I ran into an interesting problem while trying to figure out the average time a hero would spend stunned if they were attacked continuously with a bash item or ability.
For example, if I was playing Slardar, and had a 25% chance bash for 1 second, and could attack twice a second, then what percentage of time can I expect my opponent to be bashed for? I want to know what the increments are, so that I can figure out when it's worth it to level that skill.
I came up with the following state diagram to help me through it. The states represent a half-second period after each attack.
Note that new stuns will refresh old ones (not stack). For example:
ACTIVE… MISS
=ACTIVE… HIT
=STUNNED (for this round and next)… HIT
=STUNNED (for this round and next)… MISS
=RECOVERING (for this round)… HIT
=STUNNED (for this round and next)… MISS
=RECOVERING (for this round)… MISS
=ACTIVE…
Is there a formula which would fit any number of seconds, and any percent chance of stunning?
Best Answer
Pseudo-Random
As it was commented the 25% isn't a constant in each attack but more an average of times it will proc from a bigger pool of attacks.
How does it work, the real chance to stun is 8% per attack at full level, every time it doesn't proc this chance is increased another 8.5% until stuns the target and then it resets to the base of 8%.
P(T): The chance for the skill to proc 25%
P(A): The average for the skill to proc 24.90%
C: Contant value from the Pseudo Random distribution 0.08475
Max N: The minimum number of hits that would occur until the next one is a sure proc: 12
Most Probable N: The amount of hits to get a proc: 3
Average N: The average hits until get a proc 4.02
Answer:
If you hit every 0.5 seconds and the average proc it's at the 4.02 hit then the target could be stunned every two seconds.
https://webcache.googleusercontent.com/search?q=cache:wu6BspkLHVwJ:https://dota2.gamepedia.com/Random_distribution+&cd=1&hl=es&ct=clnk&gl=ec