WoL Spirits: Stats and Trait/Skill/Style Multipliers

[JiggyNinja]

I'm amused at how frequently Absolutely Safe Capsule is always the odd one out. RDO? Worst. Rank 4 multiplier? 2.046 instead of 2.5. Only summon spirit that needs another summon. Doesn't benefit from same series bonus. What other things is ASC an outlier in?

And it doesn't even have any secondary slots! You can't do anything with it! At least things like Akuma and Galacta Knight have beefy stats with literally 2.5x the RDO of ASC. (ASC = 7, Akuma = 17.4, Galacta = 15.7, 17.2 if you factor in the 10% sword boost).

Pure stats, the most powerful spirits of each type are Akuma, Galacta Knight, and Deoxys (Normal Forme). Unfortunately all 3 of those have no secondary slots. The most powerful with at least 2 secondary slots (for hazard immunity) are Cutie J, Big Boss, and Hades Final Form (or Zelda Orcarina of Time if want to pass up the Trade-Off ability).

 

[CanvasK]

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.

 

[JiggyNinja]

There's no L in my name.

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.

Correct. The RDO figure was designed to be a multiplicative. It also means that any buffs or debuffs can by multiplied right into it. For characters like Marth, Ike, or Meta Knight that use their sword for everything, a 10% weapon buff can be multiplied straight into it to calculate the overall damage output. Buffs that aren't so universal (like Fist Attack on Captain Falcon) would have to have their contributions derated.

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)

I will take your word for it. I've had enough of FOILing this equation.

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?

I did it in my head, but here's the formal derivation of it.

Spoiler

 

[CanvasK]

There's no L in my name

I never noticed. My bad. I saw your profile pic and just assumed it was the same.

I will take your word for it. I've had enough of FOILing this equation.

I did it in my head, but here's the formal derivation of it.

Spoiler

View attachment 239684

I don't blame ya. The only reason to generalize it like this for Amiibo, items, and final smashes since they all use different coefficients (at least for attack).

And thanks for going through the math for me. I think assumed some things, divided instead of multiplied, or something. But I'm on the same page now. No more needless reversing.

EDIT: DAEMON X MACHINA Spirits added, total is up to 1350. Also I changed 'Defense' Spirits to 'Shield' Spirits to match the game. Don't know why it wasn't like that to begin with.
Nothing special, most interesting thing is Bullet Walker has the 25th highest defense but that's it. Battles were interesting.

Radiant Gleam, Primary, Grab, Rank 2, 2 Slots, Jump ↑
   Atk 931 - 3725, Def 731 - 2927
Kloster (Grief), Support, Rank 3, 2 Slots, First-Strike Advantage
Bullet Walker (Brigadier General), Primary, Shield, Rank 3, 3 Slots, Shooting Items Power ↑
   Atk 845 - 2536, Def 1926 - 5779
High Line (Guns Empress), Support Rank 2, 1 Slot, Move Speed ↑

EDIT: Several days ago I noticed an odd interaction with Trade-Off Attacks ↑ with other skills. Further testing has shown that at certain thresholds the damage multiplier is reduced. This is also restricted to the kind of attack, such as Fire, Weapon, or Overall damage, so using Fist and Physical won't have their combined multiplier affected. After a total multiplier of 1.3 it is [mult]*0.5+0.65, after 1.5 it is [mult]*0.2+1.2. The top line is Poison Power Up which has a multiplier of 1.6, higher than the last threshold. I've updated the main post with this information.

EDIT: I've updated the sheet with the Tetris 99 Spirits. I-Tetrimino has the 2nd highest attack stat of any primary with a multiplier of 3.9936.

I-Tetrimino, Primary, Attack, Rank 3, 1 slot
   Atk 2494 - 7484, Def 831 - 2494
T-Tetrimino, Support, Rank 2, 2 slots, Screen-Flip Immunity
S-Tetrimino & Z-Tetrimino, Primary, Grab, Rank 2, 2 slots
   Atk 891 - 3575, Def 891 - 3575
L-Tettimino & J-Tetrimino, Support, Rank 2, 2 slots, Irreversible Controls 
O-Tetrimino, Primary, Shield, Rank 1, 0 slots
   Atk 330 - 1650, Def 990 - 4950