Quote Originally Posted by Puzz3D View Post
Unit strength isn't linearly related to unit size because each man can only strike once within a combat cycle, but he can be attacked multiple times. So, a 40 man unit is something less than 2/3 as strong relative to a 60 man unit.
Doesn't that assume that all men get a chance to strike? So it may be valid for missile combat, but with melee, unit frontages may restrict the ability of the larger unit to bring its numbers to bear. For example, in a fight between a 40 man and a 60 man unit, suppose you form up the two units in 4 ranks:

Code:
L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
       S  S  S  S  S  S  S  S  S  S
       S  S  S  S  S  S  S  S  S  S
       S  S  S  S  S  S  S  S  S  S
       S  S  S  S  S  S  S  S  S  S
On impact, the larger unit only gets 2 more men to fight - the two closest to the flanks of the smaller unit. So, it has a 20% more men in combat rather than the 50% superiority it has in total numbers. Over time, so long as it does not hold ranks, the larger unit will bring more men to bear, but so will the defenders:

Code:
                  L  L  L  L  L  
L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
    L  S  S  S  S  S  S  S  S  S  S  L
    L  S  S  S  S  S  S  S  S  S  S  L
    L  S  S  S  S  S  S  S  S  S  S  L
    L  S  S  S  S  S  S  S  S  S  S  L
    L                                L
Here, we have 22 L soldiers in combat against 16 S - a 37.5% advantage in numbers. If completely surrounded, the numerical advantage actually worsens - 32 L vs 24 S, a 28% advantage.

What I am saying is that a smaller unit may be able to punch above its weight by restricting the ability of the larger formation to bring all its numbers to bear. Think the Spartans at Thermoplyae. If terrain does not allow this, a square or ideally circular defensive formation seems best for minimising the enemy advantage of numbers. This is the lesson of fortifications throughout history and those "circle your wagons" type encounters we read about with the Boers and Zulus. A singleline formation is worst if the enemy can get behind you and so bring all his numbers to bear (as well as get a lot of unopposed rear strikes).

Now it is still true that replacing the smaller unit with a larger one will lead to a big rise in its killing power, as they will get a lot more strikes in the front row:

Code:
L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
S  S  S  S  S  S  S  S  S  S  S  S  S  S
Compared to the situation on the front row in the first diagram, they have gained 5 more strikes on impact. But this is somewhat diminished by the cost of exposing themselves to a further 3 strikes back.

I understand what Puzz3D is saying - and there is a mathematics behind it. But in practice, with TW games, it often seems to me that unit size matters less than one might think.

Another point is that in the case of cavalry, a lot of their overall combat effectiveness may not be so related to their "strikes" in combat. Specifically, the morale collapse they can engender by making charges into the enemy rear and the ability to turn tactical victories into strategic ones by sweeping up routers are both probably largely unaffected by whether the unit is size 60 or size 40. These points may apply more against the AI in campaigns rather than to MP battles. But the value of the bodyguard units in TW campaigns bring home the benefits of even small numbers of heavy cavalry.