# How can I calculate this expected rate?

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 $1 - 0.83^5$, 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.

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What is "the skill", Legionnaire, a creep, and a camp? How is the level determined? –  Daniel Trebbien Aug 6 '10 at 0:38
Is Legionnaire another name for Axe? –  Casebash Aug 6 '10 at 2:40
Legionnaire is the name for Axe in HoN. –  Jacob Greenleaf Aug 6 '10 at 3:46

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