Holy Drusera my head hurts just skimming through all this... but here it goes
Repost from this link here: http://medicatingnexus.com/2014/03/29/with-great-support-power-comes/
With Great (Support) Power Comes…
Posted on March 29, 2014
…around 0.5*Great more healing
In this post we are going to look at how three stats: Support Power, Crit Chance, and Crit Severity impact healing throughput. Note nothing we will say is really specific to healing, so if you mentally Ctrl-H (that’s Search & Replace for non-keyboard-shortcut types) Assault Power for Support Power and damage for healing, this could be a DPS post (blasphemy!).
Before diving in, let’s take a moment to discuss how we are going to make this comparison. When assessing the impact of a stat change on an ability, you can either look at the change in absolute terms (e.g., this heals for 150 more) or in percent terms (e.g., it heals for 2% more). I will be focusing on the latter, percent changes in healing, since we will see this allows one to make general comparisons without having to specify how often you are casting different abilities relative to one another, i.e., what a DPS would call a rotation.1
Suppose I currently have Crit Chance C, Crit Severity S, and Support Power, P. All healing abilities in WildStar have a base amount, B, which is proportional to your level, and scale with Support Power with a coefficient we will call M. The average healing done by the ability is:
With a little algebra (which I will spare you), we find that the percentage change in healing, ΔH/H, for a change in Crit Chance ΔC, or Crit Severity ΔS, or percentage change in Support Power ΔP, are:
The last equation depends on the ability’s base healing (B) and Support Power scaling (M) and therefore appears to be different for each ability. However, let’s suppose that for all abilities we are considering B/M is a constant, which we will denote X, and call the “Power Point” (and hope Microsoft doesn’t sue). With this assumption, the last equation simplifies to:
Now, it turns out that the WildStar Devs have designed the game so that, at Base (i.e., no Tiering), B/M is indeed a constant for (almost) all 30 abilities for a given class. The only exception to this rule across the 180 abilities is Engineer’s Shatter Impairment (for reasons unknown). Of course you need to substitute the appropriate “power” for the ability: Assault for Assault, Support for Support, and the average of Assault and Support for Utility. You can check all this yourself from the coefficients in the tooltips over at wildstar-base.2 What are the values of this mysterious Power Point? Well, I’ve done the arithmetic for you assuming a level 50 toon (this impacts the value of the Power Point, but even at lower levels the ratio B/M is the same across abilities):
Class Power Point (X)
Esper 2,668
Spellslinger 2,667
Medic 2,177
Stalker 2,176
Engineer 1,584
Warrior 1,583
What does this number mean? Looking back at the last formula above, we see that if our Support Power (P) is equal to the Power Point (X), then ΔH/H = ΔP/2, i.e., a given percentage change in Support Power is worth half as much in terms of percentage healing. So looking at the table above for your friendly neighborhood Medic, if your Support Power is exactly 2,177, then increasing your Support Power by 1% will increase your healing by 0.5%. If your Support Power is higher than 2,177, the percentage increase will be larger, if it’s lower than 2,177, it will be less. Note even as your Support Power approaches infinity (which, if they follow WoW is only a few expansions away), the percent increase in healing will always be somewhat lower than the percent change in Support Power.
There is a pattern in these Power Points: they are essentially the same within a given armor class and decrease as you go from Light to Medium to Heavy armor. I am guessing this is likely related to how stat budgets vary with armor class (e.g., for a given item level Light Armor has more Assault/Support power on average than Heavy Armor).
We can make some general observations from the structure of the formulas. Crit Chance and Crit Severity interact in a multiplicative way; so the more Crit Chance you have, the more beneficial Crit Severity is, and vice versa. Therefore these are two stats you generally want to keep “balanced”, i.e., it’s not the case that you want to always prioritize one over the other (at least ignoring crit-based procs and buffs). Support Power is a stat without diminishing returns, and since we are considering percentage changes, the more Support Power you have the more valuable a given percentage increase in Support Power is.
Now that we have some equations, we should do something practical with them. Suppose you decide to re-AMP at some point and are conflicted over whether to put Tier 1 points into Crit Chance, Crit Severity, or Support Power. Well, you can plug your current stats into the above formulas along with the values of the increments provided by the AMPs to decide what is the best AMP for you. For example, if you currently have 20% Crit, 175% Crit Severity, and 2,000 Support Power, then:
Crit Chance (ΔC = 2%) -> 2%*(175% – 1)/(1 + 20%*(175% – 1)) = 1.30%
Crit Severity (ΔS = 4%) -> 4%*20%/(1 + 20%*(175% – 1)) = 0.70%
Support Power (ΔP = 2.5%) -> 2.5%/(1 + 2,177/2,000) = 1.20%
and it’s clear that the +2% Crit Chance just edges out +2.5% Support Power for healing throughput.
Time for a few caveats:
- We are solely looking at the impact of these stats on throughput. But there are other considerations, such as abilities that are usable only after a crit (e.g., Dual Shock) or buffs that are applied on crit (e.g., the Armor Coating AMP), which might sway the balance in favor of crit. In addition, some abilities have secondary effects beyond the raw damage/healing they do.
- Crit has a bad reputation among healers because of the “OMG RNG” nature of critical heals. Although the math is true on average over the long run, it is possible to get a long string of non-critical heals at a critical moment of a fight that will make you wish that all those +Crit Severity runes you are sporting were +Support Power instead, no matter what the “optimal throughput” theorycrafting apparatchiks say.
- We’ve used the fact that the ratio of the baseline healing to the Support Power coefficient for an ability is the same across all abilities (within a class). But what about after you Tier them up? Tiering breaks this beautiful symmetry since it changes the Support Power coefficients differently for each ability, without impacting the base healing. Does that make all of this unravel? Technically, yes, but I think these formulas still provide useful general guidelines. To give you an example, let’s recompute the Power Points across all Medic Support abilities assuming each is Tier 8 (an impossible build, but we can dream can’t we?). Remember that untiered this number is 2,177 for all 10 abilities3:
Ability Tier 8 Power Point Impact of +2.5% SP
Emission 799 1.79%
Crisis Wave 1,335 1.50%
Shield Surge 1,333 1.50%
Mending Probes 1,229 1.55%
Flash 1,133 1.60%
Triage 1,381 1.48%
Barrier 1,719 1.34%
Rejuvenator 1,611 1.38%
Dual Shock 1,506 1.43%
Extricate 1,286 1.52%
The last column in the table gives the percentage increase in healing for the ability assuming the +2.5% Support Power AMP. Recall from above that in the untiered case this was 1.20% for all abilities. It has gone up (since tiering increases the Support Power coefficient), and is different for each ability, but excluding Emission it only varies by about +/- 9% from the average. Emission is a bit of an outlier; putting Tier points into Emission gives it more relative umph from Support Power than our other abilities. So tiering does break the symmetry, and bleeding-edge raiders will probably want to compute the ability-specific Power Points for their particular build, and then compute a weighted average of 1/(1 + X/P) across their abilities, using the weights from their rotation, to get an accurate sense of how much a given percentage change in Support Power is worth.
Note we’ve only touched on Crit Chance, Crit Severity, and Support Power. For healers, there is another “throughput” stat: Cooldown Reduction, which can also be increased by Tier 1 AMPs. This one is more complicated to analyze because it obviously does no good for abilities without a cooldown, which include our primary builder (Emission) and our big spenders (Crisis Wave and Shield Surge). However, it can have a large impact on the Sustained HPS4 of our cooldown abilities. As an example, for a level 50 toon with 2,000 Support Power, we saw above that the +2.5% Support Power AMP was worth 1.2% in healing, and hence also 1.2% in Sustained HPS. The 5% Cooldown Reduction AMP is worth 0% in healing, but a whopping 5.3% increase in Sustained HPS for all abilities with a cooldown (and 0% of course on those without). Which is better? It depends on how much of your healing comes from non-cooldown abilities vs cooldowns. Another important thing to remember when comparing a healing amount increase (e.g., from Support Power) to a healing rate increase (e.g., from Cooldown Reduction) is that the former will make you more Focus efficient, while the latter will make you burn Focus faster.
TL;DR:
- The following formulas can be used to calculate the percentage increase in healing throughput from a given percentage change in Crit Chance (ΔC), Crit Severity (ΔS), and Support Power (ΔP):
where C, S, P are your current Crit Chance, Crit Severity and Support Power, respectively, and X is the “Power Point” for your class, which is in the first table above.
- The more Crit Chance you have, the more valuable Crit Severity is, and vice versa.
- The more Support Power you have, the more valuable a given percentage increase in Support Power is.
———-
1 In healing, there is never really a rotation since the “optimal” sequence of things to cast depends on a lot more factors (how much healing is needed, how much time is there to get that healing done, what are other healers about to do, where is my Focus, etc.). My DPS friends will be quick to point out that they need to vary their rotation depending on factors as well (such as single- vs multi-target or stationary vs mobile), but DPS still typically have a handful of rotations where healing is more varied.
2 There are small variations in the value of X within a class, but I am assuming this is due to the limited number of significant digits we are given for B and M. Note also you will find from wildstar-base that there are much bigger variations for a few abilities (such as Medic’s Rejuvenator and Dematerialize, Warrior’s Augmented Blade and Plasma Blast, Esper’s Psychic Frenzy, Restraint, Spectral Swarm, and Reap) which are due to wildstar-base having incorrect coefficients. The correct coefficients can be found in the patch notes or via in-game testing (always the last word!).
3 These values do not include Support Power coefficient changes from Major Tier Upgrades.
4 Sustained HPS = Healing Per Second assuming the ability is cast every time it is off cooldown.
Repost from this link here: http://medicatingnexus.com/2014/03/29/with-great-support-power-comes/
With Great (Support) Power Comes…
Posted on March 29, 2014
…around 0.5*Great more healing
In this post we are going to look at how three stats: Support Power, Crit Chance, and Crit Severity impact healing throughput. Note nothing we will say is really specific to healing, so if you mentally Ctrl-H (that’s Search & Replace for non-keyboard-shortcut types) Assault Power for Support Power and damage for healing, this could be a DPS post (blasphemy!).
Before diving in, let’s take a moment to discuss how we are going to make this comparison. When assessing the impact of a stat change on an ability, you can either look at the change in absolute terms (e.g., this heals for 150 more) or in percent terms (e.g., it heals for 2% more). I will be focusing on the latter, percent changes in healing, since we will see this allows one to make general comparisons without having to specify how often you are casting different abilities relative to one another, i.e., what a DPS would call a rotation.1
Suppose I currently have Crit Chance C, Crit Severity S, and Support Power, P. All healing abilities in WildStar have a base amount, B, which is proportional to your level, and scale with Support Power with a coefficient we will call M. The average healing done by the ability is:
With a little algebra (which I will spare you), we find that the percentage change in healing, ΔH/H, for a change in Crit Chance ΔC, or Crit Severity ΔS, or percentage change in Support Power ΔP, are:
The last equation depends on the ability’s base healing (B) and Support Power scaling (M) and therefore appears to be different for each ability. However, let’s suppose that for all abilities we are considering B/M is a constant, which we will denote X, and call the “Power Point” (and hope Microsoft doesn’t sue). With this assumption, the last equation simplifies to:
Now, it turns out that the WildStar Devs have designed the game so that, at Base (i.e., no Tiering), B/M is indeed a constant for (almost) all 30 abilities for a given class. The only exception to this rule across the 180 abilities is Engineer’s Shatter Impairment (for reasons unknown). Of course you need to substitute the appropriate “power” for the ability: Assault for Assault, Support for Support, and the average of Assault and Support for Utility. You can check all this yourself from the coefficients in the tooltips over at wildstar-base.2 What are the values of this mysterious Power Point? Well, I’ve done the arithmetic for you assuming a level 50 toon (this impacts the value of the Power Point, but even at lower levels the ratio B/M is the same across abilities):
Class Power Point (X)
Esper 2,668
Spellslinger 2,667
Medic 2,177
Stalker 2,176
Engineer 1,584
Warrior 1,583
What does this number mean? Looking back at the last formula above, we see that if our Support Power (P) is equal to the Power Point (X), then ΔH/H = ΔP/2, i.e., a given percentage change in Support Power is worth half as much in terms of percentage healing. So looking at the table above for your friendly neighborhood Medic, if your Support Power is exactly 2,177, then increasing your Support Power by 1% will increase your healing by 0.5%. If your Support Power is higher than 2,177, the percentage increase will be larger, if it’s lower than 2,177, it will be less. Note even as your Support Power approaches infinity (which, if they follow WoW is only a few expansions away), the percent increase in healing will always be somewhat lower than the percent change in Support Power.
There is a pattern in these Power Points: they are essentially the same within a given armor class and decrease as you go from Light to Medium to Heavy armor. I am guessing this is likely related to how stat budgets vary with armor class (e.g., for a given item level Light Armor has more Assault/Support power on average than Heavy Armor).
We can make some general observations from the structure of the formulas. Crit Chance and Crit Severity interact in a multiplicative way; so the more Crit Chance you have, the more beneficial Crit Severity is, and vice versa. Therefore these are two stats you generally want to keep “balanced”, i.e., it’s not the case that you want to always prioritize one over the other (at least ignoring crit-based procs and buffs). Support Power is a stat without diminishing returns, and since we are considering percentage changes, the more Support Power you have the more valuable a given percentage increase in Support Power is.
Now that we have some equations, we should do something practical with them. Suppose you decide to re-AMP at some point and are conflicted over whether to put Tier 1 points into Crit Chance, Crit Severity, or Support Power. Well, you can plug your current stats into the above formulas along with the values of the increments provided by the AMPs to decide what is the best AMP for you. For example, if you currently have 20% Crit, 175% Crit Severity, and 2,000 Support Power, then:
Crit Chance (ΔC = 2%) -> 2%*(175% – 1)/(1 + 20%*(175% – 1)) = 1.30%
Crit Severity (ΔS = 4%) -> 4%*20%/(1 + 20%*(175% – 1)) = 0.70%
Support Power (ΔP = 2.5%) -> 2.5%/(1 + 2,177/2,000) = 1.20%
and it’s clear that the +2% Crit Chance just edges out +2.5% Support Power for healing throughput.
Time for a few caveats:
- We are solely looking at the impact of these stats on throughput. But there are other considerations, such as abilities that are usable only after a crit (e.g., Dual Shock) or buffs that are applied on crit (e.g., the Armor Coating AMP), which might sway the balance in favor of crit. In addition, some abilities have secondary effects beyond the raw damage/healing they do.
- Crit has a bad reputation among healers because of the “OMG RNG” nature of critical heals. Although the math is true on average over the long run, it is possible to get a long string of non-critical heals at a critical moment of a fight that will make you wish that all those +Crit Severity runes you are sporting were +Support Power instead, no matter what the “optimal throughput” theorycrafting apparatchiks say.
- We’ve used the fact that the ratio of the baseline healing to the Support Power coefficient for an ability is the same across all abilities (within a class). But what about after you Tier them up? Tiering breaks this beautiful symmetry since it changes the Support Power coefficients differently for each ability, without impacting the base healing. Does that make all of this unravel? Technically, yes, but I think these formulas still provide useful general guidelines. To give you an example, let’s recompute the Power Points across all Medic Support abilities assuming each is Tier 8 (an impossible build, but we can dream can’t we?). Remember that untiered this number is 2,177 for all 10 abilities3:
Ability Tier 8 Power Point Impact of +2.5% SP
Emission 799 1.79%
Crisis Wave 1,335 1.50%
Shield Surge 1,333 1.50%
Mending Probes 1,229 1.55%
Flash 1,133 1.60%
Triage 1,381 1.48%
Barrier 1,719 1.34%
Rejuvenator 1,611 1.38%
Dual Shock 1,506 1.43%
Extricate 1,286 1.52%
The last column in the table gives the percentage increase in healing for the ability assuming the +2.5% Support Power AMP. Recall from above that in the untiered case this was 1.20% for all abilities. It has gone up (since tiering increases the Support Power coefficient), and is different for each ability, but excluding Emission it only varies by about +/- 9% from the average. Emission is a bit of an outlier; putting Tier points into Emission gives it more relative umph from Support Power than our other abilities. So tiering does break the symmetry, and bleeding-edge raiders will probably want to compute the ability-specific Power Points for their particular build, and then compute a weighted average of 1/(1 + X/P) across their abilities, using the weights from their rotation, to get an accurate sense of how much a given percentage change in Support Power is worth.
Note we’ve only touched on Crit Chance, Crit Severity, and Support Power. For healers, there is another “throughput” stat: Cooldown Reduction, which can also be increased by Tier 1 AMPs. This one is more complicated to analyze because it obviously does no good for abilities without a cooldown, which include our primary builder (Emission) and our big spenders (Crisis Wave and Shield Surge). However, it can have a large impact on the Sustained HPS4 of our cooldown abilities. As an example, for a level 50 toon with 2,000 Support Power, we saw above that the +2.5% Support Power AMP was worth 1.2% in healing, and hence also 1.2% in Sustained HPS. The 5% Cooldown Reduction AMP is worth 0% in healing, but a whopping 5.3% increase in Sustained HPS for all abilities with a cooldown (and 0% of course on those without). Which is better? It depends on how much of your healing comes from non-cooldown abilities vs cooldowns. Another important thing to remember when comparing a healing amount increase (e.g., from Support Power) to a healing rate increase (e.g., from Cooldown Reduction) is that the former will make you more Focus efficient, while the latter will make you burn Focus faster.
TL;DR:
- The following formulas can be used to calculate the percentage increase in healing throughput from a given percentage change in Crit Chance (ΔC), Crit Severity (ΔS), and Support Power (ΔP):
where C, S, P are your current Crit Chance, Crit Severity and Support Power, respectively, and X is the “Power Point” for your class, which is in the first table above.
- The more Crit Chance you have, the more valuable Crit Severity is, and vice versa.
- The more Support Power you have, the more valuable a given percentage increase in Support Power is.
———-
1 In healing, there is never really a rotation since the “optimal” sequence of things to cast depends on a lot more factors (how much healing is needed, how much time is there to get that healing done, what are other healers about to do, where is my Focus, etc.). My DPS friends will be quick to point out that they need to vary their rotation depending on factors as well (such as single- vs multi-target or stationary vs mobile), but DPS still typically have a handful of rotations where healing is more varied.
2 There are small variations in the value of X within a class, but I am assuming this is due to the limited number of significant digits we are given for B and M. Note also you will find from wildstar-base that there are much bigger variations for a few abilities (such as Medic’s Rejuvenator and Dematerialize, Warrior’s Augmented Blade and Plasma Blast, Esper’s Psychic Frenzy, Restraint, Spectral Swarm, and Reap) which are due to wildstar-base having incorrect coefficients. The correct coefficients can be found in the patch notes or via in-game testing (always the last word!).
3 These values do not include Support Power coefficient changes from Major Tier Upgrades.
4 Sustained HPS = Healing Per Second assuming the ability is cast every time it is off cooldown.