Topic: Crusaders of the Lost Idols /
When to level cheaper 2nd DPS before main DPS

Continuing from

http://www.kongregate.com/forums/12051-crusaders-of-the-lost-idols/topics/545131-threshold-for-using-2nd-dps
At certain thresholds, if your 2nd DPS does enough damage and is cheaper than your Main dps (after the 25 lvl adjustment), then it is more efficient to level the 2nd DPS first.

**Table 1** below show the threshold for when to level your cheaper 2nd dps to the next 25 lvls first. e.g. if hermit is your main DPS and Jim your 2nd and does >44.2% of your hermit's damage, you should level up Jim first

Sarah Jim WW Sasha Kaine Natalie Jason 2nd DPS
Hermit 69.4% 58.0% 48.1% 25.9% 19.6% 14.2% 9.8%
Sarah 82.8% 67.7% 34.3% 25.2% 17.8% 12.0%
Jim 81.5% 40.0% 29.0% 20.2% 13.3%
WW 47.8% 34.0% 23.2% 15.1%
Sasha 67.1% 42.0% 25.0%
Kaine 60.5% 33.9%
Natalie 52.5%
Main DPS

**Table 2** below shows the level offset of the top DPS crusaders, e.g. Sarah is 2 levels cheaper than Hermit, and Natalie is 11 levels cheaper than Jim

Sarah Jim WW Sasha Kaine Natalie Jason 2nd DPS
Hermit -2 -4 -5 -9 -12 -15 -19
Sarah -2 -3 -7 -10 -13 -17
Jim -1 -5 -8 -11 -15
WW -4 -7 -10 -14
Sasha -3 -6 -10
Kaine -3 -7
Natalie -4
Main DPS

This means you can get the cheaper 2nd DPS to the next 25 faster and boost your dps, then depending how much faster and how much the boost is, you may get your main DPS to the next 25 faster than if you leveled the main DPS first.

**Table 3** below shows the exact percentage to the next 25 lvls given equivalent level after 25lvl per crusader adjustment. e.g. lvling Kaine up by 25 lvls cost 39.7% as much as Sarah

sarah jim ww sasha kaine natalie jason
hermit 86.3% 80.0% 73.7% 54.2% 46.1% 37.5% 28.8%
sarah 92.7% 85.4% 62.8% 53.4% 43.5% 33.3%
jim 92.1% 67.7% 57.6% 46.9% 36.0%
ww 73.5% 62.5% 50.9% 39.0%
sasha 85.1% 69.3% 53.1%
kaine 81.5% 62.4%
natalie 76.6%

Maths

let your main DPS = 1, and your 2nd DPS = x (0 < x < 1)

let cost (hence time) of Main to the next 25 = 1, and cost of 2nd = y (0 < y < 1)

=> Current DPS = 1+x

=> Time required for lvling both main and 2nd with current DPS = 1+y

now we calculate time required to get both Main and 2nd to the next 25 taking account of increased DPS from the 4x bonus when 1 of them gets to 25.

lvling main first:

initial cost = 1, initial DPS = 1+x,

remaining cost = y, boosted DPS for remaining cost = 4 + x

i.e. t1 = 1/(1+x) + y/(4+x)

lvling 2nd DPS first:

initial cost = y, initial DPS = 1+x,

remaining cost = 1, boosted DPS for remaining cost = 1 + 4x

i.e. t2 = y/(1+x) + 1/(1+4x)

we want t2 < t1 so that 2nd DPS can be lvl up first, what is the minimum value of x required?

y/(1+x) + 1/(1+4x) < 1/(1+x) + y/(4+x)

y + (x+1)/(4x+1) < 1 + y(x+1)/(x+4)

(y-1)(x+4)(4x+1) + (x+1)(x+4) < y(x+1)(4x+1)

(y-1)(4x^2+17x+4) + (x^2+5x+4) - y(4x^2+5x+1) < 0

use the quadratic formula: (-b-sqrt(b^2-4ac))/2a

a = 4(y-1) + 1 - 4y = -3

b = 17(y-1) + 5 - 5y = 12(y-1)

c = 4(y-1) + 4 - y = 3y

thus: x > (12(1-y) - sqrt(144(1-y)^2 + 36y)) / -6

All it remains is to plug in the value of y from

**Table 3** to calculate the minimum DPS thresholds found in

**Table 1**