Tactics Questions - Line and Column, Stacked or Not Stacked

[Mowgli]

Is it always better to keep your soldiers in column if you are attacking? I had always thought it would be advantageous to move into position and switch to line to increase firepower for a better chance of dislodging the enemy.

Here is my current understanding of the combat characteristics (fire/melee) of line and column. Note that I always play without "phases":

COLUMN

• Units in column have decreased fire power: *nation/scenario specific value ("Column Fire Modifier")
  
• Units in column (except for the Brits) have *1.25 melee power if they're ATTACKING (not if they're defending!). Columns also always get the *1.2 bonus for not having fired prior to melee (as units can't fire and then melee in the titles I play).
  
• Columns can be flank-charged (*1.4 melee power for attacker)
  
• Infantry fire (*1.25) and, particularly, artillery fire (*1.5) is more effective against units in column.
  
• Unless the "Column Pass Through" optional rule is active, there is no damage to units other than the targeted unit. 
  

LINE

• If fully developed, units in line have their full fire power: *1 if in "line" or "extended line", *0.75 if in "shortened line". (2-rank-infantry, which seems to be uncommon in the Napoleon titles I play, even gets a big bonus for being in line or extended line *1.5). 
  
• Units in line fight at their normal melee power.
  
• Units in line can be flank-charged (*1.4 melee power for the attacker)
  
• Fire that hits a line from any other direction than its "frontal sector" (lines protruding from the two front hexes of the unit) counts as "enfilade" fire (effectiveness =  * "Enfiladed" parameter). From taking a close look at the values ingame, it seems as if skirmishers cannot deliver enfilade fire. Very importantly, the manual also states that a unit that has received flanking fire in the enemy's turn will suffer an additional -2 (!!!) malus on any morale test it needs to conduct at the start of the turn. I haven't played enough to develop a feeling yet if this is true. 
  
• Any unit stacked "below" an infantry unit in line formation cannot be targeted by the opponent's fire unless his fire is enfilading fire (as described above).
  
• Any unit stacked "below" an infantry unit in line formation cannot fire. Units can be moved "in front of the line" by using the "Command/To Top of Stack" command, but the unit will count as moved and thus suffer a 50% malus on its fire power. Units that have already fired cannot be moved to the top of the stack anymore (the last unit to fire is the one who is in front and can be targeted by the opponent...).
  
• If artillery hits a unit in line formation, all other units in line formation in the same hex also get hit (with full power).  
  

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HYPOTHETICAL EXAMPLE (you may just skip to the conclusions below...)

Let's go through a hypothetical example and see what happens mechanically when two units (each 400 men, quality C) advance in column against a unit in line (500 men, quality C). We use the column fire modifier from Leipzig 1813 (*0.33), the attackers are Russians (musket 1@2, 4@1 hex), the defenders are French (musket 1@2, 5@1hex). Neither side has any commanders.

• The units in column step into the maximum fire range of the line (2 hexes). There is a chance for opportunity fire, but at this range, the fire is totally ineffective at best.
  
• The units in column step into close range of the line (1 hex). There is a chance for opportunity fire. Let‘s say it triggers:
  

500 men * 5 (french musket at range 1) * 1.4 (enemy target in column) * 1 (firing unit in line formation) * 0.5 (opportunity fire) = 1750
A fire value of 1750 will lead to 26 casualties on average (1.5% = the middle between the low and high fire casualty thresholds)

• Having suffered casualties, the target unit needs to check whether it needs to undergo a morale test. With 26 casulties, the chance for this to happen is 39% (the higher the casualties and the smaller the unit, the more likely it is). Let's say the unit does not need to undergo a morale check.
  

 
26 (casualties) / [ 26 (casualties) + 40 (manpower/10) ] = 0.39

• The two units in column initiate the melee attack. There is a chance for opportunity fire. Let's say it triggers again and, by chance, hits the same unit again. The fire value is the same as before, so on average, another 26 casualties are inflicted. If we assume that the manpower used for determining whether a unit needs to undergo a morale test is the current manpower (not starting/paper manpower), then the chance to cause a morale test is now slightly higher at 41%. Let's say the target unit needs to conduct a morale test:
  

unit quality = C (no leader) --> 66% chance to succeed

• To keep things interesting, let's say the unit fails the morale test. The unit is now disordered. 
  
• We continue to melee. The attackers have two units, let's calculate their combined attack melee power:
  

unit 1: 400 (men) * 1.2 (column attacking) *1.2 (not fired) = 576
unit 2: 348 (men) *1.2 (column attacking) * 1.2 (not fired) * 0.33 (disordered attacking) = 165
total melee power of attackers = 741
With the middle of the casualty thresholds for the defending side being 6%, this will result in 44 casualties on average.

• The melee power of the defender is calculated thus:
  

500 (men) = 500
With the middle of the casualty thresholds for the attacking side being 10%, this will result in 50 casualties on average.

• With 50 casualties for the attacker and 44 for the defender, the defender has won the melee and stands its ground. All attacking units are disordered and suffer (more) fatigue. I can't tell how casualties are distributed amongst the units. Let's just say that each column suffers 50% of the total casualties. The defending unit will also be disordered (it's not entirely clear to me how this works) and also suffers (less) fatigue. 
  
• Now comes the turn of the defending player. Having suffered so many casualties in the opponent's turn (44), the unit will need to pass a morale test at the start of its turn. If the unit fails, it will rout (and at least disorder all its neighbours...!). If it passes the test, it stays disordered (In any case, there is no chance for the unit to get back to good order in this turn!). Let's see the chances to pass the morale test:
  

unit quality = C - 1 (disorder) = D --> 50% chance to succeed

• Let's say the unit is lucky and passes the test. It can now fire at one of the units in column at close range. It would be wise to pick the column that has suffered the most so far (2 opportunity fires + melee): 
  

456 (men) * 5 (musket at range 1) * 0.5 (disorder) *1.4 (target in column) * 1 (unit in line) = 1596
Average 1.5% casualties = 23 casualties

• Now it's the attackers turn again. The unit which has just lost 23 men needs to test whether it needs to undergo a morale check. The chance is 43%:  
  

23 (casualites) / [23 (casualties) + 30 (remaining manpower/10)] = 0.43

• If the unit succeds, it does not need to undergo a morale test and may even get back to good order (depending on its leadership). If not, it stays disordered. Or it may even rout, leaving the other unit disordered or even routed, too.
  

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CONCLUSIONS

As you can see, there are a lot of "ifs" and there is a big random factor involved. How well a line performs against a unit advancing in column mainly seems to depend on: 

• opportunity fire (a big black box! if it doesn't trigger at all, you at least get *1.2 combat power in melee...)
  
• the manpower of the firing unit vs. manpower and morale of the advancing column. The bigger the firing line unit, the smaller the column unit and the lower the quality of the column unit, the more likely the defensive fire will disrupt the column unit (thereby reducing its melee power by 66%!).
  

However, I think it's unfair to look at such an isolated example:

• In a real game situation, the line unit will have neighbouring units, which multiplies the chances for opportunity fires. So a "battle line" of three units is more reliable than a "battle line" of only one unit. Also, regaring "neighbouring" units, one would need to check whether the fire of those neighbouring units can be degraded by parking skirmishers in front of them...
  
• Artillery in general has a devastating effect on units that approach in column (*1.5 fire power!). But then again no firepower on earth can overcome morale A (or B + leader). Morale A units will not disrupt to opportunity fire (unless already disordered or tired), no matter how much fire you throw at them. They're zombies.
  
• If both sides are and stay disordered, the line should have the upper hand: A disordered melee attacker gets -66% combat power (but still *1.2 column, *1.2 not fired), a disordered melee defender only -33%. A disordered unit fires with -50% fire power, but the column also keeps its fire malus (roughly -66% to -75%, depending on the title).
  
• Last but not least, if the columns win the melee and push the line back, it's not a catastrophe. There are no extra casualties for the loser of a melee. He just gets pushed around and takes a bigger hit in fatigue. Things only start to get ugly and one-sided if one side stays disordered while the other one doesn't, and that's more a matter of leadership and morale rather than formation. Being pushed around can be bad, but it can also be good, as it usually opens up the column's flanks to your "neighbouring units". See it that way: If a column pushes into your line, there are now 2+ enemy units with reduced morale (-1 disordered) and reduced melee power in a single hex. If you can rout a single one of them (and you do have free choice of target against units in column formation...), all the other units automatically stay disordered (so they're unlikely to assault in their next turn ...) or may even rout. This is an opportunity. If the column is not well supported, then you might even take your fresh (not disordered) neighbouring line units and flank-charge the disordered column (*1.4 melee power for you, *0.66 for the column units)!