Marketing Science

Understanding Hill functions in marketing mix modeling

A comprehensive guide to saturation curves and their application in media optimization. Learn why Hill functions can be concave or convex and how they're used in Google Meridian.

15 mai 2025
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8 min de lecture

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.

À propos de l'auteur

Cyril Noirot

Cyril Noirot

Lead Data Scientist

Data scientist freelance. Je conçois et déploie des systèmes de décision — prévision, pricing, marketing measurement, optimisation.

En pratique

Études de cas anonymisées où ces idées ont été appliquées à de vrais problèmes de décision.

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