Damage Part 2 - Scaling

Scaling for infantry battles

Fundamentally, close combat is a line of contact phenomenon - because fighting occurs only along a line of contact, the damage done can only be proportional to that line of contact.

Also doubling the number of files in a unit doesn't mean the damage doubles - if the enemy remains a ten by ten square, the rectangle of twenty by ten doesn't have a larger line of contact with the square, so either formation has to be broken so that the longer formation wraps around the shorter one or damage remains as it was. The only way to let more soldiers attack while keeping formation is to organize 200 soldiers in two units that can attack separately.

Thus, the chief advantage of having more soldiers in a unit is not that it does more damage - it can absorb more damage because there are more soldiers to replenish losses, it can push harder if it is deep, it controls more area if it is wide - but damage is determined by the length of the line of contact, not by the number of soldiers available.

That in turn means that relative damage (i.e. the percentage of soldiers wounded or killed) a unit receivesis cut in half when its number of soldiers is doubled - because absolute damage (the actual number wounded or killed) stays the same.

Scaling for ranged combat

So, ranged combat can be argued to establish an area of contact between two units - the range of the projectiles typically allow the whole area of the attackers to fight the whole area of the defenders.

Potentially, this makes ranged combat more lethal than close combat, because while typically only 20% of an infantry unit actually use weapons, it's usually all of the ranged combat unit.

Scaling for mounted units

Now, consider a war elephant against the ten by ten infantry formation. The elephant is one unit, the infantry has a hundred soldiers, so can we really conclude that the infantry takes one hundredth of the damage?

The proposition is faintly absurd. Obviously the elephant is a match for a couple of soldiers and is able to attack a larger part of the line than just the one soldier before him. So one way to think about this is to see the war elephant (or any mounted unit) as equivalent to a number of soldiers in combat - so we could perhaps state that an elephant is worth 30 soldiers, and given the soldiers deployed on the elephant, a unit of two war elephants would be worth about 70 soldiers, be able to attack a line of ten meters worth of phalanx, and all that makes the scaling seem more reasonable.

A similar issue comes up when a mounted unit is subject to a ranged attack. Consider a chariot - two horses, a driver and the warrior. To a degree, the horses can fight (they can be made to rear up and beat with their hooves for instance) and the chariot itself has nasty blades sticking out along the axle, so the unit is worth more than just a warrior in close combat. However, only the soldier shoots in ranged combat, so a chariot is really only worth a single archer when shooting. When being shot at however, it is much more substantial than a single soldier - the incoming projectile can hit the driver, the warrior, a horse or the chariot itself, and all of these may do different kind of damage (generally you need to inflict more damage on a horse and much more on an elephant than on a human to get the same effect).

Naturally this is all a bit of guesswork, but the simulation by default assumes that each horse is worth two soldiers in close combat, each elephant 30 soldiers, and that damage received by a mounted unit is roughly distributed as mass, i.e. a 600 kg horse takes on average six times the damage a human does.

Continue with Timescales.

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