Formula for calculating DPS (damage per second)

[El Demente]

I am calculating damage per second (DPS) for a character in a video game.

This character strikes twice every 4th attack. (Doublestrike)

This extra strike does 50% of your attack damage.

This extra strike, along with all other strikes, can crit, meaning meaning they do twice the damage. My character can buy an infinity edge making crits do 2.5x the damage.

If my chance to crit (CC) is at 50%, my attack damage (AD) is 100, and my attack speed (AS) is 2 attacks per second, then what is my DPS with and without the infinity edge? (Assuming that I have attacked at least 4 times to proc the doublestrike)

What is the formula? (I need the formula because I am creating a dynamic spreadsheet)

 

[I like Serena]

I am calculating damage per second (DPS) for a character in a video game.

This character strikes twice every 4th attack. (Doublestrike)

This extra strike does 50% of your attack damage.

This extra strike, along with all other strikes, can crit, meaning meaning they do twice the damage. My character can buy an infinity edge making crits do 2.5x the damage.

If my chance to crit (CC) is at 50%, my attack damage (AD) is 100, and my attack speed (AS) is 2 attacks per second, then what is my DPS with and without the infinity edge? (Assuming that I have attacked at least 4 times to proc the doublestrike)

What is the formula? (I need the formula because I am creating a dynamic spreadsheet)

Hey El Demente! Welcome to MHB! ;)

Suppose your character attacks 4 times then the regular damage is:
$$4 \times AD + 50\% \times AD = 4.5 AD$$
The damage per attack is then:
$$\frac{4.5}{4} \times AD \cdot \frac{\text{damage}}{\text{attack}}$$

Multiply by attack speed to find the base damage per second. Let's call that $DPS_{\text{base}}$:
$$DPS_{\text{base}}= \frac{4.5}{4} AD \cdot \frac{\text{damage}}{\text{attack}} \times AS \cdot \frac{\text{attack}}{\text{second}}
= \frac{4.5}{4} \times AD \times AS \cdot \frac{\text{damage}}{\text{second}}$$

Since there is 50% chance on a critical hit, the expected damage is:
$$DPS_{\text{regular}} = 50\% \times DPS_{\text{base}}+ 50\% \times (2 \times DPS_{\text{base}}) = 1.5 \times DPS_{\text{base}}$$
With an infinity edge this becomes:
$$DPS_{\text{infinity edge}} = 50\% \times DPS_{\text{base}}+ 50\% \times (2.5 \times DPS_{\text{base}}) = 1.75 \times DPS_{\text{base}}$$

Summing it up:
\begin{array}{|l|c|c|} \hline
\text{DPS} & \text{Formula} & \text{Current Value}\\
\hline
DPS_{\text{base}} & \frac{4.5}{4} \times AD \times AS & 225\\
DPS_{\text{regular}} & 1.5 \times DPS_{\text{base}} & 337.5\\
DPS_{\text{infinity edge}} & 1.75 \times DPS_{\text{base}} & 393.75\\
\hline
\end{array}

Have fun!

 

[El Demente]

Oh my god that is the perfect answer. Thank you so much. I input it into my spreadsheet and everything by the way! Kudo's and cheers! I knew I could wrap my head around it if someone broke it down for me I just got frustrated trying it forever myself on this one cause I knew I didn't quite have it.