A2’s “optimal” position (profit maximizing position) for ad is the number 2    position

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 paper¹, 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