I did some testing with max mana and mana regeneration per tick.I can say, with no doubt, that max mana increases how much mana you gain per tick.I only did a few trials and encourage other to test as well.
I removed all my gear and drained most my mana. Then I recorded mana regained per tick. Did this a few times to make sure I got good data.
Repeated this when I added 75 MP worth of gear. Only MP gear, not piety.
I put the numbers in excel.
With no gear, I was getting a slope, mana per tick, 241.
With 75 MP gear, I was getting a slope, mana per tick, 247.
The R^2 value for both of this tread line was 1, so the slope is dead on.
I didn't see any threads on this topic, so I thought I would share.
NOTE: I did my testing as a THM. No other classes were tested.