My assumption of the current situation is that we have forced Wachenheim into an unwinnable situation.
Just mantaining the current position means that he just loses in a long, drawn out artillery fight where he loses his entire army while killing a few hundreds of our screening forces.
But I assume that he does not see my out of shooting at the 5th, so his only way to do somethiing is an assault against the village, hoping to reach the 5th and disable it. This means that he will concentrate everything has on a shock assault in the north, with troops in the south trying to deal more damage to the north.
This means that his win condition is breaking our defensive line in the north, while our win condition is him being unable to keep up the assault, as each turn he doesnt assault is just a turn where his capabilites get degraded by artillery fire.
So he will charge at our front and do his very best to put as much pressure on our frontline as he can, cycling troops to put as much pressure on our line as possible. This means that he will do everything he can to ensure he always has another unit ready to charge in and continue dealing damage in case of a rout, using the strategy described above to ensure he does not lose a turn of melee damage.
Charging in not fully rested units is preferable to not dealing melee damage because of this, as getting hit by the artillery will deal more damage than they will heal by resting. Once they cant even charge in damaged units they have just lost, their only play a failure as we planned.
I wouldn't call high risk, medium reward gambling the superior choice here. Also, your assumption that melee will last a full five turns are dubious. One of us is probably routing the other's centre after 3 turns of the enemy being in range of 3 guns.
but its not high risk, medium reward? its low risk, very high reward. If we miss the enemy we have lost one artillery shot, if we hit we severely hit their damage output.
I guess if 10 infantry regiments rout in 3 turns not shooting the enemy regiment would be superior, but I just do not believe that it will be that easy.
Calculating with 3 Infantry regiments meleeing and 3 artillery regiments artillering, we cause 25 cohesion damage per turn on average. If we assume that every routed enemy causes 4 cohesion damage total, thats 40 extra cohesion damage.
The enemy infantry regiments have 143 cohesion damage. Substracting 40, thats 103 cohesion damage to punch through, which takes 3,8 turn on average.
Which is surprising? I would have expected that a giant infantry assault would have more breadth, but it looks like the resting mechanics dont really matter? If the entire army gets disintegrated in 4 turns, Resting doesnt really matter if you arent a cavalry unit routing in the first 2 turns.
But yeah, it looks like you are correct, there just arent the giant attritional melee fights i was expecting
For the current enemy, counterbattery fire is a bad choice due to insufficient artillery experience. But speaking more generally, I think it's also prudent to acknowledge the possibility of an enemy making a blunder that will harm us more in the long run. There is also the distinct possiblity of us dealing minor damage to the enemy artillery, and the enemy still deciding to attack the horse artillery in retaliation.
Your argument is that even if we save 100 infantry in exchange for losing 5 artillerists, the artillery engineers are just way more valuable? I can definitely understand that, losing an experienced, proud hobgoblin engineer to save some elven pansy infanterists is disgusting
For one, your calculation does ignore the cascading effect of routing a line infantry (-1 to all adjacent units). Additionally, bringing in a replacement also takes one turn, with the replacement only being able to enter combat on the next in mud. The battle isn't won by dealing more damage statistically, the battle is won if the enemy no longer sees a path to victory, for which the success and failure of the infantry line are more important than the average damage of a cannon. I think your consideration here is overly focused on the attrition comparison, and ignores positioning in the battle. I don't really want to fight a battle by solely focussing on attrition, this would leave our army weaker overall after each prolonged fight.
Bringing in the replacement does not take a turn, see my image above:
A demonstration of how the grind works, there can easiliy be another unit behind dark red to fight once dark red routs.
This fight is the closest we can come to attrition, with our infantry lines directly clashing against each other, though we of course stacked the deck in our favour. I am not sure what you mean by positioning here, either way we arent actually going to move anything, its just a question of which infantry line breaks first(theirs).
Reducing the average damage of the enemy cannons directly contributes to the success of the battleline, because each surviving soldier is one more soldier between our screen breaking or staying. Indeed, if we have the choice to reduce the lethality of the infantry brawl, we should always take it, as with the artillery advantage we will simply outdamage them in the long run.
They have lost this battle the moment we put the 5th into position, what we will be doing here is simply showing them why and reducing the enemy damage output is always appreciated to preserve more of our soldiers for the future.
