**4. Calculating
expected gross profits after user clicks an ad**
Let’s say an advertiser A1 has a *conversion
rate of 5%,* i.e. of every 20 visitors to her site, one of those visitors
becomes a paying customer.

Let’s also say that the *margin per
customer sale for A1 is $100*, i.e. for every sale, A1’s bottom line
gross profits (profits excluding click costs, see Glossary) increase by
$100. Ignoring repeat customers, one can then conclude that for every
visitor, advertiser A1 can expect (on the average) to make a profit of:

Expected Gross Profits = Conversion Rate
* Margin per Sale

Expected Gross Profits = 0.05 x $100 =
$5.00

Thus, if A1 is to make a Net Expected
Profit from her campaign, she can pay at most an average cost of $4.99
per click (or one cent less than Expected Gross Profits of getting a visitor
to her site).

Let’s now say that there is another
advertiser A2 who has a *conversion rate of 4%* (after someone lands
on his site) with a *margin of $75* per customer sale.

A2’s Expected Gross Profits then are

Expected Gross Profits = Conversion Rate
* Margin per Sale

Expected Gross Profits = 0.04 * $75 =
$3.00

**5. Which Advertiser
gets the top position **

Let’s make the following two assumptions
(both will be relaxed later)

1)CTR (Click Through Rate) of an ad is dependent
only on its position, i.e. the higher up the ad, the more clicks it will
get, regardless of what the ad copy actually says. Another way to
think of this assumption is that all advertiser ad copy’s are of the
same “quality”.

2)Ad position is determined solely by bid
amount (i.e. Quality Score is not taken into account); furthermore, advertiser
pays 1c + bid amount of next highest bidder.

In his paper^{1}, Hal Varian, a
Professor at UC/Berkeley implies that **the top position belongs to the
advertiser with the highest expected profits** obtained from a visitor
to their website. In the above example, that would be advertiser
A1 who has higher expected gross profits of $5.00 compared to $3.00 for
advertiser A2. Even though the proof of this is fairly mathematical,
the conclusion itself should make intuitive sense. After all, the
advertiser who can expect to gain the most per click ($5.00 in A1’s case)
is going to be able to afford to pay the most per click and thereby secure
the top position.

Let’s now take a different approach and
“concretize” this with examples using some more High School Algebra.
After doing that, we’ll also first relax assumption 1 above and then
relax assumption 2 above

**6. Calculating
Expected Net Profits **

As defined in the Glossary:

Expected Net Profits per Click = Expected
Gross Profits per Click – Click Cost, i.e.

We subtract the cost of getting the visitor
to the site from the Expected Gross Profits made to determine the final
Expected Net Profits.

For more specificity, let’s assume the
following:

i)whichever advertiser’s ad (A1 or A2)
appears on the number 2 position pays $1.00 per click (due to the existence
of more advertisers A3…..in the number 3 position and below)

ii)Ad in the number 1 position gets 10%
of clicks and Ad in the number 2 position gets 6% of clicks regardless
of which advertiser (A1 or A2) occupies the number 1 position and number
2 position

iii)There are 100 impressions of both ads
per day