It could well be that the armour upgrade could override the base armor value given for example instead of adding onto it.
No carl did the tests. A unit has the armour upgrade for each level added onto their base.

but nothing like armor X vs armor Z with upgrade Y where X should equal Y+Z
Thats exactly what i did in my tests. Billmen with 2 armour upgrades should have an armor rating of 5. Berdiche Axemen unupgraded have a defence of 5. They both get the same results v peasant archers so both must have armor values of 5, despite the billmen unit card showing armor of 2.