How to factor in critical chance to calculate damage per second?

[Tomecide]

Ok so essentially in this video game I have there are certain stats on swords. The stats are the amount of Attack animations, amount of time to compleate all of the attack animations, sword dammage and critical chance. All of the animations deal the same amount of dammage and the time to compleate all of the animations always stays the same (Dammage is done when you attack and attacking causes an animation to happen). Critical Chance has a fixed percentage of chance to occour and if a critical hit is landed, the attack will deal double damage. Sword dammage is fixed and I've figured out a formula to find the amount of dammage a sword can deal a second: Attack Animations * Base dammage / Time to preform all of the attack animations. I'm confident that this formula is correct, because I have tested it. Anyways my question is how can I factor in critical chance to my equation to reresent the stat properly. Thanks!

 

[I like Serena]

Ok so essentially in this video game I have there are certain stats on swords. The stats are the amount of Attack animations, amount of time to compleate all of the attack animations, sword dammage and critical chance. All of the animations deal the same amount of dammage and the time to compleate all of the animations always stays the same (Dammage is done when you attack and attacking causes an animation to happen). Critical Chance has a fixed percentage of chance to occour and if a critical hit is landed, the attack will deal double damage. Sword dammage is fixed and I've figured out a formula to find the amount of dammage a sword can deal a second: Attack Animations * Base dammage / Time to preform all of the attack animations. I'm confident that this formula is correct, because I have tested it. Anyways my question is how can I factor in critical chance to my equation to reresent the stat properly. Thanks!

Hi Tomecide! Welcome to MHB! (Smile)

When an animation deals damage, the damage dealt is:
\begin{cases}\text{Base Damage} &\text{with probability }1 - \text{Critical Chance} \\
\text{Base Damage} \times 2 &\text{with probability }\text{Critical Chance}
\end{cases}
The expected amount of damage is:
\begin{aligned}\text{Expected Damage} &= (1 - \text{Critical Chance}) \times \text{Base Damage} + \text{Critical Chance}\times \text{Base Damage} \times 2 \\
&= (1 + \text{Critical Chance})\times \text{Base Damage}
\end{aligned}
So the:
$$\text{Damage Per Second} = \text{Attack Animations} \times (1 + \text{Critical Chance})\times \text{Base Damage} \ /\ \text{Time}$$