Hi folks, I'm the author of the post — I wrote it because I think a lot of brands tend to pluck numbers out of thin air when they're talking about marketing targets, without knowing how they're affecting their bottom line.
This might seem like econ 101 as zwaps mentioned, but there are a lot of brands who don't take anything like this approach still.
Interesting post. "All models are wrong, some models are useful" - Box. This one seems useful and is simple to explain.
It started me thinking about the distribution of customers who convert, viewed as a function of ad spend. I am not sure there is any reason this distribution need have a particularly simple shape, or even be continuous. E.g. maybe some customers can be addressed and convert at a modest ad spend, while if you double the ad spend you don't get any more conversions, then if you double ad spend again maybe suddenly you're out bidding a competitor and the number of conversions shoots up, perhaps giving you a better overall net profit than if you stopped earlier with a modest budget.
This might mean that the curve we're trying to maximise (net profit) has more than one local maxima, or might not even be continuous.
There's probably also an explore/exploit tradeoff here as well: how much of the total budget should you spend sampling to try out different ad spends across the whole range of plausible values (from 0 up to the long term value of a conversion, I guess) to get enough data to start optimising.
That is a fascinating line of reasoning. I wonder if there is some way to leverage historical data (for other brands, maybe?) to figure out potential local optima.
I original thought this was a nice "set it and forget it" marketing scheme, but your comment makes me think otherwise.
If so, great question. I haven't looked into this much but wouldn't expect it to be parabolic - that was just an approximation to illustrate the points raised.
Alright, makes sense. I guess a parabola is the primordial (at least, to high school teachers) example so I understand why that is what you picked.
In terms of whether a parabola makes sense for the example, it's difficult for me to say. From my personal experience I would say this could maybe be done with differential equations and something akin to an R_0. Then you would also have steady states, but the advantage would be that you can actually see how your other parameters (coefficients in the differential equations) influence the conversion rate (in my analogy R_0).
This might seem like econ 101 as zwaps mentioned, but there are a lot of brands who don't take anything like this approach still.
Keen to hear people's thoughts :)