strange +1 skill item mod stacking

Sorry, if this has already been discussed I did numerous searches and didn't yield any viable answers.

Here is my main question:
Does anyone know how exactly item mods stack.

Here is why I ask:
I was a +12 fire (maxed) with a superior fire rune (+3) and the flame's eye headpiece (+1) making my character the true max of +16 fire.
But I decided to change it up a bit to get more life so I replaced the superior fire rune with a major fire rune (+2) and a flame artifact with fire +1 mod.
That being said mathematically this should be the same, but I'm only +15 fire now. The only thing I can figure is that +1 skill mods don't stack.

Doesn't the artifact with Fire +1 have a percent chance associated with it, like 20%? Your attributes will show the "guaranteed" skill level, like 12 +1 headgear +2 rune = 15 but each time you cast a fire spell you have that % chance of receiving the +1 bonus.

You'd have to watch the results to try to figure out if the bonus kicked in.

if u read the description of the flame artifact... it should say something like...

"Fire Magic +1 ( 20% chance )

... meaning when ur casting ur Fire Magic spells... u will have a 20% chance to cast a lvl 16 spell...

Thanks guys. Thats what I get for not reading the "fine print"...
Thanks again!

you can always get a glyph of elemental power +2 for your next spell so with 16 fire magic you can use that to get 18 for your next spell and still have a 20% chance of getting level 19 0.0