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made for a basil question, hope my math checks out
in retrospect it would have been better to do it the other way around instead of inverting the whole thing at the end
ideally you want your number to be the same as the cost of 1 extra %stat divided by the cost of 1 extra att
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Your formula should be correct, but can be simplified to a * s / 25 / [4*s*(1+p/100)+d].
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If it's not too much to ask for, could you upload the excel for us?
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Heero Wrote:If it's not too much to ask for, could you upload the excel for us?
no big secrets here, the cell formula's even on the image
here you go anyway (xlsx): http://www.mediafire.com/?e4ci8rm9fken2ix
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If InnerAbilityAtk = CharChardAtk = 0 cannot be assumed, the solution will be
TotalAtk * 4 * Main / (100+AtkPct) / (4*TotalMain + TotalSub)
= [Atk + (InnerAbilityAtk + CharCardAtk) / (100+AtkPct)] * 4 * Main / (4*TotalMain + TotalSub)
Bolded term is what changes, and Atk is +attack from gear & skills only.
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Only for what ever STR based class you're using or what..?
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MountLag Wrote:If InnerAbilityAtk = CharChardAtk = 0 cannot be assumed, the solution will be
TotalAtk * 4 * Main / (100+AtkPct) / (4*TotalMain + TotalSub)
= [Atk + (InnerAbilityAtk + CharCardAtk) / (100+AtkPct)] * 4 * Main / (4*TotalMain + TotalSub)
Bolded term is what changes, and Atk is +attack from gear & skills only.
uh.. sorry, what is this?
no explanation or anything
also, is it known that %att doesn't affect card and ia?
fodjgngf Wrote:Only for what ever STR based class you're using or what..?
works for all classes, but maybe not for xenon
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change in range per change in X = partial derivative of range equation
Set the partials equal to each other and solve for dX when dY = 1 to obtain the change in X that is equivalent to a 1 unit change in Y.
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MountLag Wrote:change in range per change in X = partial derivative of range equation
Set the partials equal to each other and solve for dX when dY = 1 to obtain the change in X that is equivalent to a 1 unit change in Y.
Close, but no cigar. This would tell you WHEN an increment by one in either stat will result in a similar change in damage range, not how much one of them should change by to match the unit change of the other. Key: Setting the partials (the amount of change of damage per UNIT change in each variable) equal to each other.
[spoiler=maths don't lie] ![[Image: cpq3kyx.png]](http://mathurl.com/cpq3kyx.png) [/spoiler]
I believe what we have to do instead is to integrate both sides of the the partial wrt primaryStat from currentDmg to finalDmg to get the change in damage to correspond to the appropriate change in primaryStat.
![[Image: cgw2e56.png]](http://mathurl.com/cgw2e56.png)
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Instead of trying to obtain a change in primary stat, s1, via derivatives, in this case it is cleaner to set the %stat as a separate variable, then obtain the partial derivatives from there on.
Or in this case, since there's little point trying to complicate things via partials (although it is legit), a simple (1 + K + deltaK)*s1 will do, where K is the %stat in decimals, assuming you're only doing a single-variable change.
Maybe someone should just bother to do a spreadsheet that combines all the partial derivatives together to compare two items up for grabs.
Hadriel
[Math never lies... unless you lied to yourself =P]
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Kalovale Wrote:Close, but no cigar. This would tell you WHEN an increment by one in either stat will result in a similar change in damage range, not how much one of them should change by to match the unit change of the other. Key: Setting the partials (the amount of change of damage per UNIT change in each variable) equal to each other.
[spoiler=maths don't lie][/spoiler]
I believe what we have to do instead is to integrate both sides of the the partial wrt primaryStat from currentDmg to finalDmg to get the change in damage to correspond to the appropriate change in primaryStat.
I set them equal to each other is because we are assuming change in range is equal. So I did deltaR = deltaR -> A*deltaX = B*deltaY -> deltaX = B*deltaY/A -> deltaX = B/A when deltaY=1.
The result from your last pic goes deltaR = A*deltaX -> deltaX = deltaR/A. Substituting deltaR=B*deltaY in gives deltaX=B*deltaY/A -> deltaX=B/A when deltaY = 1, which would give the same result as what I did.
I just treated dX and deltaX as interchangeable because I was lazy. Thanks for showing that they really are interchangeable with that integral down there.
hadriel Wrote:Instead of trying to obtain a change in primary stat, s1, via derivatives, in this case it is cleaner to set the %stat as a separate variable, then obtain the partial derivatives from there on.
Or in this case, since there's little point trying to complicate things via partials (although it is legit), a simple (1 + K + deltaK)*s1 will do, where K is the %stat in decimals, assuming you're only doing a single-variable change.
Maybe someone should just bother to do a spreadsheet that combines all the partial derivatives together to compare two items up for grabs.
Hadriel
[Math never lies... unless you lied to yourself =P]
Yeah I split S1 into s1*(1+K) in order to get the partial with respect to K in like 1 line. Except the variables were names S1 = TotalMain, s1 = Main, and K = MainPot in my thingy.
And for a spreadsheet it would be probably be easier to just compute the ranges for 2 different items directly than using partials. Computing it directly takes 1 computation total, computing it with partials takes 1 computation per variable involved. The partials change every time a variable is changed.
Not a bad way of checking if the maths are correct though.
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Oh oops then. Didn't exactly bother to see what's within the code because I'm not sure if I'm meant to look that closely at it either.
Hadriel
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MountLag Wrote:I set them equal to each other is because we are assuming change in range is equal. So I did deltaR = deltaR -> A*deltaX = B*deltaY -> deltaX = B*deltaY/A -> deltaX = B/A when deltaY=1.
The result from your last pic goes deltaR = A*deltaX -> deltaX = deltaR/A. Substituting deltaR=B*deltaY in gives deltaX=B*deltaY/A -> deltaX=B/A when deltaY = 1, which would give the same result as what I did.
I just treated dX and deltaX as interchangeable because I was lazy. Thanks for showing that they really are interchangeable with that integral down there.
The changes (deltaX and deltaY) being proportional is definitely true; "setting the partials equal to each other" was just a mathematical miswording, I suppose, because it doesn't say what you meant to say.
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Yeah I wasn't consistent in my definitions in that post, so it's easy to see why it could be misinterpreted.
MountLag Wrote:change in range per change in X = partial derivative of range equation suggests the partial is just A
Set the partials equal to each other and solve for dX when dY = 1 to obtain the change in X that is equivalent to a 1 unit change in Y. suggests partial is not A but is A*dx
Sorry for the poor wording there lol
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calc isn't my forte..
is what I did in the spreadsheet incorrect/naive?
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Our solutions are equivalent to each other.
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Let's put it this way. You want to convert from degrees Fahrenheit to degrees Celsius. I can either give you the formula, or give you a conversion table. If you want the quick and dirty, you'll use the table; if you want precision, you'll use the formula. Both have their uses.
Your method works, but is not mathematically efficient. You're basically doing a contour plot of the function dA/dk = [4pA / (4p*(100+k) + s)], where p = primary stat, A = (magic) attack, and k is %stat, and with k (%stat) and A ((M)ATT) as the axes. In words, you're doing a plot to map out the amount of change of A for every unit change in k. This was derived from a simple division of the derivatives, (dD/dk) / (dD/dA). Just some intermediate calculus [I think...? My education is a tad different from everyone else I think...]. A pity WolframAlpha doesn't accept Mathematica commands anymore, else you can see for yourself what I'm talking about... But because linearity holds, your spreadsheet allows a user to directly multiply values with the multiple of %stat, so that one isn't merely confined to 1%stat, something that plots don't easily tell but tables of numbers do.
But with upcoming changes, you will eventually find that comparing %stat to (M)ATT will become even less valuable than what little value it holds right now.
Hadriel
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![[Image: l6vgG4G.png]](http://i.imgur.com/l6vgG4G.png)
