De-emphasise Ad Position in Pay Per Click Campaigns
By: Nadir | Posted: 24th February 2008
1. Overview & Introduction.
Anytime a user does a search on popular search engines such as Google or Yahoo, in addition to the natural (or organic) search results, a set of sponsored links are returned as well. These sponsored links are essentially advertisements and when the user clicks on any of these ads, the user lands on a "landing page" on the website of the advertiser. In return, the advertiser pays the search engine for delivering a visitor to their website.
More specifically, the advertiser chooses a set of keyword phrases and states a bid amount for each such keyword phrase. This bid is the maximum amount that the advertiser is willing to pay the search engine when a user searches on one of the keyword phrases (that the advertiser has bid on), and clicks on the ad.
In general, when a user searches on a keyword phrase, a set of ads appear. The ads themselves are ranked by the bid amount of the advertiser, and on both Google and Yahoo, by the ad's Quality Score. (This Quality Score is calculated by the search engines - the higher the relevance of the ad copy and the landing page to the keyword phrase searched on, the higher the Quality Score).
Note that in the model described here, the advertiser only pays the search engines if someone clicks on the ad. The amount they pay can never exceed their bid amount and is usually less. It is a minimum amount required to keep the ad in position. So if all ads had the same Quality Score, the advertiser would only pay 1c + the bid amount of the next highest bidder.
2. Motivation for Article
It is a well known fact that all other things being equal, the higher up the ad appears in sponsored links sections in search engines, the more clicks it will get. Advertisers, therefore, understandably try hard to get those top positions for their ads. However, since advertisers are competing with other advertisers for those top positions, higher up positions generally cost the advertiser more per click and therein lies the tradeoff.
In this article, I demonstrate that advertisers should not obsess too much on the position of their ad in their campaigns. Given an advertiser's Expected Profits from a click and their Quality Score relative to that of their competitors, there is an optimal or profit maximizing position for their ad. At any given time, this optimal position is just as likely to be, say, in the number 8 position as in the number 1 position.
Even though this article is fairly Mathematical, it only uses High School Algebra level Math. If you'd rather not wade through the Math, then just know this: track profits against bid amounts and decide what bid amounts generate higher profits. Then, let the ad fall in whatever position it may.
3. Glossary of terms used
Click Costs is the dollar amount that an advertiser pays the Search Engines (e.g. Google/Yahoo) when users click on their ad.
Click Through Rate (CTR) is the frequency with which an ad is clicked on as a percentage of the total number of impressions for that ad.
Conversion Rate is the number of users who buy as a percentage of the users who visit the advertiser's website.
Expected Gross Profits is expected or average profits realized after someone clicks on an ad and lands on the advertiser's website.
Expected Net Profits is Expected Gross Profits minus Click Cost
Margin is the Sale Price minus all the costs incurred to support that sale excluding Click Cost.
Point of Position Indifference is the point at which an advertiser makes the same profits regardless of which one of two positions, e.g. position number 1 or position number 2 their ad appears in.
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 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
7. A2's "optimal" position (profit maximizing position) for ad is the number 2 position
Let's say that we have an initial situation where A1 is bidding $1.30 per click and her ad is in the number 1 position. A1 pays a little less, say for example, $1.25 per click because A2 is bidding $1.24 for a click. A2 is in the number 2 position paying $1.00 per click as assumed above in i) due to A3 bidding $0.99
Summary of the different parameters and their current assumed values
Conversion Rate Margin per Sale Position 1 CTR Position 2 CTR Impressions per Day Cost per Click
A1 5% $100 10% 6% 100 $1.25
A2 4% $75 10% 6% 100 $1.00
A1's daily Expected Net Profits are
Clicks per Day * Expected Net Profits per Click =
Impressions per Day * Click Through Rate * (Expected Gross Profits per Click - Cost per Click) =
100 * 0.10 * (5%*$100 - $1.25) = $37.50
A2's daily Expected Net Profits are:
Clicks per day * Expected Net Profits per Click =
Impressions per Day * Click Through Rate * (Expected Gross Profits per Click - Cost per Click)
100 * 0.06 * (4%*$75 - $1.00) = $12.00.
What if A2 was to now increase his bid from $1.24 to $1.35 and get the top position for $1.31 per click? (1c + A1's bid of $1.30). A1 would then get the second position for $1.00 per click as assumed in i) above due to A3 bidding $0.99
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
A1 5% $100 10% 6% 100 $1.00
A2 4% $75 10% 6% 100 $1.31
A1's daily Expected Net Profits now are
Clicks per Day * Expected Net Profits per Click =
Impressions per Day * Click Through Rate * (Expected Gross Profits per Click - Cost per Click) =
100 * 0.06 * (5%*$100 - $1.00) = $24.00, i.e. a decrease from the earlier $37.50
A2's daily expected profits now are
Clicks per Day * Expected Net Profits per Click =
Impressions per Day * Click Through Rate * (Expected Gross Profits per Click - Cost per Click) =
100 * 0.10 * (4%*$75 - $1.31) = $16.90 an increase from the earlier $12.00.
In order to increase her profits, A1 would now increase her bid to get the number 1 position again and A2 would respond in kind. This jostling for the number 1 position would continue until one of the advertisers expected net profits actually reduce in going from the number 2 position to the number 1 position. So which advertiser would drop out first from this rat race to the top? To answer that, let's calculate the "break even point" for each advertiser, i.e. the bid amount at which the advertiser is indifferent between the number 1 position and the number 2 position.
In tabular form:
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 10% 6% 100 Y $1.00
For A1, this "Point of Position Indifference" is when her daily Expected Net Profits from the number 1 position = daily Expected Net Profits from the number 2 position.
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 * 0.10 * (5%*$100 - X) where X is the click cost that A1 pays for the number 1 position (1c + A2's bid)
Daily Expected Net Profits from the 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 * 0.06 * (5%*$100 - $1.00)
"Point of Position Indifference" occurs when we equate these:
100 * 0.10 * (5%*$100 - X) = 100 * 0.06 * (5%*$100 - $1.00)
Solving for X; X = $2.60
Thus A1 will continue to increase her bid for the number 1 position until she is paying $2.60; after which she would prefer the number 2 position.
For A2 as well, the "Point of Position Indifference" is when his daily Expected Net Profits from the number 1 position = daily Expected Net Profits from the number 2 position.
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 * 0.10 * (4%*$75 - Y) where Y is the click cost that A2 pays for the number 1 position (1c + A1's bid)
Daily Expected Net Profits from the 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 * 0.06 * (4%*$75 - $1.00)
"Point of Position Indifference" occurs when we equate these:
100 * 0.10 * (4%*$75 - Y) = 100 * 0.06 * (4%*$75 - $1.00)
Solving for Y; Y = $1.80
Thus A2 will continue to increase his bid for the number 1 position until he is paying $1.80; after which he would prefer the number 2 position.
Thus A2, who has the lower Expected Gross Profits per click will drop out from the "race" first and will therefore settle for the number 2 position. Hence, the optimal or profit maximizing position for A2 is in the number 2 position.
8. What if A2 improves the quality of his ad copy increasing his CTR by 100%
Let's now relax Assumption 1) above where we assumed that the CTR of an ad was dependent only on its position and not on the ad copy. In particular, let's say that A2's ad copy is superior and gets twice the number of clicks compared to A1 in any given 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 $1.00
With this, let's again solve for the "Point of Position Indifference" for both A1 and A2.
For A1, nothing changes including the CTRs.
Thus X is still $2.60; i.e. A1 will continue to increase her bid for the number 1 position until she is paying $2.60; after that she would prefer the number 2 position.
For A2, the CTRs have changed, doubled to be precise. So let's re-calculate this "Point of Position Indifference" which occurs when A2's daily Expected Net Profits from the number 1 position = daily Expected Net Profits from the number 2 position.
Daily Expected Net Profits daily 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 the number 1 position (1c + A1's bid)
Daily Expected Net Profits daily from the 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 - $1.00)
"Point of Position Indifference" occurs when we equate these:
100 * 0.20 * (0.04*$75 - Y) = 100 * 0.12 * (0.04*$75 - $1.00)
Solving for Y; Y = 1.80 (i.e. Y did not change either)
So the surprising result is that "Point of Position Indifference" for A2 does not change even when A2's ad copy is so much better that it is now getting twice as many clicks as A1 for any given position.
Thus, even with a superior ad copy, A2 must, like before, concede the number 1 position to A1 who has the higher expected profits per click.
The reason that this somewhat counter intuitive result is true is that the CTR from A2's ad copy is uniformly better than A1 (twice as much in both position 1 and position 2). So even though A2's absolute daily profits can increase substantially as the CTR increases due to superior ad copy, the point of position indifference between position 2 and position 1 does not change since the ad's 100% improvement in CTR applies equally to both position 2 and position 1. (The result could be different if, for instance, the CTR on the number 1 position increases much more as a percentage than the CTR on the number 2 position).
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.
10. Summary and Conclusion
In this article we showed that every advertiser has a position for their ad that is optimal for them, i.e. one that maximizes their profits. This position need not be the top position. In fact, only one advertiser will have the number 1 position as the optimal position for themselves. In general, a scheme with eight ad positions will mean that for a certain advertiser, the number 8 position is the optimal position for themsevles, i.e. their profits are maximized in this number 8 position.
In a world without quality score, this optimal position is determined solely by expected profits. The higher the expected profits per click, the higher the optimal position for the ad. This was seen to hold true regardless of the quality of the ad copy of the different advertisers as long as the higher quality ad resulted in the same percentage increase of clicks across the different ad positions.
Finally, we saw that with quality scores, optimal ad positions are determined both by expected profits per click and quality score compared across competitors. In all cases, however, it is of paramount importance to note that for every advertiser there is a optimal position for his/her ad which maximizes their profits. Thus, advertisers should not focus too much on trying to get into the top ad spots without proper data backing these goals.
11. Bibliography
http://www.ischool.berkeley.edu/~hal/Papers/2006/position.pdf
12. About the Author
Nadir Hussain is an experienced entrepreneur who is now a COO at Media Flint (http://www.mediaflint.com). He has been a Director in eBay's Technology group, a Senior Consultant at Deloitte & Touche, and a Software Engineering Manager at IA Corporation. Overall, Nadir has over 15 years of work experience that includes product management, business development, software development and more recently in Search Engine Marketing. His education comprises of an MBA from UC/Berkeley and a MSEE from Stanford University.
Nadir can be contacted at nadir.hussain@MediaFlint.com
http://www.mediaflint.com
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Tags: google, keyword phrase, yahoo, search engine, keyword phrases, relevance, advertisers, advertiser, highest bidder, advertisements, popular search engines, motivation, tradeoff, quality score