Graphing and solving for 2-3 unknown variables in dimishing returns given 3 plot points

[potty_mousie]

Hello, I am trying to solve damage reduction formula for the mobile game RAID who don't release the exact formula for damage reduction. In their video, they gave

1) Damage Reduction (DR) of 15% at 290 Defense (DEF)
2) Damage Reduction (DR) of 30% at 655 Defense (DEF)
3) Damage Reduction (DR) of 45% at 1500 Defense (DEF), Where I estimated 1500 using basic proportions math from their bar graph they provided.

Assuming everything they provided is correct, we know it is a diminishing return.
A common formula for these kinds of games is

DR = A * DEF / (B * DEF + C)

Assuming this formula is correct (which may not be and please correct), I believe we can use the above provided data to plug into this formula somehow to find the 3 different variable. How to do so, and what's the answer? I've tried manual trial and error and so far I've gotten close with
A ~ 0.026
B ~ 0.03
C ~ 40

Please help. I can't stop thinking about it.

 

[Cubist]

The method you need is called "Simultaneous Equations". Before starting I would rearrange your formula to look like the bold line below...

DR = A * DEF / (B * DEF + C)
DR * (B * DEF + C) = A * DEF

B * (DR * DEF) + C * (DR) = A * (DEF)

Write the above formula out three times, once for each of the three scenarios that you list, substituting the values for DR and DEF. Then apply one of the methods for solving simultaneous equations and you should get exact values for A, B and C.

The only way to test if your equation holds in all situations would be to test it with more scenarios.

 

[potty_mousie]

Thanks, I tried that. That's just a simple 3 equations 3 unknown and substituting accordingly. I even searched and used 3 eq. 3 unknown calculator, even did it by hand, apparently, it has no solutions because of the nature of the graph?

 

[potty_mousie]

See below, but we know it's not correct because if it plot it on graph, it shuold be diminishing return like a log graph.

https://www.emathhelp.net/calculato...0,-655a+196.5b+.3c=0,-1487a+669.15b+.45c=0&v=

it gives solutions
a=0
b=0
c=0

which i believe corresponds to the x/y-intercept because that's the only time the graph hits there.
But that's not the solution to the damage reduction formula.

 

[Cubist]

Hmm...

[math] \frac{a\cdot D}{b\cdot D+c} = \frac{D}{\left(\frac{b}{a}\right)\cdot D+\left(\frac{c}{a}\right)} [/math]
So there's really only two constants in your equation.

[math] \mathit{D_R}=\frac{\mathit{D_{EF}}}{\mathit{D_{EF}}\cdot \mathit{c_1}+\mathit{c_2}} [/math]
Maybe this will help you to determine them, using only two of your scenarios. Then try the third scenario with the values to see if your equation is a good model.