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a mathematical notation indicating the number of times a quantity is multiplied by
itself) of some attribute of that object (e.g., its size, its rank, its height), the frequency
is said to follow a power law. Like the more standard normal or bell curve, the power
law is a probability distribution.
There are many phenomena that follow a power law distribution. Many aspects of
sponsored search follow power laws, including frequencies of terms used in queries,
the frequency of visits to Web sites, and the frequency of clicks on SERP links. This
is specifically why some keyphrases are much more expensive than others in the
same vertical. A lot more people use these selected phrases or these phrases generate
much more of revenue. These high-volume keywords are called the head. The low-
volume keywords are called the tail.
Potpourri
: Powers laws are related to a business concept known as the law
of diminishing marginal returns that, when graphed, often display power laws
distributions.
For sponsored search, the law of diminishing marginal returns [
61
] is that the
first dollar of advertising spent will generate more revenue in sales than the next
dollar. That second dollar will generate more revenue than the next dollar, and so
on. Eventually, we reach a point where it will cost more than a dollar of advertis-
ing to generate a dollar of revenue.
The phenomena of the power law also help explain why sponsored search has
lowered the cost of advertising relative to its return on investment. With mass media
approaches, such as print and television, one has to canvas all the people who are the
audience of that outlet to target the relatively small set of potential customers. However,
with sponsored search, advertisers can specifically target individual consumers.
What does the power law tell us?
The power law describes phenomena where large events are rare, but small events
are quite common. For example, there are a few very large earthquakes, but there are
many small earthquakes. There are a few megacities, but there are many small towns.
Within the English language, there are a few words (e.g.,
a
,
as
,
and
,
the
) that occur very
frequently, but there are many words that rarely occur (e.g.
obdormition
,
tanquam
).
A power law is much different than the normal distribution, which many people
are used to dealing with in statistics. A comparison of a normal and power law distri-
bution is shown in
Figure 3.8
.
In a normal distribution, there is a mean or average, which is a typical value around
which other measurements are centered. This distribution describes several phenom-
ena in the world, such as average test scores of a random population, distribution of
people's height, or distribution of people's weight. However, not all measurements
peak around a typical value. Instead, some things, objects, or events vary over an enor-
mous range, sometimes with many orders of magnitude. A classic example is wealth.
The richest person in the world has many times more wealth than the poorest person.
Such variance in magnitude makes fairly common measures, such as average,
meaningless. For example, say there is a party of thirty people in the room. As a party
