, and increases their radius. Note however that there is no talent that improves the healing you receive from Banners.
Shouts provide Burst Healing from the Grandmaster Talent, Vigorous Shouts (VS), however in the Master slot there are two “shout augmenting” talents to choose from. Firstly there is “Shrug it Off”, which automatically activates “Shake it Off!” (SIO) if you have more than 2 conditions, it has a 30 second cooldown. Shrug it Off does NOT activate your SIO cooldown, but it does Heal you like other shouts. Secondly, there is “Lung Capacity” which reduces the cooldown of your shouts by 20%.
So those are the two over-arching methods of healing, but what about the numbers? There are equations defining both methods of healing, let’s begin with Banners (NOTE: All numerical proof is done for Level 80):
Empirical Regeneration Formula:
5+(1.563*Level) + (0.125*HealingPower) = Health per Second
t*(5+(1.563*Level) + (0.125*HealingPower)) = Total Healing Done
The symbol "t" represents Time. This equation details how Banner regeneration is dependent upon your Level, and then a factor equal to 12.5% of your Healing Power stat is added, and a constant to provide the amount of health the regeneration ticks for. The left hand side of the equation is rounded up to 130 Health per Second at level 80.
For Shouts, the equation is somewhat simpler:
Empirical Shout Formula: 1192+0.8*HealingPower = Burst Heal
The number 1192 is the amount you are healed for from a Shout at 0 Healing Power. It is important to factor however that I am assuming that you are using For Great Justice, On My Mark, and SIO as your Shouts, which equates to two 25 second cooldowns and a 30 second cooldown.
So which is better?
This is one of those occasions where it’s really hard to crunch the numbers in your head, so I used a Google Spreadsheet to crunch the numbers. Since the banner equation calculates healing done per second, and the Shout equation calculates total heal, the best way to compare these builds on raw healing is to consider a steady state period of 100 seconds (which covers the duration of a banner).
I chose an arbitrary period of 100 seconds because it gives a fair representation of what might be a short boss fight for example. It is necessary to monitor the healing over a non-insignificant period because there are plenty of subjective criteria that undermine either of these builds.
This method of calculation also allows the comparison of Cumulative Healing Done over time.
In order to compare the numbers, the healing is "normalized", i.e. the Banner Healing per second is multiplied by 100 (for each second), and in the google spreadsheet (link below), the data series shows that over 100 seconds, each cell is the cumulative value of itself and the previous cell.
The spreadsheet detailing all of the numbers and charts is found here, it is assumed from here on that you refer to this spreadsheet alongside the rest of this post:
Given that this is a theoretical comparison of two builds, it is necessary to put forward some assumptions (although I prefer Initial Conditions, as i'm sure do the rest of you Mathematicians/Engineers) Just to explain the spreadsheet a little bit, the general assumptions of this model can be found as:
- At Time, t=0 you use all of your shouts, and re-use them as soon as they are cooled down (i.e. with Lung Capacity, by 20 seconds you will have used 3 shouts at t=0, and your two 20 second cooldowns are now reused, hence 5 shouts have been performed by 20 seconds).
- For the “Shrug it Off” data series, this is highly theoretical, unrealistically so in fact. It is assumed that at t=0 you use all 3 shouts, and that at every possible opportunity, your automatic SIO procs as well. This is generally unrealistic, since i'm fairly certain there is no such overwhelming condition application anywhere.
- It is assumed you remain under the effects of your Banner(s) for the entire 100 seconds.
- There are two data series relating to Shouts, one for each Master talent that invariably affects the Healing you output.
- The Banner healing is always a Linear relationship with time, and the only way to improve Banner Healing is via improving Healing Power.
- Shouts have no activation time, hence it is necessary to ignore that same activation time of Banners too.
At this point I hope you are looking at the spreadsheet. Don't worry too much about what is on the first sheet, that is just the series of numbers relating to each method of healing. The shouts column is manually input for the most part as a number (of shouts) multiplied by the Healing from a shout. At 20 seconds for example, this multiple increases by 2 (up to 5), since you have in theory re-used your shouts again. This is also assumed due to Shouts having no activation time, so it can be accurately expected that the time to activate a shout, have it cool down and use it again, is wholly equal to just the cooldown.
The cases considered are the Healing received with Healing Power = 0, 900, and a Theoretical Maximum. In order to explain the "Theoretical Maximum" I have tried to list all possible sources of Healing Power, and add them up, this includes:
- Exotic Cleric's Armour: Helm = 45, Shoulders = 34, Chest = 101, Leggings = 67, Boots = 34. Total = 281
- Weapons: MH = 90, OH = 90, Total = 180
- Jewellery: 2x Rings = 134, 2x Earrings = 112, Pendant = 90, Total = 336
- Miscellaneous: Tactics Banner = 90, Defense (30) = 300, Sigil of Life (25 stacks) = 250, Food = 70, Rune (of Water for example) = 165.
- Grand Total = 1672?
Now to explain the Charts. These are plots of the data series' you can see in the first sheet, this is a much easier representation of healing done. First of all, the Legend:
Blue represents 3x Shout Healing, with Lung Capacity.
This series uses 3 shouts whenever possible, traited with Lung Capacity.
Orange represents 3x Shout Healing, with "Shrug it Off".
This series uses 3 shouts whenever possible, traited with "Shrug it Off", which is assumed to proc every 30 seconds.
Red represents Banner Healing.
This series represents the Healing Done from a Banner over the duration as long as you are consistently under the effects of it's regeneration.
Green represents Banner + 3x Shout Healing COMBINED.
This series looks at the combination of the 3x Lung Capacity Shouts and Banner Healing.
Purple represents 2x Shouts Healing.
This series uses FGJ and SIO only, and compares the healing to Banner regen, doesn't really require much discussion, but there are scenarios where FM is good, so here are the numbers...
Light Blue represents a World vs World idea.
This series is an idea from a commenter, who suggested using FGJ, SIO and then Fear Me! for a WvW oriented build.
It is necessary to state at this point that Shrug it Off is generally discounted as a viable comparitive tool for Healing, since to actually achieve the numbers it suggests it relies on highly theoretical assumptions (i.e. that as soon as the auto SIO cools down you will immediately have it proc again, which is largely untrue). As such, Lung Capacity Shouts will be used as the legitimate comparison.
By constructing this spreadsheet, it is clear now more than ever that Shouts are the more dominant source of Healing. At the bottom of each data column are cells with %age values, showing how much MORE Shouts heal by compared to banners over that 100 second duration.
An interesting point I followed up was to run a data set of wholly unrealistic levels of healing power for 100 seconds, and compare healing done then (see "Convergence" in the spreadsheet). The Banner healing DOES begin to converge to Shout healing, but will never overtake it, even at 20000 Healing Power (yes, Twenty Thousand!). I performed this short analysis by using the equations for Shouts and Banners, and just substituting different values of HP, and multiplied the Banner equation by 100 (seconds) and the Shout equation by 17 (that's how many shouts in 100 seconds).
The chart in the sheet named "Convergence" shows the way in which Banners converge to Shouts. As you will see, the blue line on the graph is the ratio of Shout Healing to Banner Healing (for 3 shouts), and it shows that as HP approaches infinity 3x Shouts will always be ~9% more effective, they will never meet. However for the red line, this shows the ratio of 2x Shouts vs Banner healing, and it shows that at HP approaching Infinity, Banners will be ~23% more effective.
2x Shouts, or 3x Shouts?
This is a section i said I would add in for comparing 2 shouts to Banners. Refer again to the google spreadsheet and look at all the charts again. The new purple line represents Healing from using 2 shouts (FGJ and SIO). By referring to the "Convergence" sheet, you'll see the exponential curves again, this time I added a red line to represent a comparison of 2x shout healing to Banners. Note how the line is always below 100%, and converges at ~77%, this shows the theoretical convergence between using 2 shouts compared to Banners.
The main difference between using 3 shouts and 2 shouts (with Lung Capacity) is that with 2x Shouts, you ultimately use 5 less shouts across the 100 second period.
However, for achievable levels of HP, 3x shouts are roughly ~27% more effective than Banners, and Banners are roughly ~10.5% more effective than 2x Shouts. It is important to note that adding in that extra shout (OMM) every 24 seconds (totalling 5 extra shouts over 100 seconds), goes from a -11.33% to a 25.61% margin over the test period. You can draw whatever conclusions you like from this difference, but this highlights just how pivotal it is for a VS build to hinge upon 3 shouts as opposed to 2 for maximum effectiveness.
I'm sure some of you have probably seen exponential curves like this before, as such you know that it will continue until Infinity, and they will never be equal. However, this post has relied on one great generalization, the idea that this is level 80. Theoretically speaking, what if the level cap increases? I haven't done the maths on this just yet, but the Shout Healing constant of 1192 is woefully ambiguous, and needs to be properly broken down in to a factor of Level, and possibly a constant. Once I do that, i'll be able to discern if in light of a level cap increase in an expansion, if Banner and Shout Healing might be different.
The Effect of Healing Power on each method:
I originally theorized that Shouts benefited more from Healing Power than Banners do, I was challenged on this, however by comparing the numbers for HP=900 (Lung Capacity) at 100 seconds, Shouts have healed for 32504 Health, Banners have healed for 24488, the following formula allows bonus healing done as a result of healing power to be found:
(Total Healing – Base Healing)/Healing Power = Health Healed per point of Healing Power
Hence for Shouts: (32504-20264)/900= 13.6 Health per point of HP over 100 seconds.
And for Banners: (24488-(130*100))/900 = 12.76 Health per point of HP over 100 seconds.
Note: 13.6 and 12.76 are constants, and remain the same for all values of HP (but not constant with respect to Time).
The above equations show that Shouts benefit more from Healing Power than Banners do over a non-insignificant period of time, albeit not by much. I’ll explain this further. The formula above eliminates the effect of “Base Healing”, i.e. the healing you would receive from Shouts/Banners at 0 Healing Power, and so the difference between Base and Total is the Healing you have received solely from your Healing Power stat. Dividing this by Healing Power shows how much Health is gained per point of Healing Power.
Considering that 1672 is the relative Max Healing (or if it isn't, it's certainly very very close), at this level of HP, Shouts heal 26.77% more than Banners do. Despite the convergence I showed between them, at least at realistic levels of Healing power, this is the crucial numerical proof that Shouts heal more than Banners. Note however that I said Shouts heal more, not that they are universally better...
As a short justification for the method I chose to do this analysis I'd like to explain the idea of using 100 seconds in more depth. I chose to analyze the healing done over 100 seconds, because it is trivial to consider this as a transient case (i.e. the Healing over a fleeting period of time), since the numbers would be wildly skewed in favour of shouts. Whereas 100 seconds is easily enough time to encompass an entire Banner (they seem to stay down for ~90 seconds). Like most things, you need a period of time to fully establish a pattern, for example when you switch a radiator on, the room does not instantly heat up to the desired temperature, but it probably has done after 1 hour. So if by chance, Thermodynamics is your thing and you were analyzing how fast your room would heat up, you'd need to compare the heating rate from the minimum temperature, to the maximum in order to correctly reach a conclusion.
Finally, while I think i've satisfactorily proved that Shouts heal more than Banners (even in highly theoretical, stochastic and even wildly unrealistic conditions) I’ll end on a few subjective cases to compare and contrast the builds to one another, since there are characteristics outside of the Numerical side that can alter the effectiveness of each build:
- I’ll begin with the obvious, Banners are a gradual regeneration over time, some encounters don't see you taking devastating damage, there are plenty of cases where you might tank multiple weak mobs. Regeneration can actually allow you to not even drop health here. However with Shouts you would actually have to invoke your cooldowns... Regeneration can be seen as another "layer of defense" if you will.
- ...However on the flip side, when you get hit for 8k, there’s nothing like blowing your shouts and recovering most of that health right back.
- Shout Healing does benefit from two Master talents (although you may only use one at a time), whereas Banners have no such Healing augment.
- A lot of the counter-arguments I have encountered for Shouts not benefiting as much from HP as shouts do, is that people forget the “Triple Effect”, I’ve been over the fact that for VS to be viable you need to use FGJ, SIO, and OMM, so any Healing bonus you get on your shouts is effectively tripled.
- The results of 2x Shouts vs Banners showed that for high HP, Banners are more dominant. However at low HP, the healing effectiveness is almost identical.
- For VS to be viable you need all 3 Shouts, for Banners to be viable, you can basically get away with 1 Banner, with a few seconds of down-time before putting it back up.
- If by some miracle you had two Vigorous Shouts warriors, the healing provided by each would of course stack. But if you came across two Banner regeneration warriors, then sadly you wouldn't get any exponential benefit to healing, just a longer regeneration.
- Then again, 2 VS warriors are not great either, think of all the over-healing.
- The previous two points demonstrate how Banners and Shouts synergize perfectly, since neither build impinges on the method of healing of the other.
- Shouts can provide a lot of condition removal, in the sense that taking 6 Superior Soldier Runes cause your shouts to remove a condition from anyone under the effects (Shake it Off now removes 2!), which is ideal as a team-support mechanism.
- Banners provide nice buffs, Strength and Disc banners are a great DPS boost, but likewise Tactics and Defense are great for giving some extra defensive stats.
This post was generally to clarify that if you have Clerics Gear, don’t waste your talents on Banners, there are Greener Pastures for you if you run 3x Shouts. Just think about that magical Green Line on the chart showing the healing you get from running a VS Warrior alongside an IBS Warrior!
So now I leave you with this: I challenge anyone closed-minded enough to say Warriors cannot play support, here is the evidence, support your teammates!
Points to Add Later:
Compare the effectiveness of just FGJ+SIO vs Banner Healing.
- Consider the effect of a level cap increase.
Incorporate WvW elements (including FGJ+SIO+FM).
Edited by Sithicus Dias, 02 November 2012 - 07:08 PM.