For example standard operating procedure in the United States military is that a Company will fight a Platoon; a platoon will fight a squad. The idea is to always drastically out number the enemy, I believe the ratio is 3 to 1. Did armies in ancient and medieval times follow similar procedure?
Not really. The Roman army, for example, generally had an extreme degree of self confidence, and was willing to go into battle against enemies even when significantly outnumbered. This was probably helped by the fact that this confidence was, generally, quite justified. One of the more lopsided examples is the Battle of Tigranocerta, in which the Romans engaged and slaughtered an army that may have outnumbered them 2:1.