Health of Cogs

Cogs have certain amount of health that depend on their level and are determined by certain mathematic formulas. The table below shows the health of every existing Cog level.

Level	Health
Level 1	6
Level 2	12
Level 3	20
Level 4	30
Level 5	42
Level 6	56
Level 7	72
Level 8	90
Level 9	110
Level 10	132
Level 11	156
Level 12	196
Level 13	224
Level 14	254
Level 15	286
Level 16	320
Level 17	356
Level 18	394
Level 19	434
Level 20	476

Formulas

Level 1-11 Cogs

A graph showing the health growth functions of Cogs by their level.

The formula for health of Cogs from levels 1 to 11 can be:

f(x) = x2 + 3x + 2

or in a simplified way:

f(x) = (x + 1) * (x + 2)

where x is the Cog's level and f(x) is a function that returns the Cog's health value.

For example, the formula works in the following method to determine the health of level 4 Cogs.

f(4) = (4 + 1) * (4 + 2)

f(4) = (5) * (6)

f(4) = 30

Level 12+ Cogs

Level 12 Cogs previously had a 10% boost in health, putting them at 200. As of the 3.0.0 update that was released on December 3, 2021, which introduced balancing changes, level 12+ Cogs now have a unique formula to determine their health.

The formula for health of level 12+ Cogs can be:

f(x) = x2 + 3x + 16

which is the same as the formula for levels 1 through 11, but has an increase of 14 units in Y value for every unit of X. Unlike the former formula, it has no roots.

The simplified formula can also be represented as:

f(x) = (x + 1) * (x + 2) + 14

For example, the formula works in the following method to determine the health of level 16 Cogs.

f(16) = (16 + 1) * (16 + 2) + 14

f(16) = 17 * 18 + 14

f(16) = 306 + 14

f(16) = 320