The math behind shield bashes

[Rull]

The vanguard tree got me excited. But I always wondered, how much do those bashes really proc?
As I understand them, they are hard-capped to proc at most once a second. Now if you have a proc chance of 20% and attack not too fast, this is not likely to restrict you. On the other hand, if you attack 3x per second and always proc, you only get an actual bash on 1 out of 3 attacks.

One very important thing to realise is that the '1 bash per second' does not behave like like a cutoff threshold. Because ?fter that second, you still have to score your proc.
If you proc approximatly once a second, it takes on average a second to score a proc after the second of 'downtime', so you bash once per 2 seconds!

I ran the numbers for 10%-60% proc rate, on various attack speeds, and here are the results:



So with 3 attacks per second (I don't think this is reachable on sword and board), you still only get the 0,64 bashes per second even with 60% proc rate. The 1 bash per second is not nearly approached.




The same math also applies to stacks of destruction and similar effects

edit: corrected for time between attacks