Dark Knight Tank Stance Change +3.x Reprisal and 3.x Dark Dance

Da with a 15sec CD would require an entire rework of the job. I mean, where would you spend your mana?

I'm not wedded to a 15 sec cooldown but rather to the concept. It could be 10 secs or something else.

Clearly working on DA in any form would be touching the fundamentals of the job. I agree MP costs would need to change. Potencies too possibly.

However, I don't think it would be a overly difficult thing to do as you're not really adding anything new. DA is likely to need at least a 2x increase, maybe more to account for the free Da on ogcds. You might also want to increase the base mp cost of Abyssal drain and Dark passenger.

Another MP spender could be added too. Maybe add MP to dark mind.

You'd just be turning DRK into a warrior with 11 abilities locked behind stances meaning you never use half of them.

Don't like it, if anything they should just be usable no matter the stance. That would be a huge buff.

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Originally Posted by Tegernako

You'd just be turning DRK into a warrior with 11 abilities locked behind stances meaning you never use half of them.

Don't like it, if anything they should just be usable no matter the stance. That would be a huge buff.

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What is this replying to?

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Originally Posted by Reynhart

I wasn't talking about the overall effect of Blood Weapon, but the assumed increased potency. Increase speed by 10% is, in reality, reducing the delay by 10%, so you increase the DPS by 1/(1-10%).
But at 10% speed, the potency is 111 instead of 110.

If we were at 20% increase in speed, we wouldn't increase DPS by 20% but 25%, and if we were at 50% increase in speed, we would double our DPS.

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Not exactly on topic but this has piqued my interest before. In my job when I mark up a product we divide by the reciprocal. (If I mark something up 25%, I calculate as cost/.75 -- not cost*1.25). I kind of understand the nuance of the math itself (dividing by a decimal vs increasing by 25%)

But I guess my question would be - how would you know when to do which calculation? For example, if Darkside increases damage by 20% - how do you determine it should be calculated as x1.20 instead of /.80?

I'm sure a lot of it has to do with the nature of what you're trying to calculate. I don't know, it's just one of those weird things I can't quite wrap my head around lol

I don't know if this helps, but it definitely has to do with what you are comparing. I don't know that this has a general solution in all contexts of what to do.

Keeping with the damage examples, Darkside increases damage dealt by 20%. 1 GCD deals its damage and then an additional 20%. We are really comparing two different units at the same time
1 GCD deals 100 damage compared to 1 GCD deals 100 + 20% damage.

So how should we compare the following
1 GCD for 100 potency compared to
.9 GCD for 100 potency?

Rather than dealing with fractions of a GCD, I find it easier to compared 1 GCD to 1 GCD so I seek to scale my .9 GCD to 1 GCD which is achieved by dividing by .9, we scale our potency unit in the same way.

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Originally Posted by Chrono_Rising

We are really comparing two different units at the same time

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Thanks Chrono, that kinda helps. Logic was leading me into thinking along the lines of units, and I'm starting to see it also has a lot to do with the nature of comparison. Like in the speed example, if you're attacking 50% faster your actually adding twice the amount of attacks or "units". (100 divided into halves is 200). If we are only increasing damage by 50% then the attack unit is still the same 1:1, it's just 50% more potent.

Doesn't help me understand my real world situation much (why we do one vs the other) but that's not too relevant here. I just wanted to try and clarify how you know which is proper to use. I had a hard time finding anything other than long division learning example type stuff.

Thanks!

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Originally Posted by whiskeybravo

Doesn't help me understand my real world situation much (why we do one vs the other) but that's not too relevant here. I just wanted to try and clarify how you know which is proper to use. I had a hard time finding anything other than long division learning example type stuff.

Thanks!

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Yeah I don't really know business terminology myself so I don't think I can break down what a mark up is without knowing the definitions. If it makes your feel better I have no idea why your are dividing by .75 and not multiplying by 1.25 its not immediately obvious, but I'm guessing it has to do with what a mark up means.

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Originally Posted by whiskeybravo

Like in the speed example, if you're attacking 50% faster your actually adding twice the amount of attacks or "units". (100 divided into halves is 200).

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I'm no math wizard but unless I am misunderstanding what you are saying here, I am pretty sure that is incorrect.

Adding twice the number of attacks would be doubling them which equates to an increase of 100% equaling a total speed of 200% of the initial speed.

Basically, you can use the basic physics equation for calculating speed to see it.

Lets break it down.

As an equation it would look something like the following with D being distance (the substitute for "units" of damage, i.e. # of attacks in this instance, here), T being time and S being speed.
D/T = S

Now if we were to then increase speed by 50% that means that we are increasing S by 50% or in other words multiplying it by 1.5.
Then because of the Golden Rule of Equations, what we do to one side of a linear equation we must do to the other which results in it looking like this
(D/T)x1.5 = Sx1.5

Now let's use this to solve for D by cancelling out the T on the left side, leaving us with D compensated for the increase to S, by multiplying both sides by T
(D/T)x1.5xT = Sx1.5xT which is the same as Dx1.5 = SxTx1.5

This shows that increasing speed by 50% does not double the rate of or # of attacks but increases it proportionately, so only half an extra attack per attack which would equate to one extra attack every two attacks, not double the attacks.

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Originally Posted by Chrono_Rising

Yeah I don't really know business terminology myself so I don't think I can break down what a mark up is without knowing the definitions. If it makes your feel better I have no idea why your are dividing by .75 and not multiplying by 1.25 its not immediately obvious, but I'm guessing it has to do with what a mark up means.

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Markup is the term used for the price increase to an item or service based on the cost of goods. Essentially how much a store increases the price of what they had to pay for an item when they are selling it in order to cover labor/operations costs and to hopefully turn a slight profit.

So if a store sells an item for 20% greater than it cost them to acquire that item, that is a 20% markup.

As for when to divide versus when to multiply, when dealing with percents you pretty much always want to multiply. Trying to use division can lead to incorrect results.

The best way to conceptualize it is to translate the calculations into "plain language".

Let's look at the 20% markup example.
A 20% markup means an additional 20% added to the price, or 100% + 20% = 120% which equates to multiplying by 1.2

Trying to divide the price by 0.8 is incorrect because what you are actually asking is "how many 0.8's make up the price" which is something completely different than what is 120% of the price.

Here is a simple equation showing this where the price of something is $100 and the markup is 20%.

100x1.2 = $120
100/0.8 = $125

The results are not the same.

So lets play with the second calculation to see what is really happening.

100/0.8 = 125

Now let's cancel out the "/0.8" on the left side to see the relationship between the original price and 125.

(100/0.8)x0.8 = 125x0.8 which results in 100 = 125x0.8 which reorganized is 125x0.8 = 100

This shows that 100 is actually 80% of 125, not 120% of 100 is 125.

Therefore we can see that dividing a number by a percent is actually asking "X number is Y percent of what?".

Well, the simple answer I got was because it's more profit lol. As Touch ended his quote, it's not 100 marked up 20% but rather 100 divided into units of .80, of which there would be 125. That's not the same as adding 20% of 100 to 100 (which would be 120). So, I think in the long run it just has to deal with replacement cost of physical merchandise. I'll leave it at that for now. Appreciate the inputs!

Carry on DRK discussions ;)

EDIT: I couldn't leave it at that, because I think I might have actually figured it out lol. As it relates to normalizing/scaling the units that Chrono mentioned, I think by scaling to a fraction of a "unit" kind of unifies replacement costs - regardless of the cost itself. As in, at 20% markup the 5th unit sold will always cover the costs of a new one. Whereas that might not always be true if we are marking up based on the $ alone. Something like that anyways.

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Originally Posted by whiskeybravo

EDIT: I couldn't leave it at that, because I think I might have actually figured it out lol. As it relates to normalizing/scaling the units that Chrono mentioned, I think by scaling to a fraction of a "unit" kind of unifies replacement costs - regardless of the cost itself. As in, at 20% markup the 5th unit sold will always cover the costs of a new one. Whereas that might not always be true if we are marking up based on the $ alone. Something like that anyways.

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It depends on what you are considering as "20% markup".

If you consider it "by dividing by 0.8" it would actually be per every 5 units, the markup on the first 4 cover the cost of the 5th.

Essentially it would be rationalized as X% of each unit in the total pool, including the "free" one, covers the value/cost/whatever of one of those units.

Using the same equation as before ...

If you are charging $125 per unit, after 4 units sold that is an extra $100 over the $100 cost per unit, which then would pay for the 5th unit.

Basically, dividing by a percent will determine the "per units" pool that you are looking at, where the last one will always be covered by the previous sold at markup.

If you sold each unit for $200 then for each unit sold, the second would have its cost covered since the pool you are looking at is 2 which is determined by subtracting the number you divided by from 1 and then dividing 1 by the remainder.

Another example would be
$100/0.75 = $133.33... *(would be rounded up to $133.34 in most real world budgeting)
1-0.75=0.25 and 1/0.25=4
Therefore your pool of units is 4 wherein the first 3 sold at $133.34 would pay for the 4th unit.

However if you are considering "20% markup" in the sense of weighting the value of each unit as a fraction or percent of its true value, for example 80% of a unit or Unit times 0.8, then that is correct. After 5 units the 6th would be covered or "free" if you will.

Basically it depends on whether you are factoring in the markup % for all of the units, or for only the units that then pay for the "free" one.

As you said the first method results in greater net profits or gains.

I promise to not post anymore on this particular topic, but I found it mainly has to do with operating margins. If we need to maintain 25% profit margin to keep the doors open, simply multiplying by 1.25 doesn't get us there:

100*1.25 = 125
100/.75 = 133

100/125 = .80 (20% margin)
100/133 = .75 (25% margin)

Now, back to DRK please. I dun wanna get in troubles lol

Agreed, this tangent has run its course.

I do hope though that the math that has been shown and how to deal with percents, weighting the values of things, and the vast difference between dividing by a value versus multiplying, etc. will inform people on how to avoid such common mathematical faux-pas as thinking dividing by 0.8 is the same as multiplying by 1.2 (seriously, you'd be surprised how often people screw this up). I see such things happen all the time on this and other game forums when people are trying to theorycraft.

People often say that "numbers are infallible" and that is entirely untrue. Numbers are tools and can be manipulated to convey what someone wants or can be confusingly deceptive if applied incorrectly, not to mention the necessity of context.

Anywho ... that's enough waxing mathematical from me for today.

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Originally Posted by TouchandFeel

This shows that increasing speed by 50% does not double the rate of or # of attacks but increases it proportionately, so only half an extra attack per attack which would equate to one extra attack every two attacks, not double the attacks.

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Your mistake here is that increasing speed in that way doesn't actually increase our speed:

If our speed is 2.47 sec/gcd then calculating as 2.47 * 1.5 actually results in a longer gcd of 3.705 sec

As Reynhart points out:

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Originally Posted by Reynhart

Increase speed by 10% is, in reality, reducing the delay by 10%, so you increase the DPS by 1/(1-10%)... and if we were at 50% increase in speed, we would double our DPS.

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Hence 2.47 * .50 = 1.235 sec/gcd

Let's say we are averaging 225 pot/gcd and get a 15 sec buff for 50% increased speed (aka reduced gcd):

15 / 2.47 = 6 attacks
15 / 1.235 = 12 attacks

225 * 6 = 1350 (90 pps)
225 * 12 = 2700 (180 pps)

So by increasing out speed 50% we are doubling our # of attacks and resulting damage. Let's try 35% speed: (prediction 90 pps / .65 = 138 pps approx 53% damage increase)

2.47 * .65 = 1.6055 gcd

15 / 1.6055 = 9 attacks

225 * 9 = 2025 (135 pps)
2025 / 1350 = 1.5

35% speed = approx 50% damage increase. Fairly close considering I'm leaving out of a lot of decimals.

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Originally Posted by whiskeybravo

Your mistake here is that increasing speed in that way doesn't actually increase our speed:

If our speed is 2.47 sec/gcd then calculating as 2.47 * 1.5 actually results in a longer gcd of 3.705 sec

As Reynhart points out:



Hence 2.47 * .50 = 1.235 sec/gcd

Let's say we are averaging 225 pot/gcd and get a 15 sec buff for 50% increased speed (aka reduced gcd):

15 / 2.47 = 6 attacks
15 / 1.235 = 12 attacks

225 * 6 = 1350 (90 pps)
225 * 12 = 2700 (180 pps)

So by increasing out speed 50% we are doubling our # of attacks and resulting damage. Let's try 35% speed: (prediction 90 pps / .65 = 138 pps approx 53% damage increase)

2.47 * .65 = 1.6055 gcd

15 / 1.6055 = 9 attacks

225 * 9 = 2025 (135 pps)
2025 / 1350 = 1.5

35% speed = approx 50% damage increase. Fairly close considering I'm leaving out of a lot of decimals.

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Technically if we are going to define a "speed" (rate is the more accurate term here) it would be GCD/sec not sec/GCD. Increasing the speed by 50% would mean multiplying our rate by 1.5.

We can relate three quantities roughly as change in number of GCDs =r*t always rounded down, more specifically we can solve for our rate by using this relationship when change in the number of GCDs = 1 to get a relationship between our rate (r) and the known quantity the time to complete 1 GCD (t).

t= 1/r and

r=1/t

r'=1.5r where r' is the rate under the 50% buff.

This doesn't do much for us as we are actually interested in what this did to our time to complete 1 GCD but we can get that by inverting our relationship between rate and time as t= 1/r

t'=1/r'=1/(1.5r) = (1/r)/1.5 = t/1.5

Just a side to this I would love Blood Weapon to increase our speed by 50% (which decreases our time to complete a GCD by 33.333%).

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Originally Posted by whiskeybravo

snip

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D/T=S

D is the number of actions/attacks that can be taken. This is a constant we know, 1.
T is the time it takes for D to occur, or the length of the gcd which using the number you provided would be 2.47.
This then gives us S, which is the speed or rate of attack in the form of how many attacks/actions or how much of one occurs with a single unit of T, or in a second in this case.

1/2.47 = 0.404858...

Now increase the speed by 50%.

0.40485 ...x1.5 = 0.60728745
That results in 0.607... actions per second

To then find the new GCD, or time per action, divide a second by the actions-per-second since actions-per-second flipped is seconds-per-action, which is what GCD is.

1/0.60728745 = 1.6467...

So the GCD with the 50% speed increase is approximately 1.6467 and not 1.235.

Over 15 seconds that is 9 attacks which is 1.5 times the number of attacks.

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Originally Posted by TouchandFeel

Snip

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I believe we are doing the similar things, except I've left the time to complete an action arbitrary to get a forumula relating unbuffed time to complete a GCD to buffed time to complete a GCD.

*officially gives up on math*

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Originally Posted by whiskeybravo

*officially gives up on math*

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The more you know the less it seems daunting! Don’t give up!

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Originally Posted by Chrono_Rising

The more you know the less it seems daunting! Don’t give up!

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The more you know indeed.

After doing some messing around in game, I think Reynhart and myself are correct.

What we've been talking about with speed may be true in some situations, but if we look at the description of "speed" increasing effects in game they are either:

A) Flat GCD reduction (MCH rapid fire GCD flat 1.5 sec GCD, AST lightspeed flat 2.5 GCD reduction)
B) Cast/Recast % reducing effects (DRK blood weapon, MNK greased lightning, WHM presence of mind, AST arrow card)

I think the formulas being discussed might be relevant for A skills, but since the text for B skills actually reads "reduces cast time" I decided to check the numbers:

DRK
GCD = 2.38 sec
Blood Weapon GCD = 2.14 sec

MNK
GCD = 2.33 sec
GL1 = 2.21 sec
GL2 = 2.09 sec
GL3 = 1.98 sec

WHM
Cure 1 = Cast 1.97 sec Recast 2.46 sec
Presence of Mind Cure 1 = Cast 1.57 sec Recast 1.96

AST
Benefic = Cast 1.99 Recast 2.48
The Arrow Benefic = Cast 1.79 Recast 2.23
(my Ast is 32 :p)

So what Reynhart (I presume) was referring to with increasing speed is the actual reduction of our GCD. And the math works out:

DRK
2.38 * .90 = 2.142
(D/T=S says 2.163)

MNK
2.33 * .95 = 2.2135
2.33 * .90 = 2.097
2.33 * .85 = 1.9805
(interesting)

WHM
1.97 * .80 = 1.576
2.46 * .80 = 1.968

AST
1.99 * .90 = 1.791
2.48 * .90 = 2.232

So, I think we can all be at least half-right ;)

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Originally Posted by whiskeybravo

What we've been talking about with speed may be true in some situations, but if we look at the description of "speed" increasing effects in game they are either:

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I'm not disagreeing with Reynhart.

The effects you are listing are time decreasing effects, their effects on speed are characterized by a different relationship. Blood weapon decreases the recast time, indirectly we can think of the "speed" as increasing but its not by the same factor, in fact the factors are reciprocals of each other. In your last post you were discussing a "speed" bonus. Looking at blood weapon: Decreases recast time by 10% (recast time multiplied by a factor of .9) What does this do to our speed? Let our recast time be t then our "speed" to complete a GCD would be

1/t (1 GCD per unit of time t)

Our speed when recast time is decreased by 10% would be:

1/(.9t) = 1.111*1/t

In other words decreasing the recast time is equivalent to increasing the speed of attack by the reciprocal of the factor which decreased our speed. Speed buffs and time delay buffs are related but different things.

Think of it this way: I'm driving on a highway at 60 miles an hour, if I buff my speed by 50% I'll travel 90 miles an hour. If I need to travel 180 miles it will take me 3 hours at 60 mpg.

@60mph it takes me 3 hours to travel 180 miles.
@90mph it takes me 2 hours to travel 180 miles

If I increase my speed by 50% I do not increase my time spent traveling by 50% ( at 90 mph it doesn't take me 4.5 hours to arrive at my destination) but I also do not decrease my time spent traveling by 50% (which would be an 1.5 hours).

Increasing my speed by 50% (30 miles per hour) decreased my travel time by 33.333% (my time spent traveling decreased by an hour). My increase in speed can be represented by a factor of 1.5, my time spent traveling can be represented by a factor of 1/1.5 (or 2/3).

I absolutely love the idea of making blood price/weapon a passive trait. Allowing drk to gain blood faster will definitely make it a faster, more engaging class than it is now. Looking at the dev point of view though, it’s very unlikely such a change will be implemented... :(

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Originally Posted by Chrono_Rising

The effects you are listing are time decreasing effects, their effects on speed are characterized by a different relationship. Blood weapon decreases the recast time, indirectly we can think of the "speed" as increasing but its not by the same factor, in fact the factors are reciprocals of each other.

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Perhaps it was just a semantic mistake. But now that I know there is a distinct difference between our GCD and the actual concept of speed I'll be more careful.

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Originally Posted by XykeVayaris

I absolutely love the idea of making blood price/weapon a passive trait. Allowing drk to gain blood faster will definitely make it a faster, more engaging class than it is now. Looking at the dev point of view though, it’s very unlikely such a change will be implemented... :(

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Not to mention, it gives DRK an entirely unique niche. Shame something like this wouldn't be implemented outside an expansion, I fear. :(

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Originally Posted by Chrono_Rising

Snip

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Precisely.

It's all about properly interpreting and translating the information and avoiding potential mix-ups based on wording, terminology or conceptualization.

As you pointed out, reducing the time it takes to complete an action by a percentage is different than increasing the speed that actions occur by that same percent. While they conceptually seem like the same thing, since a decrease in time for an action to occur is an increase to the speed at which actions occur, they are calculated differently.

So while the statement that "increasing speed by 50% will result in twice the amount of attacks" is false, saying that "decreasing the time it takes for attacks by 50% will result in twice the number of attacks" is true. While the difference may seem like "semantics", the two statements are actually saying very different things.

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Originally Posted by TouchandFeel

While the difference may seem like "semantics", the two statements are actually saying very different things.

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Technically, yes. As it relates to this game, however, there isn't such a thing as "speed". An increase in attack speed is only achieved by reduction of our GCD. Obviously if we say we are increasing skill speed or spell speed by 50% then that has it's own equation for how it affects the GCD, and you say "increased skill/spell speed by 50%". Applying a real-life physics equation for determining "attack speed" is adding a variable that doesn't actually exist in game.

But it was mainly just me operating under the assumption that all speed increasing effects are the same. I'm sure at some point my brain saw "reduces recast time by 10%" and simplified it to "increases speed X%" for all of them. It wasn't till I recently went back and saw it doesn't actually mention speed at all, but rather the proper cast/recast terminology.

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Originally Posted by whiskeybravo

Technically, yes. As it relates to this game, however, there isn't such a thing as "speed". An increase in attack speed is only achieved by reduction of our GCD. Obviously if we say we are increasing skill speed or spell speed by 50% then that has it's own equation for how it affects the GCD, and you say "increased skill/spell speed by 50%". Applying a real-life physics equation for determining "attack speed" is adding a variable that doesn't actually exist in game.

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Yes, the rate/speed debate is one which we don't know if it exists in the game except as a calulation tool. The point I think both TouchandFeel and myself are trying to make is that this is actually fine as long as we keep our definitions straight. However, as a calculation tool speed increasing effects are exactly the same as increasing the GCD, a 50% increase in speed is a 50% increase in the number of GCDs completed, so all the reciprical arguments for speed and time are the same for time and number of GCDs.

The point though is that to keep the point straight we just need to agree on definitions and stick to them, otherwise this is where confusion can come from on both sides of the conversation. The numbers are only as good as the definitions are clear. Sorry if I seemed overly concerned with the definitions and what was being buffed where, I was just trying to keep things as straight forward as possible.

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Originally Posted by Chrono_Rising

The point though is that to keep the point straight we just need to agree on definitions and stick to them, otherwise this is where confusion can come from on both sides of the conversation. The numbers are only as good as the definitions are clear. Sorry if I seemed overly concerned with the definitions and what was being buffed where, I was just trying to keep things as straight forward as possible.

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Oh it's no problem, I am always eager to learn but usually leads to getting in over my head because once I start I gotta get to the bottom of it! Lol

Chrono,

your DRK suggestions on this forum are by far the best I have seen. Not just in this thread, but also this one.

I have played DRK a few times more and started to like the rotation. Still feeling squishy or rushed on TBN, just doesn't feel reliable.

I hope to see same of the suggested changes in 4.2!

Thanks for your good work!

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Originally Posted by ArianeEwah

Chrono,

your DRK suggestions on this forum are by far the best I have seen. Not just in this thread, but also this one.

I have played DRK a few times more and started to like the rotation. Still feeling squishy or rushed on TBN, just doesn't feel reliable.

I hope to see same of the suggested changes in 4.2!

Thanks for your good work!

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Thank you!

Speaking of which.. All that doesn't change your calculations regarding a passive Blood Weapon trait, does it? (tried finding the post where you math'd it out but couldn't)

It doesn't significantly change my opinion. As I said earlier I believe that I underestimated the gain of the time delay increase, but again, time delay buffs are very fight dependent. In a fight with no breaks this would be a large buff to darkside, in a fight with multiple breaks (ex death or neo ex death) the time delay increase would not be as valuable. The world where Dark Knight is in the same dps range as paladin and warrior is between 10 pps (low end) to 20 pps (high end), I include this for perspective on the following numbers.

Here is what I can say about the passive buff:
1. Without factoring in the time delay blood weapon as a passive trait would be an increase of about 16 pps.
2. Factoring in a time delay into the passive trait of blood weapon would be in the area of 30 pps.

30 pps is high (though only achievable when there is no down time) and would put dark knight at about 200 dps ahead of warrior. I am slightly move convinced that the time delay or resource generation might need to come down slightly.

I just want to keep in mind, numbers can always be adjusted, the above analysis assumes blood weapon would be ported in without any sort of adjustment anywhere else. Its less about the specific numbers and more about the idea/direction of changes.

Indeed. I think it's actually a cool idea, it adds more of an dps stance feel to turning off grit.

i think drk should be a dps magic user with good tanking abilties

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Originally Posted by PrincessBloom

i think drk should be a dps magic user with good tanking abilties

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I can agree with that to an extent. More dark magic in its life. Something like the Ragna Blade from Slayers.