We're still left with the problem that casters have no options vs squads. This isn't a complaint against your formula, but against the issue.(It's not like fighters don't have similar problems.)
Let's take your formula, give it to a wizard with about 15-20 INT, and put it up against a moderate force; enemy equipped with Leather Helm, Leather Armlet, Leather Cuirass, Leather Greaves, and Wood Shield-Defence is 6. It seems extreme, but it's these situations you're gonna encounter, and also what the enemy has to contend with. Wizard's got a few levels on him(Hence 15-20), but arcane research has been only moderate, so he's only got level 1 or 2 damage spells, so we'd be at the low end-5/7 damage base.
5+the 50% bonus is 7.5; just call it 7, I guess. 20 is 10. It beats it, sure, but the damage per turn is poor. As you're spending 2-4 mana per shot, that's no good at all; though the wizard can win a few fights, this is untenable.
Now there's a first rank of squad showing up, three guys for the Empire, 4 for the Kingdom. Uh-oh. 6 becomes 18/24. And instantly our Wizard has serious issues. It's not just the defence(He'll barely hit), he's got to carve through 3/4x the HP. It'll only get worse as the squad size increases and equipment gets better. Shards are a hellish expense to claim, and aren't guaranteed to be around or on type. And please remember that there's not a damage spell every spell level for every school.
There needs to be more than Shards to increase the strength of spells.