Forsaken math post: At what cost are distorted Undead (with the same modifiers) better than distorted Animalistic? When are Animalistics stronger?
TL: DR Undead are better when cost is below 16EE. At costs greater than 16EE, Animalistic are stronger for the same cost. These breakpoints happen at 60 Disgrace for Animalistic, or 40 Disgrace for Undead.
f you're instead comparing Undead to the full Stamina summon of a Flexible Peacemaker (Playful Energy), the breakpoint is instead 4EE (4). This cost is at 80 Disgrace for Animalistic or 60 Disgrace for Undead.
The math is below this line.
The difference of cost between the two of 1/4 is equivalent to Undead having 20 higher Disgrace than Animalistic. (1).
20 higher Disgrace means that at the same cost, Undead will have 40 higher Reputation Strength. (2)
The two have different multipliers. The Undead multiplier on damage, assuming a relevant Distortion, is 1.5. The Animalistic multipliers on damage, assuming a relevant Distortion, is 1.5*1.5 = 2.25. Multiply these values times the formula for the Reputation Strength and you'll have a way to compare. Their modified Reputation Strengths (3) are equal at Disgrace 60, corresponding to a Forsaken costing 16EE.
(1) The EE cost formula for standard/Animalistic Forsaken is (1000)(1/2)^(x/10), where x is the Disgrace. The same formula for Undead Forsaken is (250)(1/2)^(x/10). If we increase the Disgrace of an Animalistic Forsaken by 20, we get the expression
(1000)(1/2)^[(x + 20)/10]
(1000)(1/2)^(x / 10 + 20/10)
(1000)(1/2)^(x/10 + 2)
1000(1/2)^(x/10) * (1/2)^2
1000(1/4)(1/2)^(x/10)
= 250(1/2)^(x/10) -- same as the Undead formula.
(2) The formula for Reputation Strength is just (200 - 2x)%.
(3) The modified Reputation Strength ( y ) of an Animalistic would be 2.25(200 - 2x).
The modified Reputation Strength of an Undead with the same cost would be 1.5(200 - 2x + 40), since the 20 lower disgrace will improve Reputation Strength by 40 (keeping cost the same).
Then solve the system of equations:
y_1 = 1.5(200 - 2x_1 + 40)
y_2 = 2.25(200 - 2x_2)
I won't work out that algebra here, but the solution is the point (60, 180), meaning they both have a modified Reputation Strength of 180 at a Disgrace of 60 (80 for Undead). This corresponds to a cost of 16EE for both Chosen.
(4) If you want to compare Undead to the first summon of Negotiated (Playful Energy) Animalistic, the new multiplier is 1.5 * 2 = 3. So that is just the solution to the system:
y_1 = 1.5(200 - 2x_1 + 40)
y_2 = 3(200 - 2x_2)
The solution to this system is the point (80, 120), meaning that they're equal when the Animalistic has 80 Disgrace (the Undead will have 60). This corresponds to a cost of 4EE for both.