The MATH of the Quickness change

The MATH of the Quickness change

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Posted by: phantomFury.9168

phantomFury.9168

TLDR: The Quickness change means a 25% reduction in damage per second during Quickness, but only a 6.25% reduction in damage over the duration, given the increase in duration. No where near the many comments that I’ve seen that state ‘this change cuts my damage/DPS in half

I’ve seen a lot of comments regarding the impact of the change to Quickness, and how it affects damage output. I’ve seen it said numerous times, roughly paraphrased, that the reduction in speed (from 100% increase to 50% increase) will mean the damage/DPS will be cut in half. I think this is being a bit dramatic, and to that point, let’s do some math to clear the air. I am curious other people’s opinion on this is.

Assume current DPS (and I literally mean damage per second) is P:

  • The DPS with the old quickness (double attack speed) is: 2 * P
  • The DPS with the new quickness (50% attack speed) is 1.5 * P

So, to determine the DPS nerf, the old quickness must be multiplied by some factor, r:

  • 2P * r = 1.5P
  • 2 * r = 1.5
  • r = 1.5 / 2
  • r = .75

So, to determine the reduction in damage, we subtract r (.75) from 1:

  • 1 – .75 = .25

Multiple by 100 to get a percentage… 25%. So, algebra just proved that the change to Quickness, at a simplistic math level means, on average, a 25% reduction in your DPS during quickness. I will fully admit that a 25% reduction in DPS is nothing to sneeze at, but saying ‘it cuts damage/DPS in half’ exaggerates the damage impact twice what it actually is.

Next consider that the duration was increased. So, let’s now look at too elements of this, closely related.
1. The amount of skills that can be executed during Quickness
2. The damage (not DPS) done during Quickness

For the first, consider this:

  • Duration of Ranger’s old QZ = 4s
  • Skill speed was twice as fact, i.e., a factor of 2
  • 4s * 2 = 8s
    Ergo, QZ allowed a Ranger to execute 8 seconds worth of skills in 4 seconds.

For the new Quickness:

  • Duration of Ranger’s new QZ = 5s
  • Skill speed is 50% faster, i.e., a factor of 1.5
  • 5s * 1.5 = 7.5s
    Ergo, QZ allows a Ranger to execute 7.5 seconds worth of skills in 5 seconds.

So, using the same approach:

  • 8s * r = 7.5s
  • 8 * r = 7.5
  • r = 7.5 / 8
  • r = .9375
  • 1 – .9375 = .0625
  • .625 * 100 = 6.25%

In essence, the amount of skills that can be executed during the duration of Quickness has been reduced by 6.25%. Do the math related to the damage done during the duration of Quickness, and the same reduction applies; the new Quickness will see a 6.25% reduction in damage dealt over the duration compared to the old Quickness. I will re-acknowledge that the damage per second was reduced by 25% and this is certainly not insignificant, but let’s not blow things out of proportion.

(edited by phantomFury.9168)

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Posted by: Dojo.1867

Dojo.1867

Very good post but I think your effort will be wasted on the ranger community at this point. All they wanna hear right now is how ranger got destroyed and has become unplayable etc.

A thing to consider is that quickness not always gives a straight 50% (before patch 100%) animation speed buff. It depends on the weapons and their animations (for shortbow autoattack it was less for example). However this doesn’t change the fact that the before – after difference is much smaller than people make it.

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Posted by: Chopps.5047

Chopps.5047

It’s not wasted on me, Dojo. Forget those guys, they need practice. They are not like water, they do not flow and they do not crash, if I may quote my favorite karate master. PhantomFury, thanks for showing the math.

Tin Foil Hat Hearer »—> Ranger Extraordinaire »—> “Be like water…”

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Posted by: saurus.8290

saurus.8290

maybe lets talk about that when you have quickness on healings doesnt works?

increasing the time of quickness just make you die faster

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Posted by: ahurtcorncob.7652

ahurtcorncob.7652

You need equivalent time frames don’t you? You can’t compare the number of actions performed over 4 seconds with the number of actions over 5 seconds.

In 5 seconds with the old quickness you’d get 4 seconds of doubled speed, and 1 second of regular speed compared to 5 seconds of 1.5x speed. If you compare that then r=7.5/9, which is a 17% drop.

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Posted by: jubskie.3152

jubskie.3152

It’s too early for me to understand your math, but I like non-QQ posts I’ll just take your word for it that its only a 6.25% DPS loss :P

Also, can you post on the effectiveness of Zephyr’s Speed? (The 5 BM trait)

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Posted by: Gingelyr.3648

Gingelyr.3648

ahurtcorncob’s comment is exactly right. The 6.25% number is completely wrong.

Redo the math that gives 6.25%, except this time pretend quickness had been changed to: 1.0x attack speed (aka no increase) and 100 seconds duration. Now the math in the OP shows that this completely worthless haste is in fact better than the old haste. That means the math behind 6.25% is completely wrong.

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Posted by: Dojo.1867

Dojo.1867

His math is not wrong because he explained the way he calculated it. For a DPS comparison ahurtcorncobs comment makes sense. The DPS drop is 25% indeed like op said but still less than “we do half damage now” like people claim here.

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Posted by: Decemberween.6098

Decemberween.6098

That means the math behind 6.25% is completely wrong.

You don’t have to be such a kitten about it. The result is wrong, but it’s not completely wrong math.

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Posted by: jcbroe.4329

jcbroe.4329

Good work.
DPS isn’t why I used quickness at all though (stomp/rez took priority).

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Posted by: Chopps.5047

Chopps.5047

ahurtcorncob’s comment is exactly right. The 6.25% number is completely wrong.

Redo the math that gives 6.25%, except this time pretend quickness had been changed to: 1.0x attack speed (aka no increase) and 100 seconds duration. Now the math in the OP shows that this completely worthless haste is in fact better than the old haste. That means the math behind 6.25% is completely wrong.

Yes, his comment was very clear without your condescending example which uses an extreme to point out a logical fallacy.

Let me comment on this: this is a subtle point. What is the proper time from to measure it over? Maybe there isn’t one and we have to accept that any DPS comparison would be flawed in that it cannot account for intangibles like stun break and we can’t even decide on a good way to “solve the problem”.

And the guy that said “you have to compare over 5s”, well, why not 6s? And what is the actual number of skills? There are a lot of a priori assumptions being tossed around.

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Posted by: jcbroe.4329

jcbroe.4329

Responding to Chopps since there is a valid point on variables, DPS should not be taken over a time frame larger than 1s. It should be done on a consistent target with a steady weapon so that there is no damage range produced.

This could also be done be measuring the total damage output over the same time spans then dividing down to get a DPS measurement. It doesn’t matter what time frame as long as the time frames are equal in both tests, because we are talking about damage per second, not damage per duration. The time duration selected also doesn’t matter because as long as the times are equal and a steady weapon is used, there should be a consistent ratio.

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Posted by: ahurtcorncob.7652

ahurtcorncob.7652

Let me comment on this: this is a subtle point. What is the proper time from to measure it over? Maybe there isn’t one and we have to accept that any DPS comparison would be flawed in that it cannot account for intangibles like stun break and we can’t even decide on a good way to “solve the problem”.

And the guy that said “you have to compare over 5s”, well, why not 6s? And what is the actual number of skills? There are a lot of a priori assumptions being tossed around.

I definitely agree, there are nuances that we cannot factor in. My point wasn’t specifically that it had to be compared over 5 seconds, just that the comparison had to be made over equal time frames. You could pick some arbitrary amount of time and it’d be fine as long it was the same measure for both.

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Posted by: phantomFury.9168

phantomFury.9168

maybe lets talk about that when you have quickness on healings doesnt works?

increasing the time of quickness just make you die faster

We can certainly discuss that, but it wasn’t the point of my post. The same (i.e., the additional effects beyond Quickness of a particular skill) goes for Warrior’s Frenzy. At least we simply stop healing… they get to take 50% more damage for another second. Is not healing for one additional second going to cause death? I guess it could…

You need equivalent time frames don’t you? You can’t compare the number of actions performed over 4 seconds with the number of actions over 5 seconds.

In 5 seconds with the old quickness you’d get 4 seconds of doubled speed, and 1 second of regular speed compared to 5 seconds of 1.5x speed. If you compare that then r=7.5/9, which is a 17% drop.

It depends on how we do the comparison, but your point is an excellent and completely valid one, and really the more “fair” way to compare the change; I had actually done some of the math in my head taking that into consideration, but failed to include it in my original post.

Let me comment on this: this is a subtle point. What is the proper time from to measure it over? Maybe there isn’t one and we have to accept that any DPS comparison would be flawed in that it cannot account for intangibles like stun break and we can’t even decide on a good way to “solve the problem”.

And the guy that said “you have to compare over 5s”, well, why not 6s? And what is the actual number of skills? There are a lot of a priori assumptions being tossed around.

Emphasis mine. The larger the window that is included the lower the delta becomes, which should be no surprise. If we looked at just an untraited QZ (and no additional Quickness from pet swap), we used to get 4 seconds at double every 60, now we get 5 seconds at 1.5 every 60, a ~2.34% reduction in DPS. Traited, it is ~2.88%. (Assuming I did my quick calculations correctly).

Bottom line… yes, it’s a reduction in the theoretical amount of damage and DPS a QZ utilizing Ranger was capable of. Is it half? No where even close. The more significant impacts, in my opinion, would be the non-damage related impacts, one example being finishing off a player, reviving teammates, etc.

(edited by phantomFury.9168)

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Posted by: Solandri.9640

Solandri.9640

So, to determine the reduction in damage, we subtract r (.75) from 1:

  • 1 – .75 = .25

Multiple by 100 to get a percentage… 25%.

This part is right.

For the first, consider this:

  • Duration of Ranger’s old QZ = 4s
  • Skill speed was twice as fact, i.e., a factor of 2
  • 4s * 2 = 8s
    Ergo, QZ allowed a Ranger to execute 8 seconds worth of skills in 4 seconds.

For the new Quickness:

  • Duration of Ranger’s new QZ = 5s
  • Skill speed is 50% faster, i.e., a factor of 1.5
  • 5s * 1.5 = 7.5s
    Ergo, QZ allows a Ranger to execute 7.5 seconds worth of skills in 5 seconds.

This part is wrong. You’re comparing 4 seconds of damage to 5 seconds of damage. If you want to calculate it correctly, you need to look at the same time period for both cases. In the simplest case, assuming base (unquickened) DPS = 1.0 over a span of 5 seconds:

  • With no quickness you do 1.0*5 = 5.0 damage
  • With old QZ you did (2.0*4) + (1.0*1) = 9.0 damage
  • With new QZ you do (1.5*5) = 7.5 damage

The difference is thus 1 – (7.5/9.0) = 16.7% reduction in damage over 5 seconds. That’s still pretty huge. At least for 5 seconds.

In reality, you can’t just look at 5 seconds. You have to look at total damage output. For QZ that’s 60 seconds (48 sec if traited) before the cycle repeats. So the actual math is:

1 – (60 + (1.5-1) * 5) / (60 + (2.0-1) * 4) = 2.3% reduction in damage over 60 seconds.

But you also need to factor in the other ranger quickness skill – pet swap. Once you do all of this, you get the numbers I posted in the thread I started.
https://forum-en.gw2archive.eu/forum/professions/ranger/Effect-of-quickness-nerf-on-class-DPS/first#post1717625

And I don’t want to sound alarmist because I agree with you, the overall difference of all this is a few percent DPS. But if burst damage was the target of the change and not sustained DPS, and one assumes they were happy with the DPS balance prior to the patch, well then the patch has just scrambled DPS balance and they need to fix it. The extra 1 second added to QZ/Frenzy/Elixir U/Haste isn’t sufficient.

(edited by Solandri.9640)

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Posted by: Chopps.5047

Chopps.5047

So, to determine the reduction in damage, we subtract r (.75) from 1:

  • 1 – .75 = .25

Multiple by 100 to get a percentage… 25%.

This part is right.

For the first, consider this:

  • Duration of Ranger’s old QZ = 4s
  • Skill speed was twice as fact, i.e., a factor of 2
  • 4s * 2 = 8s
    Ergo, QZ allowed a Ranger to execute 8 seconds worth of skills in 4 seconds.

For the new Quickness:

  • Duration of Ranger’s new QZ = 5s
  • Skill speed is 50% faster, i.e., a factor of 1.5
  • 5s * 1.5 = 7.5s
    Ergo, QZ allows a Ranger to execute 7.5 seconds worth of skills in 5 seconds.

This part is wrong. You’re comparing 4 seconds of damage to 5 seconds of damage. If you want to calculate it correctly, you need to look at the same time period for both cases. In the simplest case, assuming base (unquickened) DPS = 1.0 over a span of 5 seconds:

  • With no quickness you do 1.0*5 = 5.0 damage
  • With old QZ you did (2.0*4) + (1.0*1) = 9.0 damage
  • With new QZ you do (1.5*5) = 7.5 damage

The difference is thus 1 – (7.5/9.0) = 16.7% reduction in damage over 5 seconds. That’s still pretty huge. At least for 5 seconds.

In reality, you can’t just look at 5 seconds. You have to look at total damage output. For QZ that’s 60 seconds (48 sec if traited) before the cycle repeats. So the actual math is:

1 – (60 + (1.5-1) * 5) / (60 + (2.0-1) * 4) = 2.3% reduction in damage over 60 seconds.

But you also need to factor in the other ranger quickness skill – pet swap. Once you do all of this, you get the numbers I posted in the thread I started.
https://forum-en.gw2archive.eu/forum/professions/ranger/Effect-of-quickness-nerf-on-class-DPS/first#post1717625

And I don’t want to sound alarmist because I agree with you, the overall difference of all this is a few percent DPS. But if burst damage was the target of the change and not sustained DPS, and one assumes they were happy with the DPS balance prior to the patch, well then the patch has just scrambled DPS balance and they need to fix it. The extra 1 second added to QZ/Frenzy/Elixir U/Haste isn’t sufficient.

I think you’re late to the discussion.

Tin Foil Hat Hearer »—> Ranger Extraordinaire »—> “Be like water…”

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Posted by: AlexRD.7914

AlexRD.7914

There is no such thing as too late in this forum when people keep reviving this thread:
https://forum-en.gw2archive.eu/forum/professions/ranger/Ranger-update/page/26#post1669384

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Posted by: Solandri.9640

Solandri.9640

I think you’re late to the discussion.

Heh heh, yeah. Looks like I shouldn’t have gone to eat dinner while typing all that up. =)

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Posted by: KensaiZen.3740

KensaiZen.3740

ok now to ignore the math and look at it in a mechanical way. By decreasing the speed of quickness it means you will NOT waste channeled skills like LB2 to an opponent that dodges. More of your arrows will hit meaning more damage.

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Posted by: Chopps.5047

Chopps.5047

I love how reddit downvoted me for posting this. There’s this kid that doesn’t understand that 100% boost" equals times two or 200% of the original value and the. And then all the people that thought he was right. And then all the people that think they can accurately measure the true effect of this change via a back of the envelope DPS calculation. And then all the people that forget Time Warp is a group buff when comparing the effect on ranger with mesmer (Solandri had a post on this).

And then all the people just waiting DYING to cut you down for doing a little analysis and try to start a healthy discussion. It makes me sad and really makes me want to break from the forums for a while again.

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Posted by: capuchinseven.8395

capuchinseven.8395

I love how reddit downvoted me for posting this. There’s this kid that doesn’t understand that 100% boost" equals times two or 200% of the original value and the. And then all the people that thought he was right. And then all the people that think they can accurately measure the true effect of this change via a back of the envelope DPS calculation. And then all the people that forget Time Warp is a group buff when comparing the effect on ranger with mesmer (Solandri had a post on this).

And then all the people just waiting DYING to cut you down for doing a little analysis and try to start a healthy discussion. It makes me sad and really makes me want to break from the forums for a while again.

s’understandable.

But then there are many of us here that can see full well that the sky hasn’t fallen in and I say this as someone using a power/precision build that used pet swap and in no real way have I been hinder in killing people the same way I killed them pre patch.

The bravest animal in the land is Captain Beaky and his band.

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Posted by: jubskie.3152

jubskie.3152

I love how reddit downvoted me for posting this. There’s this kid that doesn’t understand that 100% boost" equals times two or 200% of the original value and the. And then all the people that thought he was right. And then all the people that think they can accurately measure the true effect of this change via a back of the envelope DPS calculation. And then all the people that forget Time Warp is a group buff when comparing the effect on ranger with mesmer (Solandri had a post on this).

And then all the people just waiting DYING to cut you down for doing a little analysis and try to start a healthy discussion. It makes me sad and really makes me want to break from the forums for a while again.

s’understandable.

But then there are many of us here that can see full well that the sky hasn’t fallen in and I say this as someone using a power/precision build that used pet swap and in no real way have I been hinder in killing people the same way I killed them pre patch.

Yep! Exactly. This happened in other games I’ve played too. In Monster Hunter Portable 2, the Heavy Bowgun was the go to ranged damage weapon. It had huge elemental and physical damage and no ranged weapon could come close. On Monster Hunter Portable 3, it lost the elemental damage half and people cried that the sky was falling, and it was a dead weapon. Completely ignoring the fact that it still had awesome physical damage.

@Chopps don’t feel bad about downvotes in reddit. It’s only imaginary internet points XD

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Posted by: Leo G.4501

Leo G.4501

Going to have to agree with some people’s thoughts on the math…

If you’re going to compare the old quickness and new via math, you shouldn’t measure them over 2 different time frames. Old quickness lasted 4 seconds while new is 5 so you might want to compare OQ to NQ over both their time frames (both at 4 seconds, and both at 5). Likely, the factor of the speed of each animation plays a bigger role here so perhaps limit to just auto attacks for simplicity and see how many of them you can get off in each time frame then you can base the general effectiveness drop of OQ vs NQ.

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Posted by: Chaosgyro.6023

Chaosgyro.6023

All the people making comments like “you shouldn’t compare over different times” are actually making assumptions: you’re assuming that the purpose of the calculations is to show the damage difference over (for example) 5 seconds. The purpose of the OP is to show the damage difference over the duration of quickening zephyr. At that point, is is perfectly valid to compare 4s vs. 5s. If you want the other numbers, then Solandri has kindly provided them to you.

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Posted by: Killsmith.8169

Killsmith.8169

TLDR: The Quickness change means a 25% reduction in damage per second during Quickness, but only a 6.25% reduction in damage over the duration, given the increase in duration. No where near the many comments that I’ve seen that state ‘this change cuts my damage/DPS in half

I thought that there was an implied bonus before the word damage. “This change cuts my bonus damage from quickness in half”. You could also say that this change cuts quickness’ damage in half. I don’t think anyone is saying that their overall DPS is cut in half, but maybe I’m giving people too much credit.

Also, the time frame doesn’t matter if you adopt the appropriate frame of reference. New QZ gives you +50% attack speed over 5 seconds. This is equal to 5(0.5)=2.5 seconds worth of attacks.

Old QZ gave you +100% attack speed over 4 seconds. This is equal to 4(1)=4 seconds worth of attacks.

New QZ provides 2.5/4=5/8=62.5% of the attack benefit that old QZ provided. It gained the added offensive utility of a stun break, but it also came at the cost of an additional second of being unable to heal.

My advice is that you don’t look at the stun break as a defensive maneuver. Think of it as a counter to an enemy’s attempt to disengage.

(edited by Killsmith.8169)

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Posted by: Chaosgyro.6023

Chaosgyro.6023

New QZ gives you +50% attack speed over 5 seconds. This is equal to 5(0.5)=2.5 seconds worth of attacks.

Old QZ gave you +100% attack speed over 4 seconds. This is equal to 4(1)=4 seconds worth of attacks.

New QZ provides 2.5/4=5/8=62.5% of the attack benefit that old QZ provided.

Nope.

As you tried to state, those numbers are + 50% and + 100%. Meaning it’s 5*1.5 and 4*2. Hence new QZ = 7.5 seconds and old QZ = 8.

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Posted by: Killsmith.8169

Killsmith.8169

New QZ gives you +50% attack speed over 5 seconds. This is equal to 5(0.5)=2.5 seconds worth of attacks.

Old QZ gave you +100% attack speed over 4 seconds. This is equal to 4(1)=4 seconds worth of attacks.

New QZ provides 2.5/4=5/8=62.5% of the attack benefit that old QZ provided.

Nope.

As you tried to state, those numbers are + 50% and + 100%. Meaning it’s 5*1.5 and 4*2. Hence new QZ = 7.5 seconds and old QZ = 8.

There’s no need to include the base attacks. Those would be the same whether you used new QZ, old QZ, or no QZ. QZ is only responsible for the additional attacks you would make due to quickness. You don’t factor in the attacks you would get from your normal attack speed. In fact, because of the change in duration, you’re distorting your results.

Look at it this way. Suppose QZ was bugged and did abolutely nothing. Then, they decide to change the duration, but they didn’t fix the bug and it still does nothing. Using your math, which takes into acount the base attack speed, you get the following:

New QZ = 1.0*5 = 5
Old QZ = 1.0*4 = 4

And now, according to the way you’ve tried to calculate it, New QZ appears to be better than Old QZ, even though they’re bugged in this scenario and they’re both useless.

My math, on the other hand, shows this:

New QZ = 0*5 = 0
Old QZ = 0*4 = 0

Which is what it should be.

(edited by Killsmith.8169)

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Posted by: AlexRD.7914

AlexRD.7914

Assume the Axe is shot every second (which by my testing seems to be the case unless i’m wrong by a few seconds).

With no QZ, in 5 seconds you would have fired 5 shots.
With old QZ, you’d have 4 seconds of firing every .5 seconds, and 1 second of normal firing, meaning 8+1 = 9 shots
With new QZ, you have 5 seconds of firing every .6667 seconds, which is 7.5 shots total.

So Old QZ would result in a 1.8x DPS increase, while new QZ is 1.5x DPS increase.

BUT, there is something you guys are forgetting. While in QZ, we can’t be healed, so any increase to it’s duration is BAD. Honestly, i don’t know what Anet is doing.
They keep saying they have their way of fixing stuff, focusing on the small things or whatever, but that isn’t working. People stop playing GW2 every day because of disappointments such as this and no end game content.

I expected after 3 months of not playing, that they’d have improved the class a bit, but they just keep making it worse. These “bug fixes” like empathic bond, or not being able to throw your pets over the walls, or “Ranger pet cooldowns are now properly preserved when stabled.” are HUGE nerfs, both to fun and class usefulness.
HUGE nerfs without any benefits given to us in return.

EDIT; I think the global quickness nerf was very well deserved, considering how OP it was. The damage was too spiked. Still, if they want to increase the duration to compensate for the nerf, they should compensate for our no healing part, maybe giving 50% effectiveness and not 100%.

(edited by AlexRD.7914)