CPM Pricing in a Post-Last Click World


“How much should one bid on a specific impression?” is a question I have been trying to answer for years and have shared my thoughts on this blog. Today, we are approaching CPM bid price as lazy financiers approach asset valuation; assume other similar transactions were done rationally and base our pricing on their results. Well what if everyone else had made the same assumption? Are we sure the market value of an impression is equal to its intrinsic value?

CPM Pricing in the Last Click World

In the last click world, life was relatively simple. As a merchant, I know my margins and I can tell you how much % of revenue I am willing to part with for a sale. Given that information, I can back into a CPM price I am willing to pay, using best guesses for click through rate (CTR), conversion rate (CVR), average order value (AOV), and adjusting for risk (or how confident you are in your guesses). More details in this post.  To summarize in one formula, the concept looks like this:

CPM=ƒ(μCTR*μCVR*μAOV*% Sales, σCTR, σCVR, σAOV)

We have always used eCPM as the common denominator to compare performances of different pricing models, which ignored two important things; the quality of the impressions, and the value of risk transfer. The formula takes these two key points into account. Better quality of impression can be defined as an impression with a higher mean CTR and/or CVR and/or AOV, and you should be willing to pay more. Higher risk for the advertiser can be defined as a higher standard deviation for CTR and/or CVR and/or AOV and you should be willing to pay less.

Then Came Attribution

The last click model is linear but consumer journey is not. You can’t look at each marketing channel & campaigns in a vacuum, since that is not how people experience your brand and end up becoming a customer. The concept of attribution makes total sense. The issue is, in reality it is impossible to attribute a sale “accurately”. Not even the consumer will be able to tell you why she ended up buying that item on that day.

For all we know, the customer bought the item because she had a bad day, had one too many glasses of wine, and saw a handbag she liked displayed in the storefront on the way home. So we should attribute 30% of the sale to her ex-boyfriend, 40% to the bar (20% to bartender, 20% to the guy buying her drinks), 20% to the store, and of course 10% to Google because she searched for the product name to get to the purchase page.

By trying to illustrate why accurate attribution is impossible, I also just illustrated why last click is pretty much always wrong. In the above case, all these things contributed to the sale but Google just happened to be conveniently located as the last click hub of anyone knowing what she wants to buy. Where is the value in that as a marketing channel? Why would Google deserve 100% of the credit? (hint: it shouldn’t)

So we know last click is (almost) always wrong and attribution is never accurate. That’s why a whole slew of attribution companies are out there touting their attribution logic to be the most accurate. “Black box” guys hire PhD’s and crunch numbers based on consumer touch points and conversions and other data points (“Can’t explain exactly why it’s accurate but trust me, I’m a doctor”) and some are more open, incorporating the advertisers requests (“Yea, we have no idea either. Let’s prove your boss was right all along”).

No matter how imperfect attribution is, it is reality for digital marketing today because never accurate sure beats always wrong. So what does attribution mean to our little formula? Obviously, the formula needs to be adjusted but just how?

Influence is the New Click

When we review the formula, we notice that two things happen outside of the advertiser’s domain; the impression and the click. CVR and AOV happen on the advertiser side and the advertiser obviously has control over the % of Sales to be paid. In the post last click world, what we care about is “influence”. If accurate attribution was available, we would be measuring how much of the influence did this particular ad unit have to this consumer’s purchase. Clicks used to be the go to proxy for influence because it required user action and intent. But what about video ads? Interactive ads that don’t need you to click? Audio ads? A really well made static display ad that captivates you? There are so many things that can happen between an impression and a click. Click as a measurement of influence is flawed and by association, CTR is also flawed. What matters is the conversion rate between who the ad campaign reached and who visited the advertiser site. This is measuring unique users, so a user coming back to the site via retargeted ad would count as one visitor. Let’s call this conversion rate RUR for Reach to Unique Ratio.

The reason why we should look at RUR from a unique user perspective is because the consumer journey does not end when the user visits the site. It ends when the user converts or the marketer gives up. So when a user visits a product page, leaves to do additional research, the retargeting ad that brought her back should not take whole credit of the sale. The brand touch points that brought her to the site in the first place should also be credited. There’s another variable that we have to consider. How many touch points it takes for the user to become a unique visitor to the site (TP as in touch point, not toilet paper).

The New Formula

Given all these thoughts, I can finally put together the theoretical CPM pricing formula taking attribution into consideration.

CPM=ƒ(μRUR/μ#TP *μCVR*μAOV*% Sales,
σRUR, σ#TP, σCVR, σAOV)

Let me try to explain this verbally. The CPM you should be willing to bid on a given impression has to do with the average % of users you reach who turn out to be a unique visitor to your site, how many touch points it takes for you to get this user to come visit your site, and once visited, what the conversion rate, AOV are, and of course, how much of the revenue you are willing to give up. Oh, and don’t forget to adjust for risk.

You may have noticed the definition of CVR actually changed slightly in this formula because we are allowing for the eventual return of this user outside of the current session, so CVR is actually “eventual CVR”.

Ah, Crap

I hope you didn’t notice I took a major short cut. Because I just did and I want to go to bed but promised myself I would finish this post today. Attribution. Yes it is still haunting me. The assumption I made in the formula is that every impression is equal and I can use the average number of touch points to get to the CPM price. This means, if we average 4 touch points before a user visits the site or we give up, I am attributing 25% of the credit to each of the touch points.  If the whole attribution movement taught us anything, it taught us that each touch point is unique in how influential it will be. Let’s call that variable % Infl. By definition, the % infl will add up to 100% when the user visits the site or the marketer gives up.

CPM TP1→N =ƒ(μRUR * %Infl TP1→N *μCVR*μAOV*% Sales,
σRUR, σ%Infl, σCVR, σAOV)
where sum (% Infl TP1→N) = 100%

I don’t even know the mathematically correct way to denote this but the spirit is there. I think I actually used an Excel formula near the end, but whatever, I had 3 hours of sleep last night. When you are bidding on an impression, you have to know where in the consumer journey this person is and what state of mind she is in, and what touch points she has had with your brand. Given all that and with the magic of big data, and your future intent to buy this consumer’s impression, you buying this next impression will have a certain effect on this person’s psyche and hopefully purchase behavior in the future. When the % Infl adds up to 100%, theoretically the user has RUR% chance of visiting the site, CVR% chance of becoming a customer, and spending $AOV.

In Conclusion, So Many Freaking Caveats

Well at least I got to some kind of formula, no matter how weird it looks. There are a boat load of caveats and three come to mind immediately.

First, as I mentioned above, there are so much predictive algorithm that needs to happen to get to the RUR and % Infl variables. But this is the nature of being able to bid on the most granular level possible to mankind, the impression. Now most bidding currently happens on the segment level and my thought process assumes personal level, so maybe this is the kind of thing we need to think about in the future.

Another caveat, not sure if you caught this, is the question of incrementality. I went through all this trouble to calculate how much this impression is worth, but in reality, the advertiser already has some organic traffic that converts at a certain rate. Shouldn’t the advertiser spend only on the difference of the effect? There is a lot of argument that can be made for both sides but maybe some kind of discount needs to happen. Also remember way earlier in this post I mentioned that the quality of the impression not only increases CTR but potentially also CVR and AOV.

One final caveat. Won’t advertisers care about the life time value of the customer instead of the one sale? Yes, most certainly and I think the formula can be adjusted to take that into consideration. At some point in the near future, I’ll explore this idea.

Man, the future of digital marketing is full of formulas and quantitative intellectual reasoning. There has got to be someone better at this than me. I failed calculus 18 years ago (I was a terrible student back then)!


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