Game Development Reference
In-Depth Information
certainly want to attach weights to the various factors they include. The equations
also don't take into account special capabilities such as stealth or leadership. A unit
with a special capability should cost more than a unit that is otherwise identical but
lacks that capability, but there is no rule of thumb for determining just how much
more it should cost. Only play-testing and tuning can produce a balanced set of units
for all sides in the war. Be sure to read the section “Avoiding Dominant Strategies”
in Chapter 11, “Game Balancing,” before setting attributes for your units.
PRODUCTION RATES, UNIT NUMBERS, AND LANCHESTER'S LAWS
Frederick William Lanchester founded the field of operations research, which stud-
ies subjects such as logistics and production efficiency. In the course of his work, he
devised two laws regarding the relative strengths of enemy forces. One, Lanchester's
Linear Law, states that in hand-to-hand combat the relative strengths of two armies
are simply proportional to their numbers of troops. Since one fighter can only ever
engage one other fighter at a time, the force relationship is a simple one.
NOTE
Some strategy
games implement unit
AI such that when a
group of units fires
on another group,
the attackers will all
concentrate their fire
on the weakest enemy
first before moving on
to the next. This takes
the enemy out of action
more quickly, and
reduces the dilution
effect somewhat.
His other law, Lanchester's Square Law, refers to the relative strengths of forces
made up of units that can aim and shoot at one another from a distance and can
concentrate their fire. In this case, the strength differential is not proportional to
the sizes of the forces but to the
square
of their sizes. Imagine two forces, Red and
Blue, both made up of identical units. Blue has three times as many units as Red
has. It seems as if Blue is three times as strong as Red. But in fact, it's
nine
times as
strong. Here's why: Three Blue units are concentrating their firepower on each Red
unit. But Red's firepower is also
diluted
over a force three times as big. Each Red unit
is firing at only one Blue unit, and two other Blue units aren't being fired upon at
all! The combined effect is that Blue is nine times as strong.
What this means in practice is that masses of concentrated firepower are not only
effective, they're very, very effective. For strategy games, this means that if you give
one side twice as many units as the other, you're actually giving it
four
times the
advantage. You're unlikely to do this intentionally, but it might happen by accident
if you don't set the production rates of units carefully. If one side can produce units
faster than the other, its advantage is not the difference between the numbers of
units but the square of the difference—assuming that we're talking about units
with ranged weapons. Hand-to-hand units still follow Lanchester's Linear Law.
NOTE
Lanchester
was actually writ-
ing about aerial
dogfighting among
propeller-powered
fighter planes. These
are very “pure” battle-
field conditions: There
is no terrain to take
advantage of (except for
clouds) and no oppor-
tunity for resupply.
This also means that you can't balance the effect of one side's having twice as
many units by giving the other side a twofold advantage in one of its units' attri-
butes. Even if you double the smaller side's shot power, those shots are still being
diluted over a larger force. You have to give the smaller side a
fourfold
advantage in
shot power to compensate for the larger side's squared numerical advantage.
Lanchester's laws describe battle in abstract terms. They don't take into account
battlefield conditions, maneuvering, reinforcements, and so on. Nevertheless, they
serve as a valuable warning to game designers trying to balance strategy games:
