Has anyone figured out exactly what kind of bonuses they're giving for being higher in a fight?

That's because in M/M game, I use a smaller army of militia hoplite only (1st hoplite) to beat a large army of armoured hoplite (3rd) without losing a single unit because I'm higher on a steep battleground. This must only be a height advantage (not a single one! They beat the crap out of me with flat plain battles)

I managed to produce the same results in similar battles.

And I know it's harder to shoot at those higher than you.

But what is the exact benefits of height? Experts, please?