Quote:

Q: How does dodge work?

A: Dodge works with diminishing returns. As an example, let's say you have 10% dodge in your runes.

10% dodge.

You grab Ninja Tabi, which gives 11% dodge.

11% dodge +

(89 * .1) = 8.9% dodge

For a total of 19.9% dodge. (Note that the 89 comes from the percent remaining from the previous dodge percentages have been calculated.)

You then get Phantom Dancer, which gives 20% dodge.

20% dodge +

(80 * .11) = 8.8% dodge +

(71.2 * .1) = 7.12% dodge

For a total of 35.92% dodge.

That's not diminishing returns, it's increasing returns for the amount of dodge on a single bonus, and linear returns for multiple dodge bonuses.

*The amount of additional time you stay alive is MORE THAN proportional to the sum of the dodge bonuses you have.*
So for your example, 10% dodge from runes would allow you, on average, to stay alive for 1 / ( 1 - 10%) = 1.11 times as long.

combine that with the Ninja Tabi (11% dodge) and you survive for

1 / ( 1 - 10%) * 1 / (1 - 11% ) = 1.25 times as long

combine those with the Phantom Dancer (20%) and you survive for

1 / ( 1 - 10%) * 1 / (1 - 11% ) * 1 / (1 - 20% ) = 1.56 times as long

In each case, the average additional time that you survive for is greater than the sum of the dodge

percentages. There is no diminishing returns.

**Why?**
If dodge stacked additively you'd have assymptotically increasing returns. Each additional percentage of dodge would be more effective than the last.

For example, going from 0-50% dodge doubles your survival time.

Going from 50% to 75% doubles it again. You now survive four times as long.

The first time you doubled your survival time it took 50% dodge, but then it only took 25% to do it again. Each additional point of dodge becomes more effective than the last.

In fact, 100% dodge would be INFINITE returns because you'd stay alive forever no matter how many melee attacks were directed at you.

This misconception is probably one of the most persistent and annoying pitfalls people seem to have at understanding mathematics.