Today, I spent time and gold acquiring a Deadly Inferno Staff to replace my Deadly Lightning Staff because I mostly do DOT dmg and Inferno staves are supposed to increase DOT dmg according to the Ancient Knowledge passive. What I immediately noticed is that the DOT dmg portion of my abilities all showed lower tooltip dmg with my Inferno staff equipped. Nothing else changed in my build. I asked guild members if they saw the same and at least 1 other person confirmed what I was seeing. Below are screenshots of DOT dmg tooltips.

Lightning Staff:


Inferno Staff:


I also tested on dummies and confirmed that for some reason my Lightning staff yields more DOT dmg than Inferno.