ORIGINAL: DeadInThrench
All other things being equal, a unit that is twice as large as another unit, should inflict twice as many casualties, and a unit that is three times as large, should inflict three times as many casualties. But, in HPS FIW.... NADA (at least in one PBEM game I am playing as well as scenarios I am playing)... and in fact three 20 man units will inflict considerable more damage than one 60 man unit (at least it appears that way).
But you forget, not all men in a unit can fire at the same time. Only 2/3 ranks can fire at once and although several pairs of ranks can fire during the 5 minute game turn time, not all of a large unit may be able to fire.
I calculate that a 60 man unit can fire once each 3 times if the reloading time is 2 minutes OR once each 3.5 times if the reloading time is 1.5 minutes. This equates to a 180 or 210 man-firepower.
Several smaller units would have a multiple effect as each units men can fire more often than a larger unit and overall more men may get to fire in the time allowed. If the overall number of men firing is higher the possible casualty rate is higher.
I calculate that a 20 man unit can fire 3 times each at a 2 minute reloading rate or 4 times each at a 1.5 minute reloading rate. This equates to a 180 or 240 man-firepower for three 20 man units.
The extra units may also be firing from the flanks which increases the casualties caused by each by approx. 20%.
The last paragraph aside; 20x3 = 60x1 @ a 2 minute reloading rate, and 20 x 3 is 1.143 times more effecient than 60x1 at a 1.5 minute reloading rate.
NB. An increase in the reloading time to 2.5 minutes leaves both groups equal at 180 fire-manpower each, whilst a decrease to a 1 minute reloading time leaves the 2 groups level at a 360 fire-manpower rate!
NBB. All this proves then, is that by & large your theory is correct, but the exact circumstances ( historical reloading time ) MAY cause an imbalance, as may the exact placement of the extra units.
Also. Units in extended formation ( skirmish line ) in this period, should always be able to cause more casualties than a regular unit of the same or maybe larger size. Skirmishers were sharpshooters ( even Indians ). Regular units used volley fire without particular aiming. Having not even trained on targets as individuals, their fire (even if aiming was tried ) would be poor. Hitting skirmishers with volley fire is difficult given the space between each skirmisher and that units lack of depth.
These things aside, you cannot expect any fire result in a game to be a mathamatical given, in any game, in any period, but particulary not in the one quoted, considering the usual terrain here includes lots of woods, and therefore trees to hide behind whilst loading ( as smaller units & skirmishers were prone to do).