@MaxQuest Can you explain how the 25% recovery reduction from Armored Grace becomes 0.1 in your formula?

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# [MECHANICS] Attack Speed, Recovery Time, Reload Time

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#21
Posted 13 May 2018 - 04:25 AM

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#23
Posted 13 May 2018 - 06:27 AM

Easy)@MaxQuest Can you explain how the 25% recovery reduction from Armored Grace becomes 0.1 in your formula?

Tooltip writes 25% just because.

While the actual baseValue contained in statuseffects.bundle is 0.1

Hah, was about to answer "becuase the devs thought it would be a good idea" but stopped myself because I thought that maybe there was a formula that concluded with the 0.1.

Sometimes there are no reasonable answers... :/

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#24
Posted 13 May 2018 - 07:57 AM

Than you very much MaxQuest.

It would be very good if we have the damage formula too.

I already explained to somebody in the bug forum that it is not a bug if +25% damage and -25% damage do not result in base damage and I am sure there are many other confused players as well.

I have tried to make a thread about such thing but it got lost in the huge amount of new threads that come permanently.

https://forums.obsid...game-mechanics/

There will be tons of other things that many players will not understand, but damage and speed are the most importent ones because

- everybody wants to attack as fast as possible

- everybody wants to do as much damage as possible

- in both formulas +X% bonus and -X% penalty do not add up to zero

Another thing that would be interesting to know is stacking: What stacks and what not?

I have heared that all passive effects stack but active effects do not stack.

But then we have the question which effect is active and which effect is passive.

I think Boeroer said that weapon modals are active so the +2 pen does not stack with buffs ( I am not sure ).

This will also confuse many players, at least I failed the will save agains mind effecting mechanics

**Edited by Madscientist, 13 May 2018 - 07:57 AM.**

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#25
Posted 13 May 2018 - 10:20 AM

The game adds all coefficients together. Bonuses, maluses, doesn't matter.Can someone explain to me what the double inversion on negative numbers and maluses means in game terms?

In PoE1 it worked fine, since there weren't enough big maluses.

While in Deadfire a similar approach would lead to negative damage on under-penetrating graze.

A lazy workaround could be to limit the damage at 0, or 20% of original value.

A better way would be to divide sum_of_bonuses by sum_of_maluses (all numbers being positive, so the result will be positive as well, plus it ends up with meaningful result).

But Deadfire went on the path of double-inversion. Which personally I see as math shenanigans, as they use different sub-formulas for bonuses and maluses, and do not cancel-out nicely if they have same absolute values. Specifically, imagine that you have:

+25% action speed from Frenzy, which translates into 1.25 speed coefficient; and

-25% action speed from Arbalest's modal, which translates into 0.75 speed coefficient

The game takes 1.25 and transforms it into +0.25 (step_value) via [coef - 1] formula

The game takes 0.75 and transforms it into -0.(3) (step_value) via [1 - 1/coef] formula

Now it adds them together: step_sum = 0.25 - 0.333333 = -0.083333

And after that computes the final coefficient:

- if step_sum is greater than 0: final_coef = step_sum + 1

- if step_sum is less than 0: final_coef = 1 / (1 - step_sum)

In our case it's the later, thus final_coef = 1 / (1 - -0.083333) = 0.92

And finnaly: phase_time = base_phase_time / final_coef

So if you had 6s reload; with Frenzy and Arbalest's modal you will have 6.52s, even if one effect was giving you +25% action speed, and another -25% action speed.

P.S. We call it double inversion because:

- individual malus coefficients are inverted when computing their individual step values

- if step_sum is below zero, it is inverted in order to get final coefficient

It for sure feels strange.I am a little confused when it comes to dual wielding pistols, how can it be faster to reload them when your other hand is occupied, but when I have a lovely moisturised sweat free open hand just eager to reload, I am penalised with having to wait a little longer ?

But from another point of view:

- single-wielding a pistol inherently grants +12 acc.

- what should dual-wielding pistols inherently grant instead? (full-attack profit aside). Also we should take into account that there is a cost attached. If you are a quick-switching black jacket focused on 4 quick full-attacks, you would want 8 unique 1h-firearms, and also would have to enchant all of them.

thanks bruh : )

btw, from poster Tygrendes in RPGCodex:

Trash Player said: â†‘

Nope.Blunted Crits likely reduces the Crit Modifier by 25%, instead of being a -25% damage.

Crit only got a total of 39.6666666% bonus damage , regular hit got 48%.

****ing hell Obsidian

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#26
Posted 13 May 2018 - 06:12 PM

I feel with dual wielding pistols being able to shoot same target twice for burst fire or shoot 2 targets 1 time each is enough to justify a slower reload time, on top of not having the +12 acc from single wield, I wouldn't say make it twice as long to reload but maybe something like 1.5x the reload speed of a single pistol.

Kinda just want single wield pistol to be able to load faster, I would take that over +12 acc if I had to

- gGeorg likes this

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#27
Posted 13 May 2018 - 09:23 PM

I don't follow some of the points. You say "double inversion" makes attack speed maluses worse than equivalent positive bonuses, but if coefficients are computed correctly, the net effect of the first inversion is to simply turn the coefficient of penalties into the "tool-tip" negative additive bonus, and then the second inversion returns it back to a coefficient.

By "computed correctly" I mean if you have something that has a tool-tip/stated value of reduction your action speed by 25%, the coefficient would be .8, not .75 (if you naively did coeff = 1 - .25).

The values for armor recovery coefficient suggest that obsidian is storing the "correct coefficient" (e.g. .645 = 1/1.55 instead of .45 = 1 - .55 for heavy armors), at least for action speed. Unless I'm not following the equation, all the first inversion does is turn the .645 into a -.55 additive modifier, which means it has the same exact weight as any positive bonus to your action speed. The second inversion (if the penalties over-power your bonuses) simply turns it into a coefficient again in a manner that is exactly what it should be.

Maybe you have a better insight into what coefficients are being used, but in abstract I don't think the "double inversion" thing is correct.

EDIT: i realize everyone powergaming has been talking about double inversion throughout the backer beta so it might feel like i'm just coming out of nowhere with this, but I didn't really start paying attention to the math until release. I'm actually legit a little confused about this, so any correction would be helpful.

**Edited by thelee, 13 May 2018 - 09:58 PM.**

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#28
Posted 13 May 2018 - 09:30 PM

Also I might be wrong about this, but I think it is incorrect to call action speed in Deadfire "diminishing returns". The ultimate metric you are measuring is actions/second, not your recovery rate or attack speed, and so while the visible effect on your tool-tip recovery numbers looks like it becomes less and less impactful, the number you are shrinking is effectively the denominator for the true metric, which means small increases on small numbers can be just as impactful as large increases on large numbers. So while Pillars had increasing returns (up until you had zero recovery), I'm pretty sure Deadfire legitimately has **linear returns**.

**Edited by thelee, 13 May 2018 - 09:50 PM.**

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#29
Posted 13 May 2018 - 11:58 PM

There are diminishing returns because of the base formula: phase duration = base phase duration / speed coefficient

To keep things simple, lets assume we have a base duration of 100 seconds and we have enough speed modifiers to half the duration:

100 / 2 = 50

Now we add the same amount of modifiers on top of this. Now we have:

100 / 3 = 33,3

result: You have improved from double speed to tripple speed.

You had zero bonusses in the beginning. Then you added a bonus and the duration gets shorter by 50 seconds. Then you put exactly the same bonus on top of that and you get an additional duration cut of 16,7 seconds. ( 50 - 33,3 )

**Getting a bonus once reduces duration by 50 seconds and getting the same bonus on top of that gives you a reduced duration of 16,7 seconds on top of that. Thats diminishing returns.**

We need diminishing returns with the formulas we have now. Otherwise it would be possible to get a negative duration or negative damage which makes no sense. In PoE1 the devs "cheated" because all things that said "increases speed" only reduced recovery and recovery could reach zero. In PoE2 abilities really influence action speed so the devs need to make sure that the attack or casting time does not reach zero.

- grausch likes this

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#30
Posted 14 May 2018 - 02:07 AM

so the devs need to make sure that the attack or casting time does not reach zero.

Its easy - just limit speed to 80% cap, OR limit speed effect to non-stackable, when only DEX+ most powerful buff + most powerful item's passive work. Ofc, they must keep values near 25-30 to each.

Same with recovery.

And with this solution we cant have stupid situation, when CRIT do lower dmg, than HIT, or when 40% slow = 70% haste.

**Edited by Zzz, 14 May 2018 - 02:08 AM.**

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#31
Posted 14 May 2018 - 04:05 AM

- illathid and AndreaColombo like this

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#32
Posted 14 May 2018 - 05:46 AM

There are diminishing returns because of the base formula: phase duration = base phase duration / speed coefficient

To keep things simple, lets assume we have a base duration of 100 seconds and we have enough speed modifiers to half the duration:

100 / 2 = 50

Now we add the same amount of modifiers on top of this. Now we have:

100 / 3 = 33,3

result: You have improved from double speed to tripple speed.

You had zero bonusses in the beginning. Then you added a bonus and the duration gets shorter by 50 seconds. Then you put exactly the same bonus on top of that and you get an additional duration cut of 16,7 seconds. ( 50 - 33,3 )

Getting a bonus once reduces duration by 50 seconds and getting the same bonus on top of that gives you a reduced duration of 16,7 seconds on top of that. Thats diminishing returns.

We need diminishing returns with the formulas we have now. Otherwise it would be possible to get a negative duration or negative damage which makes no sense. In PoE1 the devs "cheated" because all things that said "increases speed" only reduced recovery and recovery could reach zero. In PoE2 abilities really influence action speed so the devs need to make sure that the attack or casting time does not reach zero.

That's not what diminishing returns are though. The "true metric" is DPS, or actions/second more generally. When you go from 100/2 to 100/3 in your example the same number of modifiers is giving you the same increase in DPS or actions/second, from 1x => 2x and then 2x => 3x. That's precisely linear returns.

Avoiding zero or negative recovery is simply avoiding increasing returns. You can avoid zero or negative recovery and have linear returns.

It's the same reason why deflection in pillars has INCREASING returns. Even though each point gave you one point of deflection on your tooltip, the "true metric" was your effective health, which would eventually become infinite with a sufficiently high deflection. Paying attention to what your "true metric" is very important.

- grausch likes this

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#33
Posted 14 May 2018 - 06:12 AM

**Is there a comprehensive list of coefficients anywhere?**

I think part of the confusion is that I think damage equation is legit bugged. Because from that blunted critical screenshot upthread, the damage numbers are only possible if Obsidian is naively using 1-1/.75 as the coefficient, and NOT the "correct" one of 1-1/.8 for blunted critical (assuming the damage equation is still similar to the action speed equation). Effectively this means all stated damage penalties are worth more than they actually are, regardless of whether it is combined with positives or not.

Whereas at least with action speed, when I was diagnosing a bug in the tech support thread, the "correct" malus coefficients appeared to be being used, e.g. armor, sharpshooter, overdraw.

Double inversion itself doesn't overweight negatives. It only goes so if the negative values themselves are initially stored/calculated in-game incorrectly.

EDIT: here's some rhetorical thought experiment for some obvious, well-known cases.

a) Why are armor coefficients the way they are? Why is heavy armor .645 instead of (1-.55)?

b) Back when overdraw was a +100% recovery speed penalty, I think it was confirmed that the coefficient being used was .5, not (1-1 =) 0, which would be a divide by zero error anyway. Why was it .5?

Once you've answered a and b, what *should* the coefficient for a -50% penalty be? Hopefully from A and B we can logically see that it *shouldn't* be .5 (that's the same as a -100% penalty), and that it actually should be 1/1.5 = .6667. Which means, from MaxQuest's example on the first page:

-25% action speed from Arbalest's modal, which translates into 0.75 speed coefficientThe game takes 1.25 and transforms it into +0.25 (step_value) via [coef - 1] formula

The game takes 0.75 and transforms it into -0.(3) (step_value) via [1 - 1/coef] formula

Now it adds them together: step_sum = 0.25 - 0.333333 = -0.083333

Is it actually confirmed from in-game files that the -25% arbalest modal is implemented as a .75 (=1-.25) coefficient and not a .8 (=1/1.25)? Because if this is real and not just hypothetical then Obsidian has buggy coefficients for action speed as well, because clearly they have the correct coefficients elsewhere (despite what the in-game tool-tip says) for things like armor (which says e.g. +20% recovery but is internally a .8333x coefficient, not .8x) and dual wield bonuses (which says -30% recovery time but is internally a 1.428x coefficient not 1.3x), and at least by my own calculations, something like sharpshooter penalty (a -10% recovery penalty that is implemented as a .91x coefficient not .9x).** I feel like filing bugs in the technical support forums for specific coefficients would be far more productive **than complaining about a percieved balance decision about maluses via double-inversion (which mathematically isn't an issue).

I'd check numbers in-game, but I'm at work.

**Edited by thelee, 14 May 2018 - 08:17 AM.**

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#34
Posted 14 May 2018 - 12:22 PM

The big advantage to Dual Wielding pistols is the alpha strike where both guns are fired. So they're nice on any flavor of Stealth Assassin since both shots apply to the bonus sneak attack damage, and its reportedly broken with Black Jack spam. Otherwise a single pistol is the Superior choice as you can use the Modal ability to get -50% reload, while only losing 3ACC. +12ACC bonus for 1H, -15ACC for the Modal nets -3ACC. You CAN get a faster reload on Dual Pistols if you take the Modal ability as well, but it only ends up being like a 0.4sec to 0.5sec improvement in reload, due to diminishing returns, at the cost of now -27ACC... which is really -39ACC overall since you could've had +12ACC from using a single pistol.

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#35
Posted 14 May 2018 - 12:57 PM

You CAN get a faster reload on Dual Pistols if you take the Modal ability as well, but it only ends up being like a 0.4sec to 0.5sec improvement in reload, due to

diminishing returns, at the cost of now -27ACC... which is really -39ACC overall since you could've had +12ACC from using a single pistol.

I'm waiting for confirmation/tests on action speed coefficients before making this case stronger because things might still be weird for maluses, but for bonuses that's not diminishing returns.

When your reload speed is already lowish, *smaller* *absolute decreases *are needed to achieve the same result as when your reload speed was longer; a 1s reduction at a reload speed of 5s is much, much, much weaker than a 1s reduction at a reload speed of 2s.

I put together a dumb spreadsheet to show this:

https://docs.google....dit?usp=sharing

here's a screenshot of the important chart:
**linear returns.png** **11.7KB**
1 downloads

This hypothetical scenario assumes you attack for an average of 15 damage every 5 seconds (combined attack+recovery time), and that chart shows you how much damage you do over one minute. You can make the equations as complicated and as representative of actual in-game numbers as you want, but this hypothetical abstraction is good enough for our purposes.

You'll notice that we have a straight, solid diagonal line going from 0% bonus to 200% action speed bonus. That is literally the definition of linear returns.

(For the calculus-inclined, more formally linear returns means that for a function f(x), the second derivative f''(x) = 0).

**Edited by thelee, 14 May 2018 - 12:58 PM.**

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#36
Posted 15 May 2018 - 06:11 AM

I looked at a few in-game examples last night and I can at least confirm that the maluses I saw were using correctly computed coefficients so e.g. no overweighting, just like a straight additive modifier. But that was only a few more than from above. (looked at other armor examples and a couple of weapon/shield modals that increase recovery time)

Adding to the confusion is that the tooltip doesn't show every effect. For example I had a character with a Swift inspiration, and while their tooltip recovery was correct, the listed modifiers showed only the unmodified dexterity bonus.

**Edited by thelee, 15 May 2018 - 08:16 AM.**

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#37
Posted 15 May 2018 - 07:00 AM

The big advantage to Dual Wielding pistols is the alpha strike where both guns are fired. So they're nice on any flavor of Stealth Assassin since both shots apply to the bonus sneak attack damage, and its reportedly broken with Black Jack spam. Otherwise a single pistol is the Superior choice as you can use the Modal ability to get -50% reload, while only losing 3ACC. +12ACC bonus for 1H, -15ACC for the Modal nets -3ACC. You CAN get a faster reload on Dual Pistols if you take the Modal ability as well, but it only ends up being like a 0.4sec to 0.5sec improvement in reload, due to diminishing returns, at the cost of now -27ACC... which is really -39ACC overall since you could've had +12ACC from using a single pistol.

Wait. Does not the first attack cease stealth/invisibility?

That's not what diminishing returns are though. The "true metric" is DPS, or actions/second more generally. When you go from 100/2 to 100/3 in your example the same number of modifiers is giving you the same increase in DPS or actions/second, from 1x => 2x and then 2x => 3x. That's precisely linear returns.There are diminishing returns because of the base formula: phase duration = base phase duration / speed coefficient

We need diminishing returns with the formulas we have now. Otherwise it would be possible to get a negative duration or negative damage which makes no sense. In PoE1 the devs "cheated" because all things that said "increases speed" only reduced recovery and recovery could reach zero. In PoE2 abilities really influence action speed so the devs need to make sure that the attack or casting time does not reach zero

Avoiding zero or negative recovery is simply avoiding increasing returns. You can avoid zero or negative recovery and have linear returns.

It's the same reason why deflection in pillars has INCREASING returns. Even though each point gave you one point of deflection on your tooltip, the "true metric" was your effective health, which would eventually become infinite with a sufficiently high deflection. Paying attention to what your "true metric" is very important.

Could you please advise if the figures in my char sheet are lower because the calculations are made according to that formula with other buffs taken into account. Only Dual Wield bonus is the same as it should be (30). I used to think it is a bug.

#### Attached Files

**Edited by Sotnik, 15 May 2018 - 07:14 AM.**

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#38
Posted 15 May 2018 - 07:12 AM

Than you very much MaxQuest.

It would be very good if we have the damage formula too.

I already explained to somebody in the bug forum that it is not a bug if +25% damage and -25% damage do not result in base damage and I am sure there are many other confused players as well.

I have tried to make a thread about such thing but it got lost in the huge amount of new threads that come permanently.

https://forums.obsid...game-mechanics/

There will be tons of other things that many players will not understand, but damage and speed are the most importent ones because

- everybody wants to attack as fast as possible

- everybody wants to do as much damage as possible

- in both formulas +X% bonus and -X% penalty do not add up to zero

Another thing that would be interesting to know is stacking: What stacks and what not?

I have heared that all passive effects stack but active effects do not stack.

But then we have the question which effect is active and which effect is passive.

I think Boeroer said that weapon modals are active so the +2 pen does not stack with buffs ( I am not sure ).

This will also confuse many players, at least I failed the will save agains mind effecting mechanics

Yeah, we're really at the point where we need a DPS calculator not just an attack speed calculator. Unfortunately I don't have the "chops" to write one out.

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#39
Posted 15 May 2018 - 08:14 AM

The big advantage to Dual Wielding pistols is the alpha strike where both guns are fired. So they're nice on any flavor of Stealth Assassin since both shots apply to the bonus sneak attack damage, and its reportedly broken with Black Jack spam. Otherwise a single pistol is the Superior choice as you can use the Modal ability to get -50% reload, while only losing 3ACC. +12ACC bonus for 1H, -15ACC for the Modal nets -3ACC. You CAN get a faster reload on Dual Pistols if you take the Modal ability as well, but it only ends up being like a 0.4sec to 0.5sec improvement in reload, due to diminishing returns, at the cost of now -27ACC... which is really -39ACC overall since you could've had +12ACC from using a single pistol.

Wait. Does not the first attack cease stealth/invisibility?

That's not what diminishing returns are though. The "true metric" is DPS, or actions/second more generally. When you go from 100/2 to 100/3 in your example the same number of modifiers is giving you the same increase in DPS or actions/second, from 1x => 2x and then 2x => 3x. That's precisely linear returns.There are diminishing returns because of the base formula: phase duration = base phase duration / speed coefficient

We need diminishing returns with the formulas we have now. Otherwise it would be possible to get a negative duration or negative damage which makes no sense. In PoE1 the devs "cheated" because all things that said "increases speed" only reduced recovery and recovery could reach zero. In PoE2 abilities really influence action speed so the devs need to make sure that the attack or casting time does not reach zero

Avoiding zero or negative recovery is simply avoiding increasing returns. You can avoid zero or negative recovery and have linear returns.

It's the same reason why deflection in pillars has INCREASING returns. Even though each point gave you one point of deflection on your tooltip, the "true metric" was your effective health, which would eventually become infinite with a sufficiently high deflection. Paying attention to what your "true metric" is very important.

Could you please advise if the figures in my char sheet are lower because the calculations are made according to that formula with other buffs taken into account. Only Dual Wield bonus is the same as it should be (30). I used to think it is a bug.

Boy that's confusing. IIRC, Swift Strikes is a increase of +20% action speed, right? But in that recovery speed tooltip it's listed as a -17% bonus. I mean, what the heck.

But naively just using the listed bonuses, 3.0s is correct. 5.0s/(1 + .06 /*dex*/ + .458 /*dual wield*/ + .17 /*swift strikes, apparently*/) = 2.96s rounds to 3.0s.

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#40
Posted 15 May 2018 - 08:54 AM

Not that comprehensive, but there is. They are in game files that can be accessed in the open, using a simple text editor like notepad.

Is there a comprehensive list of coefficients anywhere?

Check the statuseffects.gamedatabundle file.

It is located in /PillarsOfEternityII_Data/exported/design/gamedata/ folder.

Or you can check it's copy that I uploaded here.

Yes, you can consider this as confirmed. The stored value for arbalest modal is 0.75.Is it actually confirmed from in-game files that the -25% arbalest modal is implemented as a .75 (=1-.25) coefficient and not a .8 (=1/1.25)?

You can make a search by "Arbalest_Overbearing_Shot_SE_AttackSpeed" to verify.

Also here are a few examples for v1.0 of the game:

Btw, I had a formula in the starting post:

step_n = coef_n >= 1 ? coef_n - 1 : 1 - 1 / coef_nJust want to note that:

- for [speed] status effects: coef_n = baseValue_n

- for [time] status effects: coef_n = 1 / baseValue_n

The game converts [time] values to [speed] values before calculating steps.

First: yes, coefficients of 1.25 and 0.80 do cancel each-other.I don't follow some of the points. You say "double inversion" makes attack speed maluses worse than equivalent positive bonuses, but if coefficients are computed correctly, the net effect of the first inversion is to simply turn the coefficient of penalties into the "tool-tip" negative additive bonus, and then the second inversion returns it back to a coefficient.

By "computed correctly" I mean if you have something that has a tool-tip/stated value of reduction your action speed by 25%, the coefficient would be .8, not .75 (if you naively did coeff = 1 - .25).

step_1 = 1.25 - 1 = 0.25

step_2 = 1 - 1 / 0.8 = -0.25

step_sum = 0 => final_coef = 1

Second, Obsidian takes all coefficient values in respect to the base value. And they do use 0.75 value for coefficients when they want to denote -25% speed. And truth be told, I am not convinced yet that they should use 0.8 instead.

For example: I am going with a car at 100kmph. And at that speed going from A to B will take 60 minutes.

a). if I am asked to lower my speed by 25%, I would slowdown to 75kmph. [the speed is 25% lower, the trip duration is 33% longer]

b). if I am asked to increase the time it takes to arrive there by 25%, I would slowdown to 80kmph. [the speed is 20% lower, the trip duration is 25% longer]

The quoted malus does refer to Arbalest Modal which writes: -25% action speed, so it's a).

That's why I don't see (at least at the moment) why do you call Obsidian being naive for putting 0.75 base value for it.

Yeah you wrote "you", but I am not taking values from top of my head, but from the ingame files ^^

Swift Strikes grants +20% action [speed].Boy that's confusing. IIRC, Swift Strikes is a increase of +20% action speed, right? But in that recovery speed tooltip it's listed as a -17% bonus. I mean, what the heck.

But when you mouseover the recovery time of weapon, the game tries to display how much did Swift Strike affect the [time].

It converts speed coefficient to time coefficient: 1/1.2 = 0.8333. So a +20% increase in speed, corresponds to a -16.(6)% decrease in time.

P.S. Will reply to other stuff as soon as I have time. Do have a heavy week.

**Edited by MaxQuest, 15 May 2018 - 09:34 AM.**

- thelee, grausch, Madscientist and 1 other like this

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