Item's Attribute

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Some armor pieces have the inherent effect <Item's Attribute + 1>. It's used on common armor headgear and hero armor.

The effect is defined by the rune's attribute you use to upgrade the headgear.

Example: If a Rune of Major Divine Favor was placed on the headgear it would now be:

<Headgear Name> of Major Divine Favor

Divine Favor +1 (Stacking)

Divine Favor +2 (Non-stacking)

Health -35

Notes

Despite the actual description, headgears with this inherent modification are independent from the weapon's attribute one has equipped.
The fact of this strange description can be explained by the past behavior of hero headpieces, which at first implemented this feature. When Nightfall came out, those in fact used to be dependent on the attribute of the equipped weapon. The disadvantage was that heroes didn't get any bonus in this system if an item with the secondary profession's attribute was wielded, e.g. a caster weapon. Hence this got changed with an update - though the wording didn't change.
It could be interpreted as the headpiece being the 'item', so when you add an attribute to the 'item' (headpiece) it takes it from there.