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## Notes

• This rune gives  an additional 11.2 - ∞ (based on Minutes) health thanks to .
• This rune gives a level 18  without any an additional 7 - ∞ (based on Minutes) AD thanks to . It's doubled at 100% up to 14 - ∞ (based on Minutes) AD
• With , this runes gives an additional 2.8 - ∞ (based on Minutes) AP
• This rune will give a either 2.5 - ∞ (based on Minutes) bonus magic resistance or 4 - ∞ (based on Minutes) bonus armor when he casts his , whether he's going for AD or AP.
• The granted total bonuses at each minute throughout the game are calculated as follows:
$\pagecolor{Black}\color{White}m \in \mathbb{R}_{\ge 0}$ is the number of elapsed minutes throughout the game.
$\pagecolor{Black}\color{White}k_{AP} = 8.0$ is the AP multiplier.
$\pagecolor{Black}\color{White}k_{AD} = 4.8$ is the AD multiplier.
$\pagecolor{Black}\color{White}S\left(m\right) = \sum_{s=0}^{\left\lfloor \frac{m}{10} \right\rfloor}{s}$ gives the stacking term.
$\pagecolor{Black}\color{White}B\left(k,m\right) = k \times S\left(m\right)$ gives the bonus term.
Bonus AP: $\pagecolor{Black}\color{White}B\left(k_{AP},m\right) = k_{AP} \times S\left(m\right)$.
Bonus AD: $\pagecolor{Black}\color{White}B\left(k_{AD},m\right) = k_{AD} \times S\left(m\right)$.
Example for bonus AP ($\pagecolor{Black}\color{White}k_{AP} = 8.0$) at 32.5 minutes ($\pagecolor{Black}\color{White}m = 32.5$):
$\pagecolor{Black}\color{White}B\left(k_{AP},m\right) = B\left(8.0,32.5\right) = 8.0 \times S\left(32.5\right) = 8.0 \times \sum_{s=0}^{\left\lfloor \frac{32.5}{10} \right\rfloor}{s}$
$\pagecolor{Black}\color{White}= 8.0 \times \sum_{s=0}^{3}{s} = 8.0 \times \left(0+1+2+3\right) = 8.0 \times 6 = 48.0$.
Example for bonus AD ($\pagecolor{Black}\color{White}k_{AD} = 4.8$) at 21.5 minutes ($\pagecolor{Black}\color{White}m = 21.5$):
$\pagecolor{Black}\color{White}B\left(k_{AD},m\right) = B\left(4.8,21.5\right) = 4.8 \times S\left(21.5\right) = 4.8 \times \sum_{s=0}^{\left\lfloor \frac{21.5}{10} \right\rfloor}{s}$
$\pagecolor{Black}\color{White}= 4.8 \times \sum_{s=0}^{2}{s} = 4.8 \times \left(0+1+2\right) = 4.8 \times 3 = 14.4$.
• non-Iterative formula:
m = ⌊min / 10⌋
stacks = (m^2)/2 + m/2
AD = 4.8 * stacks or 4.8 * ((m^2)/2 + m/2)
AP = 8 * stacks or 8 * ((m^2)/2 + m/2)
Python 3 function which computes $\pagecolor{Black}\color{White}B\left(k,m\right)$:
def gathering_storm_bonus(k, m): return k * sum(range(m // 10 + 1))
Gathering storm table:
Gathering storm bonus AP and bonus AD over the elapsing minutes of a game
Elapsed minutes Total bonus AP Total bonus AD
000.00.0
108.04.8
2024.014.4
3048.028.8
4080.048.0
50120.072.0
60168.0100.8
70224.0134.4
80288.0172.8
90360.0216.0