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

[TouchandFeel]

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.

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.

[whiskeybravo]

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

[TouchandFeel]

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.

[whiskeybravo]

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.

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:

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.

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.

[Chrono_Rising]

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.

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%).

[TouchandFeel]

snip

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.

[Chrono_Rising]

Snip

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.

[whiskeybravo]

*officially gives up on math*

[Chrono_Rising]

*officially gives up on math*

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

[whiskeybravo]

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

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 )

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