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The process by which
Google determines

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which ads to display
for which queries

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consists of three key steps.

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First, Google runs an auction
where advertisers place bids

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for different queries that they
want to display their ads on.

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Next, Google uses each
bid in a metric known

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as the Quality Score,
which basically measures

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how well a particular ad
fits a particular query

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to decide a quantity known
as the price-per-click.

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Google does this for each
advertiser and each query.

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Finally, and this is where
optimization plays a key role,

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Google decides how often to
display each ad for each query.

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This problem, as
we'll see shortly,

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can be formulated as a
linear optimization model.

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Let's begin by
thinking about the data

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that we need for this model.

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In particular, let's think
about the price-per-click.

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So as we just discussed,
Google decides

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each advertiser's
price-per-click.

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The price-per-click is
how much each advertiser

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pays Google when a user clicks
on the ad for that query.

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Each advertiser also
specifies a budget.

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This is the total
amount of money

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that the advertiser
has available to pay

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for all the clicks on their ad.

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Every time a user clicks
on the advertiser's ad,

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the advertiser's budget is
depleted by the price-per-click

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for that ad for
that user's query.

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Let's illustrate this
with a small example.

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So suppose that we are Google,
and three of the major wireless

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service providers in the United
States -- AT&T, T-Mobile,

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and Verizon -- come to us
wanting to place ads on three

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different search queries: query
1, which is "4G LTE"; query 2,

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which is the "largest
LTE"; and query 3,

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which is "best LTE network".

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If you're not familiar
with these terms,

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4G and LTE basically refer
to different standards

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of high speed wireless
data communication.

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The table here shows
the price-per-click

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of each advertiser
in each query.

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So for example,
this 10 here means

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that T-Mobile will
pay Google $10

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every time a user
searches for query 1

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and clicks on T-Mobile's
advertisement.

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In this example,
T-Mobile's budget is $100.

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If T-Mobile begins
advertising and by some point

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five people have
clicked on T-Mobile's ad

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when they search for
"4G LTE", then T-Mobile

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will need to pay five times
$10, or a total of $50.

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If T-Mobile's
budget is $100, this

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means that T-Mobile is
left with $100 minus $50,

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for a remaining budget of $50.

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Now, while the price-per-click
is important to know,

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we must remember that the
price-per-click is exactly

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that, the price that
the advertiser pays

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to Google for a single click of
a given ad, on a given query.

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This price is paid only if
the user clicks on the ad.

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But typically, the people who
use Google search engine, who

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are you and me, will
not click on every ad

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that is shown to them.

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Therefore, we need
a way to capture

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how often users click on ads.

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This is where the idea
of click-through-rate

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becomes useful.

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The click-through-rate
is the probability

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that a user clicks on an
advertiser's ad for a given

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query.

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You can also think of this as
the average number of clicks

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that we expect per user.

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And this quantity is
defined, as we said,

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per advertiser and per query.

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So to illustrate this, for the
example that we just introduced

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a few slides ago,
suppose that we

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have the following
click-through-rates.

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The number 0.08 here means
that there is an 8% chance

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that a user who searches
for best LTE network

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will click on AT&T's ad
if it is shown to them.

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In terms of the number of users
who click on an ad for a given

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query, this means
that for 50 users,

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if the click-through-rate
is 0.08,

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we expect to see 4 users
clicking on the ad.

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Similarly, if there
are a hundred users who

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view the ad and 8% of
them click on the ad,

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we expect to see
eight users clicking

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on AT&T's ad for query 3.

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In the next video, we'll
define additional data

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that we'll need to
formulate the problem.

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In particular, we will see
how the click-through-rate

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and the price-per-click
can be combined together

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to obtain a new quantity called
the average price per display.

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This derived quantity
will form a crucial part

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of our linear
optimization model.