Approximating GURPS Mass Combat Troop Strength (TS) for Dwarven units

In this post, I'm trying to approximate Troop Strength (TS) for dwarves for the purpose of Mass Combat. It should be 2 according to GURPS Mass Combat p.17, but yet again it should also be 2 for orcs if we follow these rules as written (maybe less due to training and equipment). Let's see: this post is both a thinking aloud post, and way to communicate to the campaign's player how dwarves and orcs compare, and a chance to get shot down by my thoughtful readers. The punchline is 6:1 assuming parity of number and an infinite and unrestricted terrain that +Peter V. Dell'Orto doesn't love at all (and neither do I, but that is material for another post). 

Principle

The goal here is to come up with a way to quantify relative troop strength. I'd like to take into considerations weapon skills, active defense, combat damage and armor. This means that TS would vary depending on opponents, but since the Khazad-dum campaign involves a limited selection of fighters this shouldn't be too much of a problem to come up with numbers.

Where P(wpn skill) is the weapon skill of the unit, P(active defense) is the best active defense effective level (including shield and possibly retreat), DR(eny) is the DR of the opponent's torso, P(damage  >= DR(eny)) is the probability to roll a large enough damage to do penetrating damageon the torso, P(critical hit) is the base probability of a critical hit.

The idea here is to compute the Expected number of penetrating hits caused by a group of n fighters engaged in melee combat. 

Dwarven Elements

The lowest level elements of the dwarven Weapon-Host are the the Battle-guard (21 X Two-handed axes), Axmens (21 X Warhammers) and Archers (7 X H. Crossbows). 

P(wpn) -- Assuming a main weapon skill of 12, P(wpn) for the melee fighters will be 0.75. The crossbowmen are going to be assumed to fire at an average range of 15 yds (underground), which means a target number of 7, and P(wpn) = 16.2%. 

P(active defense) -- With a main weapon skill of 12, the parry will be 9. Also assuming that a parry would be assisted by a step back (+1 bonus). P(active defense) = 0.5

P(critical hit) -- This is dwarf independent. This probability is set to 0.02... an overestimate but who is going to sweat the shavings in TS?

Damage -- Weirdly enough, ST 12 great-axe and warhammer both are doing 1d+5. A crossbow with a goat's foot shoots at ST 16, or 1d+5. 

P(wound) -- Dwarves have to beat the Orcs's DR 4. 1d+5 has a base damage range of 6-11. All hits are thus expected to be penetrating. P(wound) = 1.0

In Summary:

• Weapon Host ( 3 Units ) : TS = 1840 (75 firepower)
• Unit ( 7 Attacks ) : TS = 612 (12.5 firepower)
• Attack ( 7 Lots ): TS =  87.5 (3.5 firepower)
• Lot : TS = 12.5 (0.5 firepower)
• Battle-guard (21 dw): TS = 6
• Axemen (21 dw): TS = 6
• Crossbowmen (7 dw) : TS=0.5

Orcs Elements

Let's assume an element of size 20 orcs. 

P(wpn) -- Assuming a main weapon skill of 10, P(wpn) for the melee fighters will be 0.50.

P(active defense) -- With a sheild skill of 10, the parry will be 8. Also assuming that a parry would be assisted by a step back (+1 bonus) and a medium shield (+2 DB). P(active defense) = 0.62

P(critical hit) -- This is orc independent. This probability is still set to 0.02.

Damage -- A spear weilded by a ST 8 orc does 1d-1.

P(wound) -- Dwarves' mail shirt has DR 4. The orcs do 1-5, and will do penetrating damage in 1/6, or  0.16.

In summary, an element of 20 orcs which roughly matches the Battle-guard in size, has TS = 0.8, rounded up to 1.0

How does this pans out?

This means that an equal number of dwarves and orcs engaging in a terrain that is unrestricted, the base odds would be 6:1. This may change with troop and equipment quality. This is about how I had envisioned my cinematic orcs to behave. Of course, unrestricted terrain and number parity between orcs and dwarves are two really funny assumptions to make. The former will both be a possible asset for either foes, the late broken assumption will herald trouble for the dwarves. I have not worked out the specifics of underground mass combat yet, but sieges/engineering work and reconnaissance will have special meanings. 

The advantage of this approach, although rough, is that I can figure out the effect of outfitting all orcs with blunt weapons pretty quickly... and I'm sure that the dwarves PCs hope that this shift in orc equipment isn't going to happen.