Strategikon and the Art of War has rules of thumb about how much I need for certain victory. First I want to discus Economies of Defense. In later posts I will go into Terrain and Circumstances which is discussed in the Sun Zi's Art of War (AoW for short in future discussions) but I will go into implementable examples and aids. I will then go into Force Multipliers or Dividers, these are Meta Systems that can be plugged into Game systems that do not have Mass Combat.
Economies of DefenseI found this concept very useful in both combat, in sparring and airsoft, and in Mass Combat. The concept allows me to focus on economies of Attention.
This simplifies how having greater numbers of soldiers works. That greater numbers over another force allows me to divide the defense of another side. That One against One means both having 100% of their Defense available, while Two against One halves the defense of the lesser Force.
This concept means numbers don't matter as much if the greater force cannot divide the defense of the other lesser force (numbers mean more "Shifts" of fighting, wearing down the smaller force). This simple matter means that in Narrow or Contested Ground (the Art of War: The 9 types of ground) I cannot take advantage of greater numbers as effectively.
Reiterating that in a fight of 2 to 1, the casualties of the greater force depends on how efficiently one can take advantage of the opening created by the flanking of the other. This flexible mental concept of dividing the defense is so useful it will greatly improve the GM's narrative when describing forces and organization. In the geometry of battle ranks thin to cover flanks against greater numbers. When ranks thin, gaps are not filled as quickly and when lines break flanks are exposed and the men in ranks despite how tight they may be may see too many men and fright takes over while the other side gains bloodlust.
Defense can be translated as adapting to the circumstance externally dictated. That in an organization I act defensively when I am adapting and reacting, instead of directing and attacking. This takes the concept to an abstraction for scenes not as geometric as battlefields.
Quality and Quantity of Force
Because of various biases humans use these numbers to determine their force instead of going by quality. It is easier to mass the numbers by using full-time or part-time soldiers forcing other men to fight in the army.
That in earlier eras numbers mattered more than quality and they would get all the fighting age males (and sometimes too young, too old, and women depending on the circumstance; typically aged 14-40) and herd them. One realizes that this "buffering" of numbers is why one hears about 1 out of 10 or 1 out of 5 fighting men. Spartans and Vikings (Raiding northmen) were typically 4 out of 5 fighting men (20% being servants who dont really fight but may be made to do so in the rear). In the poorest quality of troops one needs at least 1 warrior beating the shit out of people to control 8-9 other people (1-2 of these people mostly serving as servants).
One realizes that it is a Herd of humans, disciplined by violence, threats, conditioning, practice, punishment and rewards. That these marvelously arrayed blocks of battalions or regiments of humanity can be compared to herded animals. There are times of great motivations and prize to be won, but fear and pain are the most common tool of disciple. No wonder Sun Zi talks about the dangers of cornering a foe, when cornered every man becomes a fighting man.
In Sins of the Crusade, the army is made up of 1 of 4 are fighting men. Slaves, Criminals, and the many second sons and disguised daughters of a Europe that is experiencing the limits of its carrying capacity.
Using Groupings and Economies of Defense
Now begin by taking the Strategic and Tactical strength used in an Era. Great Empires during Ancient Eras waged wars in the scale of Corps and Divisions (100,000 to 30,000 per side on field of battle) where they moved pieces of Divisions (10,000). This includes the Ancient Near East Eras, Ancient Roman Era, and Most of the Chinese Eras (eras I know fought in this scale prior to renaissance eras). In other eras it was battles of Divisions to Brigades (50,000 to 10,000) with pieces of Brigades to Regiments. In the Medieval eras they fought in the scale of Divisions and Regiments (30,000 to 5,000).
Once I know what size I will be dealing with, this is broken up to its "Tactical" and "Strategic" units. These are relative terms, with the emphasis of Tactical being what is on the ground or being used. Strategic is the forces that takes more preparation, they have various stages of readiness, and factors what can be raised or what is in reserved.
A Corps of 50,000-30,000 men can be Strategic if its the total pool of manpower that State can draw from or as a Tactical unit, it is the force being deployed and used. In SotC the Strategic unit depends on who I are talking to: The Emperor or Bohemmond or Abu'l Qasim. Bohemmon's Strategic force is his whole army of a Brigade sized force of 10,000 men (but at 1 warrior out of 10 men), and his tactical units are two regiments of ~2000 controlled by his Hypodoux (visduc in french; the terms change as they don't want to use the greek terms) Tancred and Mauger. Alexios has about 60,000 and as he assigns them they are his strategic units: 20,000 which he's assigned to Megas Doux John Doukas, and 10,000 to deal with the Balkans. How these forces are deployed is their Tactical level.
Finally at the Tactical level, when forces are engaging each other I can factor economies of defense. In the Tactical scale I examine the terrain realtive to the size of the army. A man is a Pace wide (2/3 a yard or meter), so to hold a line of 40m I need 60 men. I reinforce these men with ranks, as armies are mobs that smash into each other and a line can easily fall without reinforcing ranks. In open terrain numbers are even more pronounced and important, even if the quality is questionable.
Ill go into Force Multipliers in another post.
Translating it to Dice
In 1 to 1 each has a 100% resources to defend and there is a 50% of either one to make an attack penetrate the defense then we can work with this baseline. In odds of 1 vs 3, the lesser force has 1/3 of their defense available. Multiply the defense penalty to the 50% baseline, in this case 15% chance to defend. This translates as a -35% penalty to the defender or a +35% bonus to the attacker. Just to be different I will recommend a penalty
Two forces can be of equal in number, but if one force is able to divide the Other's ability to defend this would allow the other to better overwhelm the other.
If there are penalties for "Fatigued" or "Spent" forces it would apply to their defense as well. Again, at "half" strength, the half the odds of success and translate that to dice odds.