The Math on Axe

There's been an idea that taking a double-stout shield on Axe is actually more effective for damage mitigation than other alternatives.

Now, double-Stout Shield doesn't completely stack.  However, you get a 60% chance to block 20 of the damage that gets through the first 60% chance, meaning your net block chance is 84% to block 20 damage.

There's been some controversy about the usefulness of double-stout shield on Axe as early items.  I did the math, and here's the result:

https://drive.google.com/file/d/0B4HHV8LhGPUuSUxFS1VpT0ZjNUU/edit?usp=sharing

Summary of Double-Stout on Axe:

Yes, double-stout IS actually quite effective for damage mitigation.

It's only once attack damage passes 60 per hit that the RoP + single shield option overtakes the double-Stout choice.  Thus, for almost all camps and neutrals (except Rosh), you actually mitigate more damage by using two Stout shields.