Beginner question army composition

[carlec]

Can someone explain the math or formula for determining your army composition compared to leadership? I realize that I had a leadership number that grows as I level up or even when I find a leadership flag on the map.

But even then, I seem to be limited in some way to the type of units I can purchase. I have even cleared out a stack, so thus obviously lowering the number of troops under my direct command, I still can't add a lot of other troops (like the archmage).

Can anyone help me understand what's going on here?