How to compute Shapley-value attribution and read the result honestly

How to compute Shapley-value attribution and read the result honestly

The question: you want a credit allocation with a defensible fairness property. The Shapley value — borrowed from cooperative game theory — distributes credit by averaging each channel's marginal contribution across all possible orderings. How do you actually compute and interpret it?

The playbook:

— Define each channel as a 'player' and conversions as the 'payout' of a coalition (set of channels present in a path).
— Compute each channel's marginal contribution: conversion rate of coalitions with it minus without it.
— Average those marginals across all orderings. This is the unique allocation satisfying efficiency, symmetry, and the null-player property — which is why it's theoretically clean.
— Mind the combinatorics. Channels grow the coalition count as 2^n; beyond ~10-12 channels you'll need Monte Carlo sampling to approximate.

The nuance: Shapley's fairness axioms are mathematical, not causal. It fairly divides the observed correlation between channel presence and conversion — it does not establish that any channel caused anything. Two channels that always co-occur get split evenly even if only one is doing the work. Only experiments resolve that.

Bottom line for practitioners: Shapley is the most principled observational allocator and an excellent prior. But 'fair' is a property of the math, not proof of incrementality — calibrate it against a lift test before betting budget on the split.