How should one evaluate Incremental Return on Ad Spend?

I often see statements like “We got $3 increase in revenue per ad $ spent on the campaign.” claiming the success of said ad campaign. For example, on page 255 of “Everybody Lies” (which is a fun read about what internet data tells us about ourselves) Seth Stephens-Davidowitz writes, “… paid about $3 million for a Super Bowl ad slot. They got $8.3 million in increased ticket sales …” a 2.8X ROI. Claims for internet ad campaigns are often larger.

But it seems to me that this ignores the incremental cost dC of producing and delivering the incremental revenue dR. Intuitively, your incremental spend on advertising dA can only be as large as your margin m(R) before beginning to lose money. Let me juggle this around a couple of ways:

Your margin without taking into account the advertising cost of the current campaign is m(R) = 1- dC/dR. So if you want your net to be positive

dR-dC-dA > 0 (incremental revenue less incremental cost of producing and delivering that revenue less the cost of incremental advertising)

ROAS = dR/dA > 1/m(R)

For example, for a campaign with 2.5X ROAS, the pre-advertising margin had better be > 40% before declaring the campaign a success.

Right?

(Of course the above doesn’t apply if the goal is to drive market share or total revenue without regard to profit.)

Baseline Revenue

I stop to miau to cats.

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