The importance of running away bravely

neither Blücher nor Wellington did run away as such, Wellington had to retreat to keep the possibility open for re alignment with the Prussians in that way that Blücher could send support, and Blücher retreated in that way to enable this.

In my view this was very difficult to do so, to break away and to re group and turn the wheel by that - quite an achievement and this even by two independent army commanders, impressive.

Within the context of Blucher and Wellington, a lack of energy from the enemy in the early phase of the retreat is key, to help achieve a clean break. The state of the army at the point of the decision to break and run is also vital (the Prussians were bloodied but not broken, the Anglo-Dutch army was not even beaten, though it had had a rough time on 16th. Both of these also apply to Grouchy on 19th, but Napoleon in the 18th to 20th is another story. I don't know the timeline well enough to comment on that. Does this always apply more broadly? Well an obvious example of the need for a clean break is the French Army of Portugal after Salamanca. The failure to maintain close contact as night fell gave the French just enough time to get away, even if the KGL cavalry bloodied them again the following day at Garcia Hernandez. To an extent you could make this argument again for Vittoria. None of what I've said here is exactly enlightening though. I'm reluctant to relate discipline to a clean break. Wellington blamed poor discipline for the failure to destroy the French entirely at Vittoria, but fatigue will also have played it's part.