Fantastic Frontiers: Tactical Advantage

The previous post was about figuring out who bothers to show up to fight a battle. That's only half the story. The other half of the story is figuring out who survives until the end of the engagement. Military historian Richard Gabriel, author of Man and Wound in the Ancient World, writes:

In most battles of antiquity, a victorious army could expect to suffer approximately 5.5% killed in action, and 6% wounded, or approximately 12% of its force. A defeated army could expect to suffer horrendous casualty rates of approximately 37% killed and 35% wounded. These levels of dead and wounded were inflicted usually after the battle formations were broken and the enemy was surrounded or caught in the pursuit. (from Scipio Africanus: Rome's Greatest General)

That's a very "swingy" result to model in a game!

But even this doesn't adequately reflect what happens during an Age of Discovery between early-modern explorers with muskets and bronze age tribal warriors with clubs. If we accept that Cortes had a force of 400+ rondeleros fighting for the better part of four hours against a continuous stream of Tlascallans, then even a modest rate of one attack eliminated every five minutes per Spanish soldier gives a total casualty tally of 4*12*400 = 18,200. (Of course, a lot of these "casualties" were probably not kills, but enemy warriors who lost their nerve at the sight of horses and guns and ran away. That's already covered by the morale check system.) This would be against the recorded outcome of about 60 casualties (mostly wounded and with only a few immediate deaths) on the Spanish side. In other words, the ratio of casualties is about 300 to 1 in favor of the high-tech side!

The difference here probably had less to do with firearms, since matchlocks were slow to reload and Cortes only had a dozen of them anyway. The critical difference was steel. Europe had gone through several iterations of armor-piercing technology, and by this point Toledo steel was proofed to the point of being able to withstand crossbow bolts and musket balls. Stone age weapons like obsidian-studded clubs could do little more than hack at the exposed lower legs of a swordsman. Despite the common assumption that the age of armor dominance was in the high middle ages, this later period of primitive firearms actually represented the apex of enthusiasm for heavy 50 lb plate armor.

So the casualty system really needs to meet two criteria:

• generate huge disparities in casualty rates when appropriate
• give a hefty advantage to superior armor

Small marginal RPG-like differences like 5% bonuses to hit just aren't going to cover this kind of asymmetry. Instead, we need an almost logarithmic scaling to combat results.

The bottom-line number that's important here is the ratio of attackers to casualties. We need a dice roll to generate this number directly, for both sides. Here's a familiar-looking 3d6 bell curve table for RPG statistics:

Let's reinterpret this as giving the multiplicative ratio for attackers to casualties. When your army is attacked, roll 3d6 and look at the table. A result of +3 means that for every 3 attackers, you take 1 casualty. A result of -3 means that for every 1 attacker, you take 3 casualties. You can see that with this interpretation, the most common results of +1, 0, or -1 are all pretty much the same thing, an easy 1:1 ratio. (Presumably each side will be making its own roll, or better yet, the results are anticorrelated so that a +3 for one side is a -3 for the other.)

But now let's factor in armor. Let's say that some of your force is outfitted in plate mail and a shield, which my old RPG intuitions tell me should have an armor value of 7. With a dice result of +3, this now results in a ratio of 10 attackers to 1 casualty. Even with the worst result of -3, the ratio is still 4 attackers to 1 casualty in your favor. And now there's an important difference between +1 and -1 results. On average, it will take a force 7 times larger than the plate-armored one, in order to wipe it out completely.

So a force of 500 Spanish swordsmen won't go down unless it's attacked by 3500 Tlascallans -- which the morale system won't allow to happen all at once! On the other hand, the Spanish can realistically kill a number of unarmored enemy warriors equal to themselves. This is probably enough to clear out at least two "morale boxes" from the previous example. So if the morale roll is around 7, the highest boxes will be killed, and the lowest boxes will run away. This result looks like it's perfectly reasonable, a sign that this approach is on the right track.

Next project: Making a mock-up battle board and doing a fully detailed example that includes box placement, ranged and artillery barrages, a morale check, and the application of casualty results.