Slitherine

for example thureophoroi and hoplites are both considered protected, so i guess they use variations of linothorax and what not

but thureophoroi do not have a negative modifier when in rough ground. what does that mean in real life? is their formation like the light infantry's formation, do they use both line formation of the hoplites and light infantry formation?

if they use both formations, why do they have a negative modifier against heavy infantry?

Formation not as tight as heavy infantry. Though not as dispersed as light.

Heavy infantry= Shoulder to shoulder, almost exclusively Western.

Medium Infantry= Enough Space to fully swing a sword or spear and not hit the other teammate. Out of one's personal space, but still close.

Light infantry= Skirmish formation, with tons of space between 2 men. Enough so an elephant or chariot can pass through (and also why these types are good historically against elephants and chariots.

At least this is how I envision it.

When heavy infantry enters rough ground they won't be able to hold their tight formation and lose the advantage and confidence they would get from that in the open. Medium infantry doesn't have that advantage in the first place so they are not negatively effected by rough ground when compared to "heavy" units.

The armor level of unit (protected, armored etc) and the weight of armor doesn't directly effect the unit being heavy or medium as that refers to the tactics, organization and capabilities of the unit.

It's worth noting that the Thureophoroi are rated as Protected because of their large shields. As far as we know very few of them, if any, wore body armour.