**What happened so far**

This post is the third part in a series of posts to reveal the secret of AdWords quality score.

Previous posts:

The first post was about everyone viewing quality from a different perspective. This issue stands in the way of understanding quality score. The second post was about Google addressing quality, but actually being more interested in short-term profits. All that talk about quality appears to be part of a marketing campaign.

**Assumptions**

In this post we hold on to this assumption: Google ultimately wants to maximize profits. Statements with regard to quality will be ignored for the time being. This reduces the quest for quality score to a fairly easy question: How can Google maximize its earnings?

Not all of Google’s statements about quality score seem to come from their marketing department. There are some technical details they have issued which hardly fit into the category of marketing. Still, they are very limited and sometimes vague.

One such technical detail is how the ad auction works. For the ad auction, the bid and quality score for each participating ad are considered the factors. By multiplying these two factors, you get the “Ad Rank” which determines the order for the ads. The higher your “Ad Rank”, the better your ad will rank in the paid results.

To get to the bottom of quality score, the following assumptions need to be made:

**Assumption 1:** Google is trying to maximize profits.

**Assumption 2:** The ad auction works as described:

Ad Rank = Bid * Quality Score

**Hence:** The ad auction has to maximize profits.

The ad auction consists of bids and quality scores for a certain number of ads. Bids and participating ads are set, so the only variables are the quality scores.

**So the pivotal question becomes:** How does quality score need to be conceived in order for the ad auction to maximize profits?

**Conclusions**

Google earns money only when someone clicks on an ad. But the click isn’t guaranteed: not every user clicks an ad. So it’s not only important how much an advertiser bids for a click, but also how many clicks he actually makes.

While the ad auction is running, it is uncertain whether there will be a click or not. The only thing that is certain is that there is a search where ads are to be displayed. So we have to determine what order of ads maximizes the profit Google makes from these impressions. That’s surprisingly straight forward.

The potential profit from an ad per impression is determined by multiplying its maximum bid by its click-through-rate (CTR). This way a bid for a click can easily be calculated into a bid per impression (the instance an ad is displayed on the search results page).

Example:

Advertiser A bids $1.00 per Click and has a CTR of 10 %

This means Advertiser A bids $0.10 per impressionAdvertiser B bids $1.50 per Click and has a CTR of 40 %

This means Advertiser B bids $0.60 per impression

Of course, click through rate is dependent on ad position. In this example, let’s say Advertiser B was always in the first position and Advertiser A was always in the second one:

Advertiser A had a CTR of 10 % in second position.

Advertiser B had a CTR of 40 % in first position.

These click-through-rates can’t be compared on the same level: Advertiser B had a much higher CTR, but also had the better position. The influence of ad position has to be eliminated in order to make the CTR’s comparable. The question is which CTR each ad would yield in the same position.

To simplify things, let’s assume that an ad’s CTR would be cut in half when its position is changed from #1 to #2. Mathematically, this can be expressed by using “position CTR coefficients”:

For position 1: 1.0

For position 2: 0.5

With these we can calculate CTR’s for other positions. Normalized for the first position, this leads to the following:

Advertiser A would get a CTR of 20 % on the first position (10 % / 0.5)

Advertiser B would get a CTR of 40 % on the second position (40 % / 1.0)

Now we can also calculate comparable bids per impression:

Advertiser A bids $1.00 per click and has a CTR of 20 % for position 1

It follows that Advertiser A bids $0.20 per impression on position 1Advertiser B bids $1.50 per click and has a CTR of 40 % for position 1

It follows that Advertiser B bids $0.60 per impression on position 1

With the help of our position CTR coefficients we can now calculate impression bids for other positions:

Bid per impression on position X

= Bid per click * CTR for position 1 * position CTR coefficient for position X

So for position 2 one would have to multiply the impression bids by a factor of 0.5:

Advertiser A bids $0.1 per impression in position 2

Advertiser B bids $0.2 per impression in position 2

Looking at the possible ad orders, it’s easy to see which one is the best for Google. In this case there are only two options:

Advertiser A in position 1 (impression bid: $0.2) and Advertiser B in position 2 (impression bid: $0.3) add up to a total impression bid of $0.5.

Advertiser B in position 1 (impression bid: $0.6) and Advertiser A in position 2 (impression bid: $0.1) add up to a total impression bid of $0.7.

The last combination represents the highest and therefore most profitable “total impression bid”. Of course, one doesn’t have to go through all combinations every time: the optimum order is always one of the impression bids for position 1 (in this case: first the ad with an impression bid of $0.6, then the one with the $0.2).

Comparing this approach with the ad auction, it’s obvious what quality score has to be:

Official ad auction: Ad Rank = Bid * Quality Score

Optimal ad auction: Ad Rank = Bid * position adjusted CTR

Thus, expressed in equations:

From

Official ad auction = Optimal ad auction

It follows that

Quality score = position adjusted CTR.

**Could this be right?**

To get right to the point: Yes, this theory is correct. Still, one small component is still missing. The final “secret of quality score” will be solved in the next post.

{ 1 comment }

Our company is very puzzle by the QS. Make it very hard to know what to do. The only advise we get from Google Team is to increase to bid. Your post throw some light into what is going on in the black box.

Thanks for sharing. Looking forward to your next post.

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