A common but rather mislead assumption you're making is that armies would just randomly meet and start battle. Whilst not an impossible idea, it rarely happened - armies have screens, special soldiers (normally riders) would effectively screen an army by staying far away from the main core, being possibly several days of a ride ahead of them. These riders served the purpose of both concealing the true strength of the army from the enemy, as well as a form of reconnaissance (and in some cases, a form of disruption and early attack), and so therefore this scenario would already be unlikely to happen.

However, I would take it that your question also stands if, say, an army ambushes another, or if they try to obtain certain objectives (e.g. crossing a river, relieving a siege). These battles are as diverse as any other battle, and would really need a more case-by-case analysis. I'm without a book or any reachable source right now, however the most notable ones I can think of right now on the spot would be the Battle of Teutoburg Forest, however that's out of my area of knowledge so you'll probably have to do some research or ask a followup question.