Math - help

[NuclearSilo]

So, i'm gonna play a game, i'm trying to figure out what's the best combination of stats to have the best dmg output.

Let's say you have 4000 stat points and you have to spread them over your stats. You know that each 10 Str gives you 1 dmg, each 100 agi +1% attack speed, each 100 energy +1% dmg amplify.
The dmg can be translate like this:
DMG = (base_power + X)*Y*Z where
X=STR/10
Y=1+(AGI/100)%
Z=1+(ENE/100)%
STR+AGI+ENE=4000

So, what's the max of DMG?

[poehalcho]

1400/10 * 1300/100 * 1300/100 = 140 * 13 * 13 = 23660 MAX damage
even a slight bit of like 141 * blaba*blabla = 23646
I suppose my awnser may be off by 1 or 2 since i didn't bother with decimal's but that's pretty near to where it gets...

[NuclearSilo]

how do you do that? To find 1400 1300 1300

[Jaapii]

Sorry if it's a stupid question but what's the value of the base_power?

[Goobronicus]

Highest I got was:

(1334/10) x (1333/100) x (1333/100) = ~23704

Just like volume, biggest volume is if all 3 are close to the same multiplier.

[NuclearSilo]

Sorry if it's a stupid question but what's the value of the base_power?

base_power is a variable independant from stats (like weapon or skill) but it can vary from 0 to even 10000

I just want to know how do you all found around 1300 coz the stuffs i said about attack speed, dmg amp are just an exemple. Is there any global equation to find these value?

[SM-Count]

You guys aren't even attempting to solve this. Easily shown that if x=2000 y=1000 z=1000 then you get 24k+.

Give you a hint, maximize the second part:

[Jaapii]

Y & Z actually are basicly the same, so if u spend stat points to Y or Z it doesn't matter much lulz
And if the base_power is over 1000, u should be taking Y (or Z) only, cuz then 100 agi points = 1% = 10 extra dmg, 100 str = 10 extra damage as well.
So I guess it's something like;
if base_power < 1000: put stat points in str.
base_power > 1000: put stat points in Y/Z
base_power = 1000: doesn't matter where u put ur stat points.
Isn't it something like that?

[SM-Count]

There is going to be a point where it's advisable to max y&z and not x, but since the question doesn't give use base_damage we just assume it's 0. The answer changes if base damage changes. Best way to do this is what I did but leave 'b' in and create the function, then differentiate to maximize. (Or by inspection without calculus)

[Stress]

Allright.

You have a multi-variable function, and you're trying to determine its maximum, when there is a link between the variables.
I don't have the time for all of the calculations, but here's an Idea: the Lagrange multiplier. Ever heard of it?

f(x,y,z)=(base_damage+x)*y*z;

x=STR/10
y=1+(AGI/100)
z=1+(ENE/100)

we have STR + AGI + ENE = 4000. Now, express STR, AGI and ENE in function of x, y and z respectively.

Now, take a look at this article, and do the calculations yourself:
http://en.wikipedia.org/wiki/Lagrange_multipliers

Good luck

[SM-Count]

You can do it without multivariable calculus if you're good at diophantine inspection, saves a lot of time.

[poehalcho]

how do you do that? To find 1400 1300 1300

I..uh...counted D: we haven't had these kind of things with maths yet, so I just tried by couting. I'm fairly good at guessing. but really, there's bound to be a formula for that stuff somewhere.

[Jaapii]

It is actually some kind of sequence (idk how it's called in english but I guess like that lolz, it's seq on my calculator )
if u(n-1) < 1000: u(n) = u(n-1) + X
u(n-1) > 1000: u(n) = u(n-1) * Y or Z
u(n-1) = 1000: doesn't matter.
and u(n) would be the damage, n = 400 in the first case, 40 in the 2nd.

[NuclearSilo]

Y & Z actually are basicly the same, so if u spend stat points to Y or Z it doesn't matter much lulz
And if the base_power is over 1000, u should be taking Y (or Z) only, cuz then 100 agi points = 1% = 10 extra dmg, 100 str = 10 extra damage as well.
So I guess it's something like;
if base_power < 1000: put stat points in str.
base_power > 1000: put stat points in Y/Z
base_power = 1000: doesn't matter where u put ur stat points.
Isn't it something like that?

uhm, no, it's not simple like that. You have to multiply with rest of the variable too.
So 100 extra str gives 10 dmg but the total dmg will be added by 10*Y*Z.
100 extra agi gives 1% attack speed and the total dmg (over time) will be added by (base+X)*0.1*Y
So what you need to compare is 10*Y*Z and (base+X)*0.1*Y but since both have different variables, how do you do to compare them?

@SM-Count: I can't resolve your equation Oo

[Snoopy]

Just seeing all these numbers makes me feel ill.