I couldn't quite follow what the problem is. I would define the revenue in the ROAS formula as revenue per time period, and the marketing spend also per time

I couldn't quite follow what the problem is. I would define the revenue in the ROAS formula as revenue per time period, and the marketing spend also per time period Then I would qualify the revenue, as that part of the revenue that can be tied to the marketing activity (cookies, refer URL, etc) And then the ROAS ratio becomes an ordanary division, because both values are known; no need to infer them as in the rest of the article.