There are often close relationships between top level business metrics. For instance, it's well known that retention has a super strong impact on the valuation of a subscription business. Or that the % of occupied seats is super important for an airline. A fun little toy model that I can up with generates a curious relationship between conversion rates and revenue.

Erik Bernhardsson

A toy mathematical model explores the nonlinear relationship between conversion rates and business revenue. Using a model where marginal customer acquisition cost grows as a slow function of volume, the analysis shows that improving conversion rate by 20% leads to a ~58% increase in both total volume and gross profit. Doubling conversion rate yields a 5.7x increase in gross profit. The key insight is that inverting a slow-growing acquisition cost function produces a superlinear relationship between conversion rate and profit, with the effect being most pronounced in large markets like mortgages or groceries where marginal acquisition costs grow slowly.

Why conversion matters: a toy model