9. Taking
Quality Score into account
We have seen above that A1 will continue
to bid for the number 1 position until $2.60 and that A2 would continue
to bid for the number 1 position until $1.80 thus leading to the result
that A1’s optimal position is the number 1 position and A2 should settle
for the number 2 position as his optimal position. What happens if,
say, A2’s quality score is now twice that of A1 and A3? (Bid amount
of A3 in number 3 position was what determined the click cost of $1.00
of advertiser in the number 2 position).
In tabular form, again, here are the parameters
and (new) values

Conversion Rate 
Margin per Sale 
Position 1 CTR 
Position 2 CTR 
Impressions per day 
Cost per Click in Pos. 1 
Cost per Click in Pos. 2 
A1 
5% 
$100 
10% 
6% 
100 
X 
$1.00 
A2 
4% 
$75 
20% 
12% 
100 
Y 
$0.50 
First note that A2 now pays only $0.50 for
a click in the number 2 position because A2’s quality score is now also
twice that of A3, so he has to now pay only half as much as before or half
of $1.00.
Now the result changes for A2 as below:
“Point of Position Indifference” for
A2
Daily Expected Net Profits from the number
1 position
Clicks per Day * Expected Net Profits per
Click =
Impressions per Day * Click Through Rate
* (Expected Gross Profits per Click – Cost per Click) =
100 * 0.20 * (0.04*$75 – Y) where Y is
the click cost that A2 pays for number 1 position
Daily Expected Net Profits daily from number
2 position =
Clicks per Day * Expected Net Profits per
Click =
Impressions per Day * Click Through Rate
* (Expected Gross Profits per Click – Cost per Click) =
100 * 0.12 * (0.04*$75  $0.50)
“Point of Position Indifference” occurs
when we equate these:
100 * 0.20 * (0.04*$75 – Y) = 100 * 0.12
* (0.04*$75  $0.50)
Solving for Y; Y = 1.50
So if A2 is willing to go all the way until
$1.50 for the number 1 position, then the only way that A1 will get the
number 1 position is if she bids till $3.00 for the number 1 position (2
* $1.50) because her quality score is half of A2. But A1 is going
to stop at $2.60 thus giving A2 the top position here.
(As an aside, note that the reason Y went
from $1.80 to $1.50 is that after A2’s Quality Score doubled, he was
paying only $0.50 rather than $1.00 for the number 2 position).
So when Quality Scores are taken into account,
expected profits alone will not determine optimal ad position. Rather,
one must take into account the fact that an advertiser with a lower Expected
Gross Profit may still have the number 1 position as their optimal position
because they will be allowed to bid less for that top spot due to a higher
quality score.