Attribution Modeling: Multi-Touch, Shapley Values, and Media Mix Models

A user sees a Facebook ad on Monday, a Google ad on Wednesday, and clicks an email link on Friday. Which channel gets credit for the conversion? Attribution models answer this — and the answer determines how hundreds of millions of marketing budget are allocated. Last-click is wrong. First-click is also wrong. Shapley-based attribution is principled. Media mix models handle what user-level data cannot.

Attribution is the problem of assigning credit for a conversion (purchase, signup, subscription) to the marketing touchpoints that preceded it. Get attribution wrong and you systematically misallocate marketing budget: over-investing in channels that look good under your model but are actually stealing credit from others.

Why single-touch attribution is wrong

Last-click attribution: 100% credit to the last touchpoint before conversion. Simple, measurable, completely wrong. It penalises brand awareness channels (TV, social, display) that initiate demand and rewards direct/email channels that capture it. Users who were never prospected by brand channels would not have converted via email — but last-click ignores this dependency.

First-click attribution: 100% credit to the first touchpoint. Opposite problem — ignores the role of the channels that closed the deal. A user who saw a brand ad six months ago and then responded to a conversion-focused email gets all credit attributed to the brand ad.

Linear and time-decay models

Linear attribution: divide credit equally across all touchpoints. Better than single-touch but still arbitrary — why should a Facebook impression three weeks ago receive equal credit to the email that triggered the purchase?

Time-decay attribution: exponential decay with recency. More recent touchpoints get more credit. Captures the intuition that recent interactions are more causally proximate but still relies on a heuristic decay function.

Shapley-based attribution: principled credit allocation

Shapley values from cooperative game theory provide the unique fair allocation of value among players given a set of axioms (efficiency, symmetry, dummy, additivity). Applied to attribution: each touchpoint is a "player"; the conversion is the "value"; the Shapley value of touchpoint i is its average marginal contribution across all possible orderings of the other touchpoints.

For touchpoints {Google, Facebook, Email}: Shapley value of Google = average over all orderings of adding Google to a subset and measuring the incremental conversion probability. If Email always converts at 80% without Google, but 85% with Google, Google's Shapley value is 5% of the conversion credit. Data-driven Shapley attribution is now available in Google Analytics 4 and is considered the most defensible attribution model for within-channel credit allocation.

The fundamental limit of user-level attribution

User-level attribution only captures touchpoints in your data. It cannot attribute conversions to touchpoints with no user-level signal: TV ads, billboards, podcast sponsorships, word-of-mouth. And it conflates correlation with causation — a user who saw a Google ad and converted might have converted anyway. Attribution models tell you which channels touched converters; they do not tell you which channels caused conversions. That requires incrementality testing (see Post 84).

Media Mix Models: the aggregate approach

Media Mix Modeling (MMM) bypasses the user-level tracking problem by modelling aggregate relationships. Inputs: weekly marketing spend by channel, weekly sales/revenue. Model: revenue_t = f(TV_spend_t, Digital_spend_t, Search_spend_t, ..., controls_t) where controls include seasonality, holidays, economic indicators. MMM estimates the marginal impact of each channel on revenue at the aggregate level.

Key MMM techniques: adstock transformation (marketing spend has decayed effects over time — a TV ad seen today still influences purchases next week); saturation curves (diminishing returns at high spend levels — each additional dollar of spend yields less incremental revenue); Bayesian MMM (with informative priors from past experiments to regularise channel coefficients, especially important when channels are correlated). Robyn (Meta's open-source MMM) and Meridian (Google's) are the most widely deployed frameworks.

The gold standard: geo experiments for channel incrementality

Neither user-level attribution nor MMM gives true causal estimates. The gold standard: geo-level randomised experiments. Split geographic markets into treatment and control. Run the channel in treatment markets; hold back in control. Measure the difference in revenue. This is the only way to estimate the true incremental lift of a channel. Geo experiments require months of data collection and are expensive to run, so they are used to calibrate MMM coefficients rather than replace them.

Try on Colab: simulate a user-level conversion dataset with 5 touchpoints per user (drawn from a Markov chain model where each touchpoint affects conversion probability). Compare last-click, linear, and Shapley attribution for each channel. Then aggregate the data to weekly totals and fit a simple Bayesian MMM with adstock and saturation. Compare the MMM channel coefficients to the Shapley values — observe which channels are systematically over- or under-attributed by Shapley.