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Recursion describes the interaction of percentage-modifying stacking of champion statistics. To have a recursion you need 2 or more multipliers, each one increasing the other's effect, infinitely but with diminishing returns.


All formulas of different interactions can be found by making an equation system of all the variables. For example considering Master Yi OriginalSquare Master Yi's Wuju Style Wuju Style and Guinsoo's Rageblade item Guinsoo's Rageblade old effects (the first giving bonus % total attack damage and the second giving % bonus ad) we have this:

Wuju Style increases total attack damage, so we have: WujuBonus = (base + bonus + GuinsooBonus)  ×  WujuStyle's multiplier

Guinsoo instead increases bonus attack damage: GuinsooBonus = (bonus + WujuBonus)  ×  Guinsoo's multiplier

By resolving the system you find the values of WujuBonus and GuinsooBonus based on your base and bonus attack damage. The total attack damage is going to be = base + bonus + WujuBonus + GuinsooBonus which is:

$ \pagecolor{black}\color{White} {{BaseAD \times (1 + Wuju Multiplier) + FlatBonusAD \times (1 + Wuju Multiplier) \times (1 + Guinsoo Multiplier)} \over {1 - (Wuju Multiplier) \times (Guinsoo Multiplier)}} $

The numerator is the simplest since you multiply the base or bonus attack damage by their multipliers, while the denominator changes depending on how many recursion interactions are there. With two it's 1 - (Wuju Multiplier) × (Guinsoo Multiplier). With three (e.g A, B and C) it's:

$ \pagecolor{black}\color{White} 1 - A \times B - A \times C - B \times C - 2 \times A \times B \times C $

Other recursions

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