>Or did their mere presence stop any thought of routing?

Let me tell you a secret about warfare: The average soldier has no idea what the hell is going on.

Even with all of our drones and radios, the average infantryman is really clueless about anything he can't personally see or hear. And in battle, 99% of your attention is focused on the enemy.

Now imagine you in the Napoleonic Wars. To your left, right, and rear are just close-packed soldiers wearing tall hats. You're already half deaf from gunfire and all of your attention is focused on the complicated process of loading your musket. If more guys are coming up from behind to help, you probably wouldn't notice.

It is not uncommon to see accounts of soldiers fleeing the battlefield, claiming all is lost, even when their side was actually winning. For example, at Waterloo British soldiers fled from battle and encountered Prussian reinforcements. Rather than being inspired to return to the fight, they told the Prussians the battle was already lost.