Guild Wars 2

Hey all, while we’re on the discussion of high-power builds and toughness feeling relatively pointless, it seems as though Toughness has an innate flaw with the way damage is calculated, in that due to diminishing returns, it becomes significantly weaker point-over-point when compared to power, which against a steady armor foe will gain a linear boost to potency.

Obviously, this isn’t an issue when the number’s are similar, as any number divided by itself is 1, so 2300 power versus 2300 armor will be the same as 2000 power versus 2000 armor.

However, each point gained in power is not affected by diminishing returns against a steady armor foe, where as increased armor loses value at a significant rate per point over a foes power stat. This issue is amplified by precision and ferocity, as these gains can be increased, where toughness is a stand-alone stat.

Is there a way to fix this without making toughness too potent, but making is a viable stat choice that isn’t subjected to such harsh diminishing returns?

Napkin math:
Based on a standard “1000” weapon damage (WD x Power / armor)
Assume 1.0 attack Coefficient (for ease of math)

OP = Over Previous
TOB = Total Over Base
AOB = Added Over Base (per step)

1. = Numerical difference per variable change.

2300 Power OP TOB AOB # Reduction added
1150 – 2000a
958 – 2400a -16% -16% 16% gain. 192 damage reduction.
821 – 2800a -14% -29% 13% gain. 137 damage reduction.
719 – 3200a -12% -37% 8% gain. 102 damage reduction.
639 – 3600a -11% -44% 7% gain. 80 damage reduction.

2300 armor.

869 – 2000 OP TOB AOB # Boost added
1043 – 2400p 20% 20% 20% gain. 174 damage gained.
1217 – 2800p 17% 40% 20% gain. 174 damage gained.
1391 – 3200p 14% 60% 20% gain. 174 damage gained. (3200 power isn’t really feasible, just shown for pattern recognition)

ronpierces’s point is that while power’s effectiveness increases linearly, the effectiveness of toughness decreases exponentially, albeit with an exponent of -1.

I’ve attached 2 graphs which complement ronpierce’s napkin math to aid the discussion. The first graph (blue line) shows the damage reduction (on the Y axis) as a function of toughness (on the X axis), where the damage reduction is scaled from 1800 toughness so that the damage at 1800 toughness=1, and higher toughness values decrease the damage fraction (0.5=half damage).

The bottom graph shows the same results but plotted in a slightly different way. This graph (red line) shows the damage reduction in percent as a function of increasing 100 toughness. For example, increasing your toughness from 2000 to 2100 decreases your incoming damage by ~4.3%, and increasing your toughness from 2600 to 2700 decreases your incoming damage by ~2.5%.

It is important to note that because the damage reductions in these graphs are shown as a percentage, they are wholly independent of the power, weapon damage, or damage coefficient. One way to increase the effectiveness of toughness (i.e., to increase the negative slope of the blue line) would be to increase the toughness exponent. For example, making the toughness exponent -1.2 instead of the current -1.0 would allow toughness to scale more effectively. This would, however, need to be compensated: damage across the board would go down, so either weapon coefficients or power would have to be increased by some factor.

Salamander.2504:

ronpierces’s point is that while power’s effectiveness increases linearly, the effectiveness of toughness decreases exponentially, albeit with an exponent of -1.

Actually a function of the from x^-1 (which is the case for armor/toughness) doesnt decrease exponentially. A exponential decay would be something like a^-x (see https://en.wikipedia.org/wiki/Exponential_decay). So while the decrease in effectiveness (diminishing returns) is there it is not as bad as exponential decay…

Sorry i couldnt resist…

Perhaps this design choice is due to how healing scales with toughness and vitality? xD… Just kidding, I have absolutely no idea what I’m talking about.

IDK how to fix it, but I agree. Investing in toughness isn’t rewarding.

Been a problem since launch that has gone completely awry with the latest +30% stats to amulets.

Best part is power creep in other areas like traits are also tipped heavily to the offensive side, diminishings toughnesses effectiveness even more.

OP needs a math lesson.

Yes, the damage reduction from Toughness decreases with each successive stat point i.e. it has diminishing returns. However, the increase in time-to-die is linear. Each successive point of Toughness will increase how much total damage it takes to kill you by the same amount.

Using the formulas:

Damage = (weapon * power * coeff ) / Toughness
TimeToDie = HitPoints / Damage

If weapon, power, and coeff are constant, then only toughness is variable and increases as:

Damage = 1 / Toughness

Plug that into the other equation and you get:

TimeToDie = HitPoints / (1 / Toughness) = Hitpoints * Toughness

That’s a linear increase.

Exedore.6320:

OP needs a math lesson.

Yes, the damage reduction from Toughness decreases with each successive stat point i.e. it has diminishing returns. However, the increase in time-to-die is linear. Each successive point of Toughness will increase how much total damage it takes to kill you by the same amount.

Using the formulas:

Damage = (weapon * power * coeff ) / Toughness
TimeToDie = HitPoints / Damage

If weapon, power, and coeff are constant, then only toughness is variable and increases as:

Damage = 1 / Toughness

Plug that into the other equation and you get:

TimeToDie = HitPoints / (1 / Toughness) = Hitpoints * Toughness

That’s a linear increase.

The math can be extended in terms of Feeocity, precision (which is something I didn’t feel like delving into the math for),
That’s true in terms of seconds shaved/added, but also (and I didn’t feel like delving this deep into the math), it doesn’t consider Precision and Ferocity which clearly throws off that 1:1 ratio, and doesn’t take into consideration of value of seconds shaved. For instance, 5 seconds off of a 10 second TTK is more valuable than 5 seconds gained, which goes a bit beyond basic math when taking into consideration reaction time and rebound-ability. Things I touched on in the original topic but didn’t go through the math for. Feel free of you want, but definitely not worth the effort, considering it’s not likely to change anyways.

The Math above only takes into consideration the ratio of benefits of power-thoroughness, but like I said, the benefits get pretty skewed with added benefits to damage.

ronpierce.2760:

Exedore.6320:

OP needs a math lesson.

Yes, the damage reduction from Toughness decreases with each successive stat point i.e. it has diminishing returns. However, the increase in time-to-die is linear. Each successive point of Toughness will increase how much total damage it takes to kill you by the same amount.

Using the formulas:

Damage = (weapon * power * coeff ) / Toughness
TimeToDie = HitPoints / Damage

If weapon, power, and coeff are constant, then only toughness is variable and increases as:

Damage = 1 / Toughness

Plug that into the other equation and you get:

TimeToDie = HitPoints / (1 / Toughness) = Hitpoints * Toughness

That’s a linear increase.

The math can be extended in terms of Feeocity, precision (which is something I didn’t feel like delving into the math for),

Well if you extend the math in terms of Ferosity and precision, shouldnt you also include stats like vitality and healing power (which will actually make the math ugly because its effectiveness depends on the skills you take etc.). After all those states also would increase the TimetoDie. Also keep in mind to keep the calculation fair we would have to assume that the sum of every stat distribution is equal (which in reality isnt, compare cele vs zerker etc.)

I think if we include every relevant stat the math becomes ugly rather quickly…

So just to clarify things:

Toughness doesn’t have diminishing returns in terms of your effective HP (i.e. how much damage you can take before dying), which is what really matters. So we can disregard the OP’s math.

But OP’s overall point still has merit, which is that the power stat works with precision & ferocity to increase your damage more significantly than toughness, vit, and healing power work to mitigate it, so that overall TTK in this game is fairly low. I’m personally OK with a fast-paced, bursty meta, but I can understand that other people feel differently.

Muchacho.2390:

ronpierce.2760:

Exedore.6320:

OP needs a math lesson.

Yes, the damage reduction from Toughness decreases with each successive stat point i.e. it has diminishing returns. However, the increase in time-to-die is linear. Each successive point of Toughness will increase how much total damage it takes to kill you by the same amount.

Using the formulas:

Damage = (weapon * power * coeff ) / Toughness
TimeToDie = HitPoints / Damage

If weapon, power, and coeff are constant, then only toughness is variable and increases as:

Damage = 1 / Toughness

Plug that into the other equation and you get:

TimeToDie = HitPoints / (1 / Toughness) = Hitpoints * Toughness

That’s a linear increase.

The math can be extended in terms of Feeocity, precision (which is something I didn’t feel like delving into the math for),

Well if you extend the math in terms of Ferosity and precision, shouldnt you also include stats like vitality and healing power (which will actually make the math ugly because its effectiveness depends on the skills you take etc.). After all those states also would increase the TimetoDie. Also keep in mind to keep the calculation fair we would have to assume that the sum of every stat distribution is equal (which in reality isnt, compare cele vs zerker etc.)

I think if we include every relevant stat the math becomes ugly rather quickly…

The difference between defensive stats and offensive ones is how they work together. Healing power and vitality, for example have additive benefits together where power, precision and Ferocity multiply together.

ronpierce.2760:

Muchacho.2390:

ronpierce.2760:

Exedore.6320:

OP needs a math lesson.

Yes, the damage reduction from Toughness decreases with each successive stat point i.e. it has diminishing returns. However, the increase in time-to-die is linear. Each successive point of Toughness will increase how much total damage it takes to kill you by the same amount.

Using the formulas:

Damage = (weapon * power * coeff ) / Toughness
TimeToDie = HitPoints / Damage

If weapon, power, and coeff are constant, then only toughness is variable and increases as:

Damage = 1 / Toughness

Plug that into the other equation and you get:

TimeToDie = HitPoints / (1 / Toughness) = Hitpoints * Toughness

That’s a linear increase.

The math can be extended in terms of Feeocity, precision (which is something I didn’t feel like delving into the math for),

Well if you extend the math in terms of Ferosity and precision, shouldnt you also include stats like vitality and healing power (which will actually make the math ugly because its effectiveness depends on the skills you take etc.). After all those states also would increase the TimetoDie. Also keep in mind to keep the calculation fair we would have to assume that the sum of every stat distribution is equal (which in reality isnt, compare cele vs zerker etc.)

I think if we include every relevant stat the math becomes ugly rather quickly…

The difference between defensive stats and offensive ones is how they work together. Healing power and vitality, for example have additive benefits together where power, precision and Ferocity multiply together.

True they work differently together. But i think the math for defensive stats (especially with healing power) is more complicated then you make it be.

So i am not sure if we just can say (power, precision, ferosity)>(toughness ,vitality, healingpower) yet. But feel free to show me the math on it (which i am sure is rather ugly).

ronpierce.2760:

Muchacho.2390:

ronpierce.2760:

Exedore.6320:

OP needs a math lesson.

Yes, the damage reduction from Toughness decreases with each successive stat point i.e. it has diminishing returns. However, the increase in time-to-die is linear. Each successive point of Toughness will increase how much total damage it takes to kill you by the same amount.

Using the formulas:

Damage = (weapon * power * coeff ) / Toughness
TimeToDie = HitPoints / Damage

If weapon, power, and coeff are constant, then only toughness is variable and increases as:

Damage = 1 / Toughness

Plug that into the other equation and you get:

TimeToDie = HitPoints / (1 / Toughness) = Hitpoints * Toughness

That’s a linear increase.

The math can be extended in terms of Feeocity, precision (which is something I didn’t feel like delving into the math for),

Well if you extend the math in terms of Ferosity and precision, shouldnt you also include stats like vitality and healing power (which will actually make the math ugly because its effectiveness depends on the skills you take etc.). After all those states also would increase the TimetoDie. Also keep in mind to keep the calculation fair we would have to assume that the sum of every stat distribution is equal (which in reality isnt, compare cele vs zerker etc.)

I think if we include every relevant stat the math becomes ugly rather quickly…

The difference between defensive stats and offensive ones is how they work together. Healing power and vitality, for example have additive benefits together where power, precision and Ferocity multiply together.

Healing power and vitality are NOT additive to toughness. The amount of effective HP you get per point of vitality increases as you increase your toughness.

To use a simple example, if one guy takes 50 damage per hit, then giving him an extra 100 hp would let him take two more hits. If another guy with higher toughness only takes 5 damage per hit, then giving him that same amount of extra hp would let him take 20 more hits. The same rationale applies to healing power.

Precision also isn’t really a bonus. It’s more accurate to think of precision as a limitation on ferocity. Ferocity affects your crit damage, and precision determines how frequently you crit. In other words, precision determines how frequently your damage is multiplied by your ferocity. The highest you can go is 100% crit chance, meaning that your ferocity applies with every attack. Going any higher than 100% crit chance doesn’t increase your damage.

You’re trying to explain the low time-to-kill in this game through math, but you’re focusing on the wrong variables. You should instead be looking at either the damage/healing coefficients on skills, the stat distribution on amulets, or the ratio at which points of precision are converted into additional crit chance, or ferocity to crit damage.

ResJudicator.7916:

ronpierce.2760:

Muchacho.2390:

ronpierce.2760:

Exedore.6320:

OP needs a math lesson.

Yes, the damage reduction from Toughness decreases with each successive stat point i.e. it has diminishing returns. However, the increase in time-to-die is linear. Each successive point of Toughness will increase how much total damage it takes to kill you by the same amount.

Using the formulas:

Damage = (weapon * power * coeff ) / Toughness
TimeToDie = HitPoints / Damage

If weapon, power, and coeff are constant, then only toughness is variable and increases as:

Damage = 1 / Toughness

Plug that into the other equation and you get:

TimeToDie = HitPoints / (1 / Toughness) = Hitpoints * Toughness

That’s a linear increase.

The math can be extended in terms of Feeocity, precision (which is something I didn’t feel like delving into the math for),

Well if you extend the math in terms of Ferosity and precision, shouldnt you also include stats like vitality and healing power (which will actually make the math ugly because its effectiveness depends on the skills you take etc.). After all those states also would increase the TimetoDie. Also keep in mind to keep the calculation fair we would have to assume that the sum of every stat distribution is equal (which in reality isnt, compare cele vs zerker etc.)

I think if we include every relevant stat the math becomes ugly rather quickly…

The difference between defensive stats and offensive ones is how they work together. Healing power and vitality, for example have additive benefits together where power, precision and Ferocity multiply together.

Healing power and vitality are NOT additive to toughness. The amount of effective HP you get per point of vitality increases as you increase your toughness. To use a simple example, if one guy takes 50 damage per hit, then gaining +100 hp would let him take two more hits. If another guy with higher toughness only takes 5 damage per hit, then gaining that exact same amount of HP would let him take 20 more hits. The same rationale applies to healing power.

Precision also isn’t really a bonus. It’s more accurate to think of precision as a limitation on ferocity. Ferocity affects your crit damage, and precision determines how frequently you crit. In other words, precision determines how frequently your damage is multiplied by your ferocity. The highest you can go is 100% crit chance, meaning that your ferocity applies with every attack. Going any higher than 100% crit chance doesn’t increase your damage.

You’re trying to explain the low time-to-kill in this game through math, but you’re focusing on the wrong variables. You should instead be looking at either the damage/healing coefficients on skills, the stat distribution on amulets, or the ratio at which points of precision are converted into additional crit chance, or ferocity to crit damage.

I said together, not to toughness. Each Power-based stat benefits the other, much more than defensive stats do. Regardless, the proof is in the game. 3600 toughness 19000 HP, you can still die in about 3-4 seconds given a properly set up burst. Going for damage (specifically burst) is far superior than alternative methods, except for cases where the base-build cannot survive long enough to support playing Burst. Burst damage being so high (which may be the bigger issue than toughness, to be completely honest) is causing an issue where defensive stats are less important, and Blocks/Blinds/Evades are greatly increased in value, which don’t scale, and thus are equally potent on high-damage builds. Overall, you will find Burst + secondary defenses greatly outweigh actual defensive stats, where you can not as easily make up for lacking damage through secondary effects, like you can for defenses.

Healing power would synergize better with other stats if this game had critical healing like other games do.

ronpierce.2760:

Burst damage being so high (which may be the bigger issue than toughness, to be completely honest) is causing an issue where defensive stats are less important, and Blocks/Blinds/Evades are greatly increased in value, which don’t scale, and thus are equally potent on high-damage builds. Overall, you will find Burst + secondary defenses greatly outweigh actual defensive stats, where you can not as easily make up for lacking damage through secondary effects, like you can for defenses.

That part I agree with: active defenses are generally far more important than passive ones. I’m not sure that’s a bad thing, though. Speaking, personally, it makes the game more exciting.

There was a period back before the celestial meta where burst damage was so low that people didn’t even bother running DPS builds in tournaments. Instead, they ran CC classes that could knock a bunker off the point long enough to get a decap. Tournaments would usually end via time-out, with the winning team having something like 130 total points. There’d be one teamfight in mid that never went anywhere, and the game would be decided based on who’s decap engies did a better jot at far.

Also, just to be clear, it isn’t really accurate to say that precision and ferocity scale together. It’s more accurate to say that precision sets the boundaries in which ferocity benefits your damage. The most benefit you can get is 100% of your ferocity being converted to damage (if you have 100% crit chance). And a theoretical 0% crit chance would mean that ferocity wouldn’t affect your DPS at all.

On Toughness and Diminishing Returns:

As I showed before, Toughness itself does not have diminishing returns as a whole; only the damage reduction portion. However, it does have diminishing effectiveness relative to other stats. After a point, you get more effective HP from adding vitality than adding toughness. To make a character more survivable overall, you want both toughness and vitality, and possibly some healing power.

However, you can’t do this in PvP. The PvP stat system needs fixed. Other than a couple combinations, you either get far too much Toughness and no vitality or excessive vitality with no Toughness. The other possibility is both, but with limited offensive power (no precision or not enough power).

So the crux of the problem is really the PvP stat system. Power builds ideally want 5-6 stats (power, precision, ferocity, toughness, vitality, and maybe healing power) in different quantities. ANet needs to split the PvP amulet into multiple items and allow players to mix-and-match like they can in PvE/WvW.

Exedore.6320:

On Toughness and Diminishing Returns:

As I showed before, Toughness itself does not have diminishing returns as a whole; only the damage reduction portion. However, it does have diminishing effectiveness relative to other stats. After a point, you get more effective HP from adding vitality than adding toughness. To make a character more survivable overall, you want both toughness and vitality, and possibly some healing power.

Well Power is the same. After a point, you get more effective damage inceasing your precision or ferocity (or both) than power.

One can consider those two opposite stats : effective damage and effective HP. The division of the two giving you the time to kill someone.

Effective Damage increases linearly when you increase power, precision (up to 100% crit chance cap) and ferocity. Yes, all those three stats have linear returns on effective damage. But of course the three combined together give us something different. Roughly, effective damage = O(power*precision*ferocity)

Effective HP is much more difficult to work with, because of healing. If we assume say that each player can and will use a single healing skill in a fight and nothing else, effective HP is = O(toughness*vitality*healing)

Which is the same as damage :p

BUT, something to consider which is rather hard to put in maths is : the longer you live, the more times healing power is applied to your survivability. Each extra second of life can mean an extra tick of regen. Every 20s of survival means one more cast of your 20s cooldown heal.

In that sense, effective HP scales MUCH faster from healing power than toughness*vitality*healing. When you get enough HP and toughness that you can cast one extra heal before you die, you get that much closer to casting yet another heal. Up to a point where you can outheal the damage received. Which means you’ve reached a point where you have infinite effective HP. Something that can only be reached through a scale like O(thoughness^healing power) or something absurd like that.

This risk of infinite effective HP and the explosive nature of the scaling of that through the synergy between toughness and healing power is the reason why healing power has such a tiny contribution to heals.

All that is why you cannot really compare the scaling of damage and survivability : because the game is trying to walk a thin line between “impossible to survive” and “impossible to kill” and that any slight increase on one side or another can send you straight into an extreme.

In order to prevent living forever, total stats have a cap, ANet hasn’t put nomad into PvP (and probably won’t), and has limited the coefficients on healing power to the point where it’s only useful to a handful of builds. The first one is the most important.

However, this is getting off the original topic. The problem the OP is seeing is that you need the multiplicative effect of having both Toughness and Vitality (and healing power) to compete with Power, Precision, and Ferocity. Toughness alone stacked to large amounts just isn’t as good.