Shapley Value Methods for Attribution Modeling in Online Advertising

Kaifeng Zhao; Seyed Hanif Mahboobi; Saeed R. Bagheri

AI summary · arXiv: 1804.05327v1 · econ.EM

Shapley Value Methods for Attribution Modeling in Online Advertising

Kaifeng Zhao, Seyed Hanif Mahboobi, Saeed R. Bagheri

Original paper Submitted to arXiv on 15 Apr. 2018 License: NONEXCLUSIVE-DISTRIB 1.0

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The essentials

The paper derives a simpler Shapley attribution formula and an ordered extension, illustrating both with a real advertising campaign dataset.

Question

How can Shapley value attribution for online advertising be calculated more efficiently while accounting for the order of channels in users’ conversion journeys? The paper also examines how attribution metrics should represent campaign and channel contributions.

Method

The authors derive a mathematically equivalent Shapley formula that weights the revenue associated with channel coalitions, then extend it by dividing coalition contributions according to each channel’s touchpoint. They illustrate the methods on a 3-month campaign with 18 channels across three categories and 153,814 revenue-generating observations, comparing overall, touchpoint, and user-segment attribution.

Findings

Result The simplified formula reduced the reported analysis time from 17 hours to about 2 minutes on an ordinary PC while producing similar numerical attribution results.
See the passage in the paper
However, they differ substantially in computational efficiency: the analysis time is reduced from 17 hours to about 2 minutes on an ordinary PC using our simplified formula.
Result Overall attribution was highest for paid search, followed by DSPs and publishers.
See the passage in the paper
As we can see in the chart, it is suggested that the paid search category has the highest attribution value at 47%. DSPs category is assigned a lower yet very close attribution value (40.43%). Lastly, publishers get the lowest value of 12.58%.
Result The first touchpoint received most of the attribution credit, and credit declined rapidly at later touchpoints.
See the passage in the paper
The longest conversion journey in the current dataset consists of 11 touchpoints. As shown in Figure 3, touchpoint 1 gets most of the credits (91.59%), and attribution value declines very fast as users visit more channels.
Result Among users whose journeys contained more than two channels, DSPs received the largest category-level attribution, while paid search received 24.43%.
See the passage in the paper
On the contrary, paid search channels usually make the moderate contribution to the revenue, and get the attribution value of 24.43%.
Authors’ interpretation The authors interpret some high early paid-search credit as potentially reflecting unobserved offline advertising and loyal users’ prior willingness to convert.
See the passage in the paper
As we do not have the relevant data at this point, most of the offline channels’ credits are allocated to the first online channel that these users usually visit, which is mostly paid search in this dataset.

Limitations

The analysis lacks offline-channel data, which may distort attribution of online efforts, particularly paid search.
See the passage in the paper
We note that the attribution analysis carried out in the paper has certain limitations. It is suspected that the abnormally high attribution value assigned to paid search at the early stage of the campaign partially comes from the offline channels.
The empirical demonstration is based on a single three-month campaign dataset, limiting the evidence reported here to that campaign.

Why it matters

The authors argue that the simplified formula makes Shapley attribution more computationally practical for large-scale and omnichannel analysis, while the ordered extension reveals channel attribution at different journey stages. They also suggest the approach can be extended to time-dependent attribution and combined with campaign planning.

Written by AI from the paper. Passages are checked word for word against the text we analysed; the rest may contain errors.

AI-generated keywords: Shapley value marketing attribution online advertising customer journey channel contribution

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Comprehensive Summary
Layman's Summary
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Original abstract

The paper examines how to allocate credit for conversions or revenue among the online advertising channels a user encounters. It focuses on the Shapley value, a cooperative game theory method that assigns each channel the average of its marginal contributions across possible channel combinations. The authors argue that earlier attribution formulations can overlook much of a campaign’s value when users do not visit every channel and may produce negative marginal contributions. They therefore define a coalition’s value as the revenue from converting users whose recorded channel visits are confined to that coalition. The paper’s first contribution is a simplified calculation of Shapley values. It represents campaign value as the sum of contributions from user groups, classified by the sets of channels they visited. Under this definition, a channel’s Shapley value is calculated by summing the contributions of every user group whose channel set includes that channel, with each group’s value divided equally among the channels in the set. The authors show that this approach is mathematically equivalent to the standard Shapley calculation for their game definition. It makes the allocation and its properties more transparent: total channel credit equals total campaign value, channels with no contribution receive zero, and equivalent channels receive equal credit. It also reduces computation by avoiding repeated evaluations of marginal contributions across coalitions. The second contribution is an ordered Shapley method that separates a channel’s credit according to where it appears in a conversion journey. When a user visits the same channel more than once, the method divides that user’s contribution evenly across those touchpoints. Summing touchpoint-specific credits gives the ordinary Shapley value for each channel, while summing across channels gives the total credit at each journey stage. This approach shows not only which channels receive credit, but also how their attributed contributions vary between early and later stages. The authors demonstrate their methods on a three-month campaign involving 18 channels across three categories: publishers, demand-side platforms (DSPs), and paid search. The dataset contains 153,814 revenue-generating observations and about $14.31 million in revenue. In the category-level Shapley analysis, paid search receives 46.99% of the attribution, DSPs 40.43%, and publishers 12.58%. The simplified method produces results similar to those of the original calculation while reducing reported analysis time from 17 hours to about two minutes on an ordinary PC. In the ordered analysis, the first touchpoint receives 91.59% of total credit, followed by 6.76% at the second touchpoint and 1.15% at the third. The authors caution that this pattern does not show that first-touch attribution is sufficient. Paid search receives a large share at the first touchpoint, which the authors suspect is partly due to loyal users who convert after few online exposures and may have been influenced by unobserved offline advertising. When users who convert after exposure to only one channel are excluded, paid search’s first-touch share falls from 43.76% to 8.25%. Excluding journeys involving only one or two channels reduces it further to 4.37%. In this latter segment, DSPs receive 39.63% of the overall credit and paid search 24.43%, while publisher credit rises. At the channel level, D1 is reported as the leading contributor, receiving roughly 40% in the analysis of users with journeys involving more than two channels. The paper concludes that the simplified formula makes Shapley attribution more practical and that the ordered method can reveal differences across journey stages. These findings are descriptive attribution results, not proof that a channel caused the credited revenue. Missing offline exposure data may shift credit to the first recorded online channel, especially paid search. The authors identify adstock, integrating online and offline data, and combining attribution with predictive modeling and budget planning as areas for further work.

Who Gets Credit for an Online Conversion?

When someone makes a purchase after encountering several ads, which advertising channel deserves credit? A conversion might follow a paid search ad, a publisher placement, and one or more ads served through a demand-side platform. Crediting just the final click can overlook earlier exposures, while dividing credit evenly may ignore how different journeys unfold.

In “Shapley Value Methods for Attribution Modeling in Online Advertising,” Kaifeng Zhao, Seyed Hanif Mahboobi, and Saeed R. Bagheri explore a way to allocate revenue across channels using the Shapley value, a concept from cooperative game theory. Their work introduces a more efficient calculation and a second method that breaks channel credit down by its position in the customer journey.

A clearer way to define campaign value

The Shapley value assigns each channel its average marginal contribution across possible combinations of channels. But the result depends on how a coalition—a particular group of channels—is valued. The authors argue that earlier formulations can miss much of a campaign’s value when users do not visit every channel. They may also produce negative marginal contributions, making the resulting credit harder to interpret.

The paper defines a coalition’s value as the revenue from converting users whose recorded channel visits are confined to that coalition. It then groups users according to the sets of channels they encountered. This makes it possible to calculate credit directly from those groups rather than repeatedly evaluating the marginal contribution of each channel across many coalitions.

Under the simplified calculation, each user group’s revenue is divided equally among the channels in the group. A channel’s total Shapley value is the sum of its shares across every group that includes it. The authors show that this direct formula is mathematically equivalent to the standard Shapley calculation under their definition of coalition value.

The approach also makes several desirable properties easier to see:

Total credit assigned to channels equals the campaign’s total value.
A channel that contributes nothing receives no credit.
Channels that contribute in equivalent ways receive equal credit.
The calculation avoids repeatedly recomputing marginal contributions across coalitions.

Adding the journey’s timing

The authors’ second contribution is an ordered Shapley method. Instead of reporting only how much credit a channel receives overall, it separates that credit by the channel’s position in a conversion journey. If a user encounters the same channel more than once, that user’s contribution is divided evenly across those touchpoints.

When touchpoint credits are added together, they recover the ordinary Shapley value for each channel. Looking across channels instead shows how total credit is distributed by journey stage. This offers a view of whether a channel’s attributed role is concentrated early, late, or across multiple points in the journey.

What the campaign analysis found

The paper tests the methods on a three-month campaign covering 18 channels in three categories: publishers, demand-side platforms (DSPs), and paid search. The dataset includes 153,814 revenue-generating observations and approximately $14.31 million in revenue.

In the category-level Shapley analysis, paid search receives 46.99% of the credit, DSPs receive 40.43%, and publishers receive 12.58%. The simplified calculation produces results similar to the original calculation, but with a striking difference in efficiency: reported analysis time falls from 17 hours to about two minutes on an ordinary PC.

The ordered analysis gives the first touchpoint 91.59% of total credit, the second 6.76%, and the third 1.15%. At first glance, that might seem to support a first-touch attribution model. The authors caution against that conclusion. Paid search accounts for a large share of first-touch credit, and they suspect this pattern partly reflects loyal users who convert after few recorded online exposures. Those users may also have been influenced by offline advertising that does not appear in the data.

Why missing exposures matter

The authors explore this issue by excluding users who convert after exposure to only one channel. Paid search’s first-touch share drops from 43.76% to 8.25%. When journeys involving only one or two channels are also excluded, its share falls further, to 4.37%. In this group of longer journeys, DSPs receive 39.63% of overall credit, paid search receives 24.43%, and publisher credit increases. At the individual channel level, D1 is the leading contributor in the analysis of journeys involving more than two channels, receiving roughly 40%.

These shifts illustrate how attribution depends on which journeys are observed and included. A channel may appear to dominate when many conversions have only a short recorded online path, while the picture changes among users who encounter several channels.

Useful attribution, not proof of causation

The methods make Shapley attribution more practical and help analysts inspect how credit varies across journey stages. But the results are descriptive: they allocate observed revenue according to recorded channel visits; they do not prove that any channel caused the revenue it receives. In particular, missing offline exposure data may shift credit to the first recorded online channel, especially paid search.

The authors point to several directions for further work, including incorporating adstock, integrating online and offline data, and connecting attribution with predictive modeling and budget planning. For marketers, the central lesson is to treat attribution as a structured way to understand observed journeys—not as a definitive measure of causal impact.

Created on 05 Nov. 2026

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Shapley Value Methods for Attribution Modeling in Online Advertising

The essentials

Question

Method

Findings

Limitations

Why it matters

Read further

Definitions

Who Gets Credit for an Online Conversion?

A clearer way to define campaign value

Adding the journey’s timing

What the campaign analysis found

Why missing exposures matter

Useful attribution, not proof of causation

Ask questions about this paper to our AI assistant

Tools for this paper

Advanced tools Premium

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