I have a few things to say in this post. The first being there are DAEMON X MACHINA Spirits that will show up soon to promote the game. I'll log them once they come out.

Second, for JigglyNinja, is it accurate to say that, in a match where character A is fighting character B and they both have spirits, A's overall RDO is equal to A's RDO divided by B's RDO and vice versa for B? Example Akuma v Akuma would be 1 (17.442/17.442), Akuma v Dark Emperor is 1.395 (17.442/12.503) or 0.7168 for Dark Emperor v Akuma.

Third I redid the RDO equation but did it in terms of Defense just to check both sides. After doing the calculus, it came out to be D ~= 0.5P + 417. Assuming D = P - A, A = 0.5P - 417

D = P - (0.5P - 417)

D = P - 0.5P + 417

D = 0.5P + 417

Both sides check out. You can use either the A or D equation and get the result for the other by subtracting it from P. Also the 417 is more accurately represented by 10000/24 or 1250/3, equaling 416.66... It's a very small difference and it doesn't change any rankings. Only thing it does clean up some of the 'true RDO'/'ideal RDO' ratios, namely the ones that are close to 96% which ended up being 96.0000014% and turn into a clean 96% with the fraction. Again, very small difference and you were probably going to cut off anything past the second decimal place anyways; it is safe to stick with 417.

Fourth I was intrigued by the symmetry of the A and D equations, so I tried my hand at generalizing the generalized RDO equation, allowing for any coefficient for both Atk and Def. The resulting equation is:

A = (P*C.a*C.d + C.a - C.d) / (2*C.a*C.d)

C.a and C.d are the coefficients for Atk and Def respectively. Solving for A where P = 10000, C.a = 4E-4, and C.d = 6E-4 gives A ~= 4,583, the same as the first RDO equation. Solving for A and keeping P variable gives A = 0.5P - 417, same as the second RDO equation.

(I can take a picture of my notes if anyone wants to see how I worked it out. I didn't want to type it out since it would like alphabet soup)

Fifth and last, again for JigglyNinja, you mentioned (below) how the stat after an ability multiplier is equal to the stat + a constant, times the multiplier, and - a constant, or ((S+C)*M)-C. I've been trying to work out how you came to this formula. I'm not denying that it works, plugging things in gives the same answers as my previous method of multiplying it out and then going in reverse, I just want to understand how it was derived. My attempts at getting the same thing always have something off about them. If you don't mind, could you walk me through how you got it?

The stats don't work like that because they are an **addition** to the damage you do, not an overall multiplier. The +1 in the equation means you need to add a constant value, then perform the multiplication, then subtract the constant back out. 850 Attack with a 1.1 multiplier should do as much damage as a 1,185 Attack spirit. For Attack the constant is 2,500 (1 / 0.0004) and for Defense it is 1,667 (1 / 0.0006). The conversion for 850 Attack with a 1.1 multiplier is (850 + 2500) * 1.1 - 2500 = 1185.