Shapley Value Attribution: Fair Credit, Borrowed From Game Theory

Imagine three colleagues land a deal together and have to split the bonus fairly. You could give it all to whoever signed the contract (last-click), or divide it evenly (linear). Or you could work out what each person actually added by testing every combination of who was and wasn’t in the room. That last approach is the Shapley value, and it is one of the most mathematically respectable ways to do attribution.

What is Shapley value attribution?

Shapley value attribution applies cooperative game theory to marketing, treating each channel as a “player” and each conversion as a payout to be shared. It assigns credit to a channel by averaging its marginal contribution across every possible combination of channels, so a channel is rewarded for the lift it consistently adds, not for where it happens to sit in the journey.

The method comes from Lloyd Shapley, who won the 2012 Nobel Prize in Economics for this work. As Treasure Data describes it, you credit each channel “by calculating a Shapley value, a weighted average of each player’s marginal contribution to all the possible coalitions of players in the game”.

How it works

Think of every subset of your channels as a “coalition”. The model works out the conversion rate for each coalition, then measures how much adding a particular channel improves it. Do that across every possible ordering and combination of channels, average the results, and you get that channel’s fair share of the credit.

The appeal is that this satisfies a set of fairness axioms that heuristic models simply ignore. A channel that adds real marginal lift in many combinations earns more credit than one that merely shows up last. Channels that add nothing, in any combination, get nothing. It is attribution by contribution, not by position.

An example

A buyer is exposed to three channels before converting: paid social, email, and organic search. A Shapley model asks what the conversion likelihood looks like with each channel present and absent, across every grouping: social alone, email alone, social plus email, all three, and so on. If email rarely moves the needle on its own but reliably lifts conversion when combined with paid social, the model captures that interaction and rewards email accordingly. A position-based model would never see it.

Strengths and weaknesses

Shapley value attribution is, in theory, the fairest credit allocation available when you have rich journey data. It draws on real user paths rather than fixed rules, and it handles the messy reality that channels interact rather than work in isolation.

The catch is cost, in two senses. Computationally, it requires evaluating every combination of channels, which scales as n factorial: manageable for a handful of channels, brutal for many. (In practice, vendors use approximations to keep it tractable.) And like every path-based model, including Markov chains, it rests on correlation. It distributes credit beautifully among the channels it can see, but it still cannot tell you what would have happened if you had not run them at all. For that question, you need incrementality testing.

Questions to ask yourself

As a modern growth or agile marketing professional, ask yourself the following about Shapley value attribution:

Do I have enough channels and journey data to justify a combinatorial model?
Am I interested in channel interactions, or would a simpler model answer my question?
Do I understand the approximations my tool uses to make Shapley computable?
Am I treating “fair credit” as the same thing as “causal impact”, when it is not?
Would the output actually change how I allocate budget?

About Growth Method

Growth Method is the growth platform designed for experiment-led and data-driven marketers.

Learn more on our homepage, connect with me on LinkedIn or Twitter, or book a call here.