Game Development Reference
In-Depth Information
Referring back to our Guess Two-Thirds example, the group that we had iden-
tified as random guessers seemed to be a uniform distribution across the range from
0 to 100. We could get away with modeling their guesses as random numbers
from 0 to 100. However, the distribution of the slightly more thoughtful group was
certainly
not
uniformly distributed (Figure 11.2). If we wanted to model the guesses
that group would yield, we would need a slightly more involved approach.
Perhaps the most well-known of all probability distributions is the
normal distri-
bution
. People often refer to it as a
Gaussian distribution
after Carl Friedrich Gauss,
the 19th century German mathematician and scientist. Most of us best know this
function, however, by its colloquial name of the
bell curve
. The reason for this is
purely visual coincidence—in its standard form, it looks like a bell.
We find the hallmark of the bell curve in all its shapes and sizes all throughout
nature, science, sociology, astronomy, and behavior. Even in just observation of
humans, much of what we can measure ends up on a bell curve somewhere. Height,
weight, strength, speed, and intelligence (IQ) are measurements that tend to lie in
a bell curve. Even statistical processes as simple as flipping multiple coins or rolling
multiple dice churn out bell curves. It is this connection that makes normal distri-
butions one of the most valuable components in modeling behavior… and, there-
fore, one of the ones we will examine in greater detail.
P
ROPERTIES OF
N
ORMAL
D
ISTRIBUTIONS
Every normal distribution has key components (Figure 11.4). These properties reflect
the size and shape of the distribution—and therefore the population it represents.
If we know these properties, we can make assumptions about the population.
Additionally, and more importantly to AI developers, we can also reasonably re-
create the curve that the distribution shows.
Range
The
range
of a distribution is a measurement of the distance between its lowest and
highest members. Sometimes, this is a function of the parameters of what we are
trying to measure. For example, in the Guess Two-Thirds Game the minimum
guess was 0 and the maximum was 100. The range could not be any wider than 101.
As long as at least one person guessed 0 and one guessed 100, the range would be
101.
