Lanchester’s Laws and RTS Design

(I’ve been playing a lot of World of Tanks lately. I can’t talk much about it because of the NDA, but as soon as the open beta rolls around I will make a post about the game.

I have a few other articles I’ve written this month that are awkwardly close to completion. Hopefully I’ll get them up soon. Here’s a short post to tickle your brain while I put together more substantial content.)

Predicting casualties is easy when two even-skilled sides are fighting in melee, says Lanchesters' Law:

In ancient combat, between phalanxes of men with spears, say, one man could only ever fight exactly one other man at a time. If each man kills, and is killed by, exactly one other, then the number of men remaining at the end of the battle is simply the difference between the larger army and the smaller, assuming identical weapons.

But what about when units with ranged weapons engaged? The same simple model can no longer hold.

With firearms engaging each other directly with aimed fire from a distance, they can attack multiple targets and can receive fire from multiple directions. The rate of attrition now depends only on the number of weapons firing. Lanchester determined that the power of such a force is proportional not to the number of units it has, but to the square of the number of units. This is known as Lanchester's Square Law.

This fact is of critical importance for RTS design. Games that mix melee and ranged combatants can face strange balance issues that arise because of asymmetric forces of melee and ranged combatants combining in different ways. Ranged units may be balanced against one another, but when melee units are added the balance is damaged more than the addition of another ranged unit would have. 

In games that consist entirely of ranged units, like Company of Heroes, balance is a fickle thing. When developers make even a small change to a unit’s capabilities, the squared effect of that change can cause ripples through the entire metagame and cause certain crazy strategies to become viable (pioneer spam was one such issue in CoH).

This fickleness applies to both unit strength and the cost of units. Adding to a numerical advantage by cheapening a certain unit for one faction in an RTS can cause very severe issues if the other faction isn’t also adjusted, because the asymmetry will cause a much larger effect on the battlefield than most anyone will expect.