Detailed Explanation
After evading once your next attack deals 3x your damage (not 2x like the description might have you believe).
To understand this mechanic, we have to understand a few important hidden mechanics of this item:
As soon as you evade, you get a damage boost of 1.5x your damage for 3 seconds. But your next attack after evading first is 2x that (so 1.5x * 2x ) => 3x damage.
After 3 seconds your damage goes back to its normal.
However, if you keep evading within the 3 second time window, you can actually deal up to 3x damage with one copy of this item. (and then it would be 3x * 2x => 6x damage on the first hit, and then 3x dmg for the next 3 seconds)
Details:
1. Before any evades: 1.0x
2. After 1st evade (stacks = 1): 1.5x
3. After 2nd evade (stacks = 2): 2.0x
4. After 3rd evade (stacks = 3): 2.5x
5. After 4th evade (stacks = 4, cap): 3.0x
Further evades → still 3.0x, just refresh the timer.
Here you can see with 1 copy you can evade up to 4 times and it deals 3x damage. If you evade after 4th evade you will keep dealing 3x damage as your base for 3s. The first hit after evading the 4th damage (and when your damage is now 3x) your first hit after this evade will be 3x * 2x => 5x damage.
Furthermore each evade gives you +25% attack speed. With 1 copy this also maxes out after 4 evades at +100% attack speed.
You also can +50% movement speed with 1 copy. This is gained immediately after evading once. Evading further will not give you more movement speed.