Over at the RKG blog, George Michie wrote an article on a very interesting question: How much do you matter to Google? Or, in other words: How much would it cost Google to lose an advertiser?

George looked at the decline of CPC’s in different scenarios of ad auctions where the top advertiser dropped out. He concluded that it matters a great deal how tightly packed an auction is. If there are a hundred advertisers with similar bids and quality scores the top advertiser is easily replaced with minimal declines in CPC’s. But even in loosely packed auctions the decline isn’t that big.

I was fascinated with the idea and started to play with the numbers myself. But I didn’t want to look only at CPC’s as they are just one part of the equation. While CPC’s matter a lot to advertisers, Google’s attention is on revenue. So how much revenue would Google lose if an advertiser dropped out of an auction?

Words of Warning

This is a long post, full of math and Excel stuff. If you don’t care about the methodology, you can skip to the conclusions.

Also, be aware that this post relies heavily on the assumption of quality score being closely related to the chance an ad get’s clicked (a.k.a. click-through probabilty, or expected CTR). I have published an article on this a year ago: The Secret of Quality Score. Even though some of the brightest minds in the industry agree with this, I also know that there are a lot of people who still buy into the idea of quality score being something else – like a magic formula for “true quality”.

I will post more on this in the future, but for the moment you will have to decide for yourself if you can live with the assumption. If you believe that quality score has little to do with click-through probabilities, reading on will be a waste of your time.

Calculating Revenue per Auction

Allright, still here? Then let’s go: How much revenue would Google lose if an advertiser dropped out of an auction?

To answer this we have to identify Google’s revenue in the ad auction, which is surprisingly simple. Take the effective CPC and multiply it by the chance that there is actually a click and you have the expected revenue for an ad:

Expected revenue from showing an ad = Effective CPC x Effective click-through probability

For example, if effective CPC is $1 and effective click-through probability is 10%, Google would expect a revenue of $0.10 ($1 x 10%) from showing this ad.

Effective CPC is determined in the ad auction, so we know how to calculate this. For the effective click-through probability there are two things to consider: the click-through probability of the ad itself and the influence of the position it ends up in (even a great ad won’t get many clicks if it ends up on the last position). In other words, we need to know:

1. How likely is it that an ad gets clicked if it is seen (“a priori click-through probability”) and
2. How likely is it that the ad is seen (the position’s visibility).

Okay, great, so where do we get those two?

As I’ve already hinted, the ad’s own click-through probability is closely related to quality score. As shown in the article The Secret of Quality Score, in order to maximize revenue, quality score would have to be Google’s best estimate of an ad’s click-through probability. As an estimate it is, of course, not 100% accurate but for the following calculations let’s assume that it is.

That leaves us with the visibility of the individual positions. Only Google knows the correct values, so I made up some numbers:

This assumes a lot of visibility for the top spots and much less on the right hand side. The top spot on the right hand side still gets 10% visibility, then it drops of to 5%, then step by step down to 2% for position 11. Any position beyond that doesn’t appear and has a visibility of zero. I’m sure there are more accurate ways to model this, but this works.

Building a Spreadsheet

Now we have everything that we need in order to simulate an auction and calculate Google’s revenue. Excel’s random numbers generator gets us some bids and quality scores and we calculate the rest. The following table was generated with random bids from $1 to $10 and quality scores between 0.05 and 0.40:

In order to calculate Google’s revenue we now need the three factors mentioned above: the effective CPC, an ad’s click-through probability and the corresponding position’s factor. When we have those, we can multiply them for each ad. So let’s go.

To calculate the effective CPC we can use the formula:

Effective CPC (for the current advertiser) = Ad Rank (of the next advertiser) / Quality Score (of the current advertiser)

But we actually won’t need this. Let me rearrange the equation:

Effective CPC x Quality Score = Ad Rank (of the next advertiser)

In order to arrive at an ad’s expected revenue for Google, we need to calculate

Effective CPC x Click-Through Probability of the Ad x Position Factor

which is the same as

Effective CPC x Quality Score x Position Factor

which is the same as

Ad Rank (of the next advertiser) x Position Factor

Okay, let’s look at some numbers:

The expected revenues for each individual ad add up to the total expected revenue for Google from this auction. Not to anyone’s surprise, most of the revenue comes from the top positions. With different factors for position visibility, this would, of course, look different.

Now let’s expand the table to look at what would happen if one advertiser dropped out. In this case, every ad below the dropout would move up one position. This means a higher expected revenue for each of the climbing ads. To account for that, I’ve added a column for the revenue each ad would have in the position above.

Another effect is that the ad directly above the dropout no longer has to meet the dropout’s ad rank but the ad rank of the ad directly below the dropout. This lowers the revenue from the ad directly above the dropout. The new revenue goes into another column.

With this we can calculate the expected revenue if one advertiser dropped out. Let’s say the one in position 5 drops out. In this case revenues for positions 1-3 remain the same, position 4 has to meet the ad rank of former position 6 and positions 6-12 move one up. With this we can calculate the new revenue if an advertiser dropped out. We can also calculate the revenue lost as both an absolute number and a percentage. This is the resulting table:

Oops – look at the revenue lost for the first two ads. It’s the same number. Whether the first or the second advertiser drops out makes no difference. That doesn’t look right, right?

It took me quite some time to get my head around this, but it’s actually correct. A small example helps to understand why. Imagine there are three competitors in an auction. Don’t think of an AdWords auction, just a simple auction on eBay or somewhere else. The competitors are A, B, and C. Their bids are bids $a > $b > $c. Since A only has to pay enough to match B’s bid, and B only has to match C’s bid, they alltogether have to pay $b + $c.

If A drops out, B still has to pay $c:

If B drops out, A only has to meet C’s bid:

As you can see, the total is the same. This goes for any such auction: Whether the first or the second contestant drops out makes no difference for the total revenue.

Back to the ad auction example. As you can see, losing the top advertiser would Google around 11% of the expected revenue for this auction. Losing advertiser #3 would hurt as well while losing any advertiser from position 4 or below has rather little impact. The reason for this is the little importance of those positions. There’s simply not much to lose there because most revenue comes from the top positions, which are unaffected by changes below.

Building an Excel Environment for Simulation

Now that we have the spreadsheet we are almost ready to run some simulations. We will need to be able to create different scenarios quickly which is hard with the above spreadsheet. Whenever we create new random numbers, we will have to sort the table again. After playing around with Excel for a while, I found a way to do this without having to sort everything manually.

First, I created a second table with random bids, random quality scores, and the resulting ad ranks. Next to the ad ranks I put a column for the position. This column has a simple formula:

=RANK(the Ad Rank field next to it;the whole Ad Rank column)

This identifies the position the ad with this ad rank would end up in.

Now back to the old spreadsheet. In the Ad Rank column we can now use a simple VLOOKUP to determine what’s the ad rank for each position. Whenever we press F9, we will get a full set of new ad ranks in the correct order. Yes, I’m very proud of this 🙂

Next I expanded the whole thing a little. For bids and quality scores I added fields where a range for these random values can be specified. I also added a field to specify the number of advertisers. These fields now control the environment for the simulation.

Last but not least, we need a tool that can run a large number of simulations. We can employ the Monte Carlo method, which basically means that we run a great number of simulations and collect the results. A simple and sufficient tool to do this is MonteCarlito. It’s actually an Excel spreadsheet that comes with a macro. All we have to do is write the number of simulations to run into a field, put the values to monitor right next to it, select those fields and one row below, and hit CTRL-W. After a few seconds (or minutes/hours/days/… depending on the number of simulations) the tool outputs the averages of the monitored values.

Running the Simulation

Okay, let’s go. First, I put in some similar number as George did in his simulations. Here are my results (1000 simulations each).

The results in the first two cases are similar to the representative auctions George presented. He focused on CPC’s and the advertiser in position 1 dropping out. When that happened, effective CPC’s would decrease by 10.61%, 3.44%, and 0.02%, respectively. The findings above suggest that Google loses a little more in revenue, especially in the tightly packed 100 advertisers auction. While it certainly doesn’t hurt Google too much, they would still feel the departure of the top advertiser, even when there are lots of other candidates.

The following table is a good example of such an auction (parameters as in the third table above: bids $1-$10, QS 0.3-1.0, 100 advertisers in the auction).

I also ran some simulations with my own parameters. With quality scores being click-through probabilities (instead of numbers from 1 to 10) when it comes to the auction, a reasonable range could go from 0.01 to 0.4. An ad with a quality score near zero would probably be hardly relevant. An ad with a score above 0.4 would have to be a branding ad or at least very special in some way.

I kept this range for quality scores, set bids to $1-$10 and played with different numbers of advertisers. Here are the resulting numbers:

These results basically confirm what we knew all along. The more advertisers there are, the easier it is to replace one of them.

I also wanted to know what would happen with fewer advertisers, which revealed a massive pitfall: Without minimum bids the last advertiser has to meet an ad rank of zero and therefore catches a free ride. I played around with different ways to establish a minimum ad rank, but the attempt proved to be futile. Results would always be heavily influenced by the way the minimum threshold was implemented, preventing any new insights. So I couldn’t run any simulations with only a few advertisers and that was the end of that.

Well… how much do your advertising dollars matter?

While the above numbers give an idea on how much a single advertiser matters in the auction, they actually don’t answer the most interesting question: How much does my money matter to Google? If someone pulled $1 million in advertising budget from AdWords, how much would Google’s income shrink?

To find out about that I went back to the scenarios above and compared Google’s losses to the money an advertiser pulled from the auction. Take a look a these numbers:

At the end I added another column: Ratio of Revenue Lost to Revenue pulled. This is what Google would lose (column Revenue Lost) compared to what the ad contributes to the auction (column Expected Revenue). It’s a percentage to be interpreted as follows: If that advertiser were to pull $1 in advertising budget, Google would lose this percentage of the money.

These numbers were a little unexpected, at least to me. First off, the top advertiser’s dollards matter the least. All the other ads make much more of an impact, some even more than 100%!? This looks strange, but it can happen.

The top advertiser spends the most money in the auction, so you would expect his dollards to matter the most. As shown before, his departure would indeed hurt the most. Still, he pays a lot (per auction) and doesn’t drive up anyone else’s bid. The main reason the ad generates so much revenue for Google is the high visibility of position #1 – and that effect isn’t lost if the advertiser leaves the auction.

Also notice the big impact of #4 leaving the auction. The #4 ad generates much less revenue than the one directly above ($0.18 compared to $1.15), mainly because the ad above has five times the position visibility. While advertiser #4 doesn’t spend much in the auction, he drives up the cost for the advertiser above. Because of the increased visibility there, the effect is massive.

I imagine that the difference in visibility of these two spots is actually much bigger than factor five, which would make the effect of #4 leaving even bigger. However, in reality there is another element at work which hasn’t been incorporated in this simulation: the top-of-page threshold. Even if there is a big gap in ad rank after the last top spot (#3), the ad there still has to meet the threshold instead of #4’s ad rank.

Since it is unknown how exactly this threshold works, it can’t be considered in this simulation. This means that the big impact of #4 leaving should be ignored. It also means that if a top ad departs from the auction, the spot isn’t necessarily reassigned. In such cases a leaving top ad would have a much bigger impact.

Let’s also look at the very big impact from #6 leaving. In this case the visibility gaps around this position aren’t that big. But there is a huge drop in ad rank towards #7. If #6 dropped out, the more visible #5 ad would have to pay significantly less.

Last but not least, let’s take a look at ad #12. This ad does nothing but drive up cost for the ad above. Yes, in reality there is a minimum bid which isn’t considered here. But no doubt there are many cases where the #12 ad would meet the minimum bid no problem, but the page is already full. In these cases an advertiser paying nothing has an impact on Google’s revenue. If you ask whose advertising dollars have the most leverage, it’s this guy’s.

Here are some numbers for the same scenarios as above:

I crossed out the effect on the #4 position for the reasons mentioned above. As you can see, the effect of pulling one advertising dollar from AdWords almost always reduces Google’s bottom line by much less than that.

Again, I tried exploring what happens with less ads. I played with different ways to implement a minimum bid: the last ad has to pay in full, half, or nothing. This was problematic for the same reasons as mentioned above, but it provided an insight nonetheless. Here are the numbers on the effect of budget being pulled from different positions (same as above):

While I wouldn’t put much trust in these numbers, one thing becomes clear: an impact of more than 100% isn’t uncommon in small auctions. It’s easy to explain: an advertiser doesn’t just spend his own money in an auction, he also drives up the bid of the advertiser directly above himself. In small auctions with big gaps between ad ranks this often makes a significant difference.

Resources

If you want to play around with the numbers, you can download the Excel sheet I used.

You will need to enable macros in order for the simulation to work. If you aren’t comfortable with macros coming from my file (I know, new blog, we just met), you can download MonteCarlito and copy the contents from my spreadsheet into their XLS.

Caveats

While it was certainly interesting to play with the auction dynamics, there are some assumptions that impact several aspects of the results:

• Thresholds: Minimum bid thresholds had to be ignored in these simulations. In the wild there are dynamic thresholds for both appearing above the organic listings (positions 1-3) and appearing at all. I suspect that this has a big effect on loosley packed auctions. In tightly packed auctions these thresholds are probably irrelevant.
• Rounding: The effects of rounding have been ignored as well. In real ad auctions, effective CPC’s are rounded up to the next cent.
• Probability distributions: For these simulations, random bids and quality scores were evenly distributed. However, in reality there can be some advertisers in a league of their own. For example, big brands like Amazon attract more clicks than lesser known advertisers. At the same time, because of higher margins, better conversion rates, and/or higher order values, they can afford higher bids. This can lead to separate ad rank brackets. This effect hasn’t been considered in these simulations.
• The same problem arises when generic and specific keywords collide. For example, if someone searches for “sony kdl-32bx420 lcd tv” – some advertisers target the specifc product, others are after “sony lcd tv” or just “lcd tv”. This, too, results in different brackets of bids and quality scores.

… and probably a lot more.

Conclusions for the Ad Auction

From Google’s perspective, the impact of an advertiser leaving the auction depends on how high up the ad is:

• The higher up an ad is in the auction, the more its dropping out would hurt Google’s bottom line.
• One of the top two ads dropping out has the biggest impact. Strange but true: which one of those two drops out makes no difference.
• Even an ad that doesn’t appear on the page can contribute to Google’s revenue by driving up the cost for the last ad on the page.

More important is, however, how tightly packed an auction is.

• The bigger the differences between ad ranks, the more an individual ad matters.
• Thresholds (top of page, minimum bid) can prevent ads from moving up. If an ad dropping out leads to fewer ads on the page, this has a bigger impact on Google’s bottom line.
• The same is true when there simply aren’t enough ads in the auction and positions are left blank.
• With different bids and quality scores, ad ranks are usually distributed over a wide range.
• Tightly packed auctions occur when there is a large number of advertisers competing in an auction.

This boils down to:

• The higher up an ad is, the more it matters.
• The less advertisers there are in an auction, the more the individual advertiser matters.

Conclusions for your Advertising Dollars

While the effect on ad auctions might be interesting, the more important question is what your advertising dollars are really worth to Google. Again it’s extremely important how tightly packed the auction is. Position also plays a role, but the simulations suggest that it is rather minor.

Let’s look at what this means for different types of businesses and keywords.

Say you are a retailer for something like consumer electronics, shoes, or pet supplies.

• Do or do not spend $1 million on generic keywords like “lcd tv”, “shoe shop”, or “dog food” – there are probably hundreds of others bidding on the same terms. The auction is tightly packed and if you pull your million, to Google it feels more like $10k.
• Spend your money on less generic terms and the field becomes much smaller. Here, your advertising dollars matter a lot more to Google.
• Target the long tail and you might be alone or with few other advertisers. Reduce your budget by a million dollars in this area and Google’s income might shrink even more than that.

Say you are a local business in a small town.

• Your competition is probably limited. Spending money on Google drives up prices for everyone else. Unless you go for the top spot.
• Spend $10k and Google’s revenue might increase even more than that. To Google your business might just be more important than the retailer spending $1 million just on generic terms.
• Because of Google making more money from you than what you actually spend, giving you a $100 dollar AdWords voucher is a good idea, even if you stop advertising after using up the voucher.

Say you bid on terms that no one else bids on. Say you’re this guy:

• It’s not really an auction now. Your money goes directly out of your pocket and into Google’s.

To sum up: How much your dollars matter to Google largely depends on how much other advertisers bid on the same terms:

• None: Your spend is Google’s income.
• A few: If you don’t go for the top position, Google might make more from your participation than you actually spend.
• A lot: The revenue that Google attributes to you is far smaller than what you actually pay.

For Google all of this is an additional incentive to go after new markets for AdWords: local businesses, highly specialized businesses, foreign markets. For us advertisers it suggests that a high spend doesn’t necessarily translate into being important to Google. Some advertising dollars are just worth a lot more than others.

Martin Roettgerding

Martin Roettgerding is the head of SEM at SEO/SEM agency Bloofusion Germany. On Twitter he goes by the name @bloomarty, and you can find him regularly on #ppcchat.