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.<p>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.<p>Keen to hear people's thoughts :)
Really, you're going to use a logarithm because it fits one data point better?<p>Besides you might as well just use all your datapoints directly. There's no real need to interpolate between them (and if you really want to optimize your ad costs that finely, don't use a function that predicts -infinty gross profit if you don't use ads).
Fun reading for a university class, but the real world doesn’t work this way. Optimizing for a target cpa is never a possibility because at an agency or in house marketing team your given x budget and expected to spend it.<p>I’ve never seen someone underspend a budget and be thanked for it.
Contrary to the dominant narrative of this <i>Hacker News</i> post’s comment thread, I find this mathematical modeling exercise to be rather informative and inspiring. Life sustaining. It can be considered practice that keeps the vital muscles active.
How more convoluted can this explanation be?
The question is equivalent to just "Find the maximum of nb_conversion × (cost_per_conversion - margin_per_conversion)", and the only interesting question is the relationship between the cost per conversion and the number of conversions, which is not a matter of math but of practical statistics.
Much more easily, instead of plotting profit versus ad spend, plot (profit - ad spend) vs ad spend. Choose the highest point. If it looks like there might be a higher point not covered by your points, like how in OP it looks like the cheapest ad spend is the best, try going even lower. Instead of extrapolating, test. Extrapolating is much harder than interpolating and often requires some causal or structural understanding.