Champions

Champions can be hired to automatically attack Teemo for you. There are 3 types of champions; Attack Damage [AD], Ability Power [AP], and Hybrid (AP/AD). A champion will become stronger from items based on their type. They can also be leveled to increase the amount of damage they do and unlock personal upgrades at higher levels. They have a base cost which increases exponentially and base gold per second [GpS] which increases linearly.

Cost
The cost of the champion increases exponentially using the following formula:

$$Cost = base * 1.2^{current.level}$$

For example, Ryze has a base cost of 10 gold. His cost at level 20 would be:

$$Cost = 10 * 1.2^{20} = 10 * 38.37 = 383.7 gold$$

Gold Per Second
The GpS a champion provides increases linearly using the following formula:

$$GpS = base * current.level$$

For example, Ryze has a base GpS of 0.1. His GpS at level 20 would be (assuming his upgrade was not purchased and no items):

$$GpS = 0.1 * 20 = 2 GpS$$

Although a simple calculation and not much of an increase in GpS, buying items can buff champions significantly and their respective upgrades double their GpS.

AD/AP Scalings
Champions scale with either AD, AP or both to increase their gold generation:
 * AD champions gain 1% increased GpS for every 50 AD.
 * AP champions gain 1% increased GpS for every 33.3 AP.
 * Hybrid champions have both of the above scalings, and gain 1% increased GPS for every 50 AD plus 1% increased GpS for every 33.3 AP.