In DotA, there is a character called "Axe". Every time he is attacked, he has a chance to spin (17%) his blade and deal damage based on what level the skill is, 100 / 125 / 150 / 175 damage for levels 1, 2, 3, and 4. When the spin activates, it triggers the cooldown of 0.7 / 0.65 / 0.6 / 0.55 seconds, so that attacking Axe does not generate a chance to spin.
I was trying to calculate an average damage per second that this skill generates, given that most of the time you will find Axe taking around 5 attacks per second (average 1.667 attacks per second from creeps, 3 creeps per camp), so I figured that would mean the probability of him spinning in any second is 1 - 0.835, so given the damage from earlier, we should expect him to deal 60.61 / 75.76 / 90.91 / 106.07 damage per second?
I got this calculation, but then I realized that I have to factor in the cooldown somewhere, but I have no idea where to start.