Hello Zu Pferd, hope you don't mind me commenting on your post.
I am in two minds about luck and chance in wargames. Unfortunately for most I don't think the element of chance would go down well in a wargame, especially with a game as complex as HW. With so many factors deciding whether or not a unit will rout, ie factors I know the game uses to calculate the result, off the top of my head :
Fatigue.
Morale.
Cohesion.
Unit type (inf, cav, art, guard, elite).
Strength of attacking unit.
Strength of defending unit.
Losses.
Calibre of attacking unit (Guard, Elite, cavalry, light inf/cav, med inf/cav, heavy inf/cav).
Calibre of defending unit (Guard, Elite, cavalry, light inf/cav, med inf/cav, heavy inf/cav).
Allied artillery, presence of.
Enemy artillery, presence of.
Calibre of commanding officer, Charisma/knowledge.
Calibre of enemy commanding officer, Charisma/knowledge.
Presence of supporting forces/Calibre (inf, cav, art, guard, elite)/type/strength of allied forces, position of, frontal, flank, lateral, rear...
Presence of enemy forces/Calibre (inf, cav, art, guard, elite)/type/strength of enemy forces, frontal, flank, lateral, rear...
Fleeing, allied/enemy...
Loss of commander.
Loss of flag.
Terrain.
Weather.
Visibility.
Lines of communication, allied/enemy/loss of and capture of.
A die roll then thrown into this mix imo would make all the above irrelevant...
With so much being thrown into the equation, to a certain degree it is already a game of chance, I think there is very few people here that could even begin to calculate the outcome of any confrontation in this game mentally...
The only thing you could be sure of for example is a small battle of 10,000 guard v 6,000 line say, the outcome would be fairly certain, all logic says the guard would prevail, but with a die roll who knows what would happen...
But 10,000 guard as an element of 2 x 100,000 man armies attacking a certain part of the line with all the above factors thrown in would not be certain victory...
I understand that introducing an element of chance could create some interesting results, but to see a good strategy and sound tactics unrewarded because of chance would not go down well with most... After all I think most of us fancy ourselves as armchair generals who try to reproduce Napoleon's great victories in the face of over whelming odds, but I think the chance/luck is in most cases already there...