Marketing Mix Modeling (MMM) is a statistical analysis technique that helps marketers understand the impact of various marketing activities on sales. One of the fundamental concepts in MMM is the saturation curve, which models the diminishing returns of marketing spend.
The Hill function, originally developed in biochemistry to describe enzyme kinetics, has found powerful applications in marketing analytics. It elegantly captures the S-shaped relationship between marketing spend and response.
Where: - R is the response (e.g., sales, conversions) - X is the marketing spend - K is the half-saturation constant - n is the Hill coefficient (shape parameter)
The Hill coefficient (n) determines the steepness of the curve. Higher values create sharper transitions, while lower values produce more gradual saturation.
About the author
Cyril Noirot
Lead Data Scientist
Freelance data scientist. I design and ship decision systems — forecasting, pricing, marketing measurement, optimization.
Seen in practice
Anonymized case studies where these ideas were applied to real decision problems.