MBA Digital Attribution Concept Card Template

Digital Attribution Concept Card: [Brand, funnel or course]

A concept card for multi-touch attribution as a brand and digital marketing elective teaches it: rules-based models (last click, first click, linear, time decay, position-based), algorithmic models (Shapley value and Markov chain removal effect), the data-driven models in today's analytics tools, the difference between attribution and incrementality, and the privacy changes that limit user-level tracking. It is for MBA students and for managers who read channel reports and must decide how much each channel really earns. It builds on the core card mba/mba-marketing-mix-card (average versus marginal return, allocation) and on its sibling elective cards mba/mba-marketing-experiments-card and mba/mba-marketing-mix-modeling-card, and does not re-teach them. Source basis: Shapley (1953), Shao and Li (2011), Dalessandro et al. (2012), Li and Kannan (2014), Anderl et al. (2016), Berman (2018) and Gordon et al. (2019, 2023), written up in original words with fictional Northfield Outdoor Co. data. Every number was computed in Python and is shown with its Excel formula. Replace every [bracketed] value and every row marked Example.

Document control

When to use it

One-sentence rule: use attribution to describe how customer journeys are made up and to share credit consistently across digital touchpoints for day-to-day optimisation; do not use it on its own to decide how much a channel adds to total sales.

The idea in plain language

A customer who buys online often touches several channels first: sees a social ad, later searches the brand, opens an email, then buys. Attribution decides how to split the credit for that purchase among the touchpoints. Rules-based models apply a fixed rule (all to the last click, equal shares, more to recent touches). Algorithmic models use the data on converting and non-converting journeys to decide the split.

Two facts limit every attribution model:

1. Attribution allocates all conversions on tracked paths to channels. It has no "would have bought anyway" bucket. A loyal customer who would have bought regardless and clicked a brand-search ad on the way gives that ad full credit under last click. Experiments measure that missing base directly (mba/mba-marketing-experiments-card).
2. It sees only what is tracked. Offline exposure, views without clicks, other devices and users who decline tracking are partly or wholly invisible, and the visible share is shrinking.

Berman (2018) showed formally that common attribution rules can reward publishers for showing ads to people who would have converted anyway, and Li and Kannan (2014) found with a field experiment that last-click rules misstate the contribution of several channels. Gordon et al. (2019, 2023) compared observational ad measurement with large experiments and found the observational methods often far off. Attribution remains useful, but as a description and a consistent bookkeeping rule, checked against experiments.

Models and formulas

Rules-based models for a converting path with touches $j = 1, \dots, m$ (in time order) and $d_j$ days before conversion:

Shapley value (Shapley 1953). Treat channels as players and a value function $v(S)$ as what a set $S$ of channels achieves together. Each channel gets its average marginal contribution over all orders in which channels could join:

$\phi_i = \sum_{S \subseteq N \setminus \{i\}} \frac{|S|!\,(n - |S| - 1)!}{n!}\left[v(S \cup \{i\}) - v(S)\right]$

The Shapley value is the only allocation that is efficient (credits sum to $v(N) - v(\varnothing)$), symmetric, gives zero to a channel that never adds anything, and is additive. A simple, common choice in attribution is to estimate $v(S)$ as the conversion rate of users exposed to exactly the channels in $S$; Dalessandro et al. (2012) set out the link between attribution and the Shapley value, building on the data-driven models of Shao and Li (2011).

Markov chain removal effect (Anderl et al. 2016). Model journeys as transitions between states (start, channels, conversion, null). $P(\text{conv})$ is the probability of reaching conversion from start. The removal effect of channel $c$ is the share of conversions lost if $c$ is removed (its visits go to null):

$RE_c = 1 - \frac{P_{-c}(\text{conv})}{P(\text{conv})}, \qquad \text{credit}_c = \frac{RE_c}{\sum_k RE_k} \times \text{conversions}$

With transient-state matrix $Q$ and absorption vector $r$ into conversion, the conversion probabilities from each state are $b = (I - Q)^{-1} r$ (Excel: =MMULT(MINVERSE(I-Q), r)).

Assumptions and limits

How managers use it in practice

• Analytics tools (dated fact, checked 28 October 2026). Google Analytics 4 offers data-driven attribution, paid and organic last click, and Google paid channels last click; Google's help page states that the first click, linear, time decay and position-based models were removed in November 2023 (GA4 attribution help). Rules-based models therefore live mainly in spreadsheets, warehouses and other tools. Check the current list before you rely on it.
• Browser and mobile privacy (dated facts, checked 28 October 2026). Apple requires apps to obtain permission through App Tracking Transparency before tracking users across other companies' apps and websites or accessing the advertising identifier, on iOS, iPadOS and tvOS 14.5 or later (Apple user privacy and data use); Apple's privacy-preserving ad attribution frameworks (SKAdNetwork and the newer AdAttributionKit, available from iOS and iPadOS 17.4 per Apple's developer documentation) report aggregated, delayed results instead. Google announced on 22 April 2025 that Chrome would keep its current approach of letting users choose about third-party cookies rather than introduce a new standalone prompt, and on 17 October 2025 that it was retiring several Privacy Sandbox technologies, including the Attribution Reporting API (Privacy Sandbox update). These rules change: re-check the official pages, and treat consent and tracking as legal questions for counsel, not for this card.
• Triangulation. Mature teams use attribution for within-channel optimisation, MMM for cross-channel budgets (mba/mba-marketing-mix-modeling-card) and experiments to calibrate both (mba/mba-marketing-experiments-card).
• Incrementality factors. A holdout result divides attributed conversions into incremental and non-incremental; the ratio is then applied to attribution reports until the next test.

Worked example A (fully solved): Northfield's three digital channels

Situation (fictional). In one quarter Northfield Outdoor Co. records 1,650 online purchases on journeys that touched paid search, paid social or email (30-day lookback). Spend: search USD 90,000, social USD 60,000, email USD 10,000. Average order value USD 110.

Converting paths (days before purchase in brackets):

Step 1: rules-based models

Time-decay weights, half-life 7 days: raw weight =POWER(2,-days/7), normalised by the path total. P1: raw 0.3715 and 0.9057, normalised 0.2909 (social) and 0.7091 (search). P3: 0.1344, 0.3278, 0.5378. P5: 0.3557, 0.6443. P6: 0.1905, 0.3451, 0.4644. P8: 0.3333, 0.6667. Channel credit is =SUMPRODUCT(weights, purchases) over the paths.

Social's credit ranges from 80 to 750 purchases depending on the rule: a factor of more than nine. Nothing in the data says which rule is right; each encodes a belief about how journeys work.

Step 2: Shapley values from conversion rates

The analytics team also has all users in the quarter, grouped by the exact set of channels they were exposed to, including users with no paid touch and users who did not buy:

Take $v(S)$ = conversion rate of the set. For a user exposed to all three, the rate exceeds the no-touch base by $3.75 - 0.40 = 3.35$ pp. Search's marginal contributions: joining nothing 0.60 pp; joining social 1.50 pp; joining email 1.50 pp; joining both 2.35 pp. With three players the weights are 1/3 for the empty and full coalitions and 1/6 for each one-channel coalition:

$\phi_{\text{Search}} = \tfrac{1}{3}(0.60) + \tfrac{1}{6}(1.50) + \tfrac{1}{6}(1.50) + \tfrac{1}{3}(2.35) = 1.4833 \text{ pp}$

Likewise $\phi_{\text{Social}} = 0.6833$ pp and $\phi_{\text{Email}} = 1.1833$ pp; the three sum to 3.35 pp (efficiency). Excel: put the eight rates in a table and compute each marginal contribution by subtraction, then =SUMPRODUCT(weights, marginals).

From rates to purchases. For each channel set, purchases at the base rate (0.40% of its users) go to a "base" bucket and the rest are split by the Shapley values of the channels in that set. For example, search and social: 15,000 users, base 60, incremental 240, split search 157.5 and social 82.5. Summed over all sets:

Step 3: money

ROAS = credited purchases times USD 110 divided by spend; for example, last-click search =1000*110/90000 = 1.22.

Step 4: interpretation

• Social looks like a disaster under last click (ROAS 0.15) and a winner under first click (1.38). Its users have a conversion rate on their own (0.50%) barely above the base (0.40%), and the Shapley view gives it 10% of purchases. But Shapley on observed rates is still not causal: social reaches colder prospects, so its users differ from non-exposed users before any ad.
• Email looks excellent under every model. Most email recipients are existing customers with high purchase propensity; the Shapley base bucket shows that part of what rules-based models credit to channels would have happened anyway, and email is the channel most exposed to this selection.
• Search keeps the largest share under every model; much of it is brand search by people already looking for Northfield.
• Decision. Do not move budget on any of these numbers alone. Use them to frame the next experiments: a social holdout (the channel with the widest disagreement and the largest spend relative to credit) and an email holdout (likely the largest gap between credit and increment). The paid-social holdout in mba/mba-marketing-experiments-card is exactly this test.

Worked example B (half solved): two-channel Shapley and time decay

Two channels A and B. Conversion rates: no touch 0.5%, A only 1.3%, B only 0.9%, both 2.1%.

1. With two players, $\phi_A = \tfrac{1}{2}[v(A) - v(\varnothing)] + \tfrac{1}{2}[v(AB) - v(B)]$ = $\tfrac{1}{2}(0.8) + \tfrac{1}{2}([\ ])$ = [ ] pp.
2. $\phi_B$ = [ ] pp. Check: $\phi_A + \phi_B$ = $v(AB) - v(\varnothing)$ = [ ] pp.
3. 12,000 users saw both channels. Split their 252 purchases into base, A and B: base [ ], A [ ], B [ ].
4. Time decay with a 7-day half-life for the path Social (12 days) then Email (2 days) then Search (0 days): raw weights =POWER(2,-12/7) = 0.3048, =POWER(2,-2/7) = [ ], 1.0000. Sum [ ]. Normalised weights [ ], [ ], 0.4706.
5. Under last click, which channel gets this path's purchase? Under position-based? [ ]
6. In one sentence, why is the Shapley split of the 252 purchases still not proof that A caused 120 of them? [ ]

Exercise C (unsolved): Markov removal effect

Northfield's mobile app team has 1,600 journeys (fictional), each starting at "Start" and ending in purchase or null:

1. Count transitions between states (Start, Social, Search, Email, Purchase, Null) and convert them to probabilities.
2. Compute $P(\text{purchase})$ from Start with the absorbing-chain formula. Check it against 115/1,600.
3. Remove each channel in turn (send its visits to Null) and compute the removal effects.
4. Normalise the removal effects and allocate the 115 purchases. Compare with last click.
5. Which channel gains most moving from last click to the Markov view, and why?

Connections to other cards

• Core marketing mix: mba/mba-marketing-mix-card for average versus marginal return; attribution ROAS is an average.
• Experiments: mba/mba-marketing-experiments-card measures what attribution cannot: the increment.
• MMM: mba/mba-marketing-mix-modeling-card for the top-down, all-channel view.
• Game theory: the Shapley value comes from cooperative game theory (mba/mba-game-theory-card covers the non-cooperative side).
• Customer value: mba/mba-customer-lifetime-value-card, to value a credited new customer beyond the first order.
• Brand: mba/mba-brand-equity-card. Brand search volume is partly an outcome of brand building, which last-click attribution credits to search.
• Course map: mba/mba-marketing-analytics-guide.

Common mistakes and misconceptions

1. Treating attributed conversions as incremental. Every rules-based model gives the whole 1,650 to channels; the Shapley view puts 476 in a base bucket, and a holdout may find more.
2. Cutting upper-funnel channels on last-click ROAS. Social at 0.15 under last click and 1.38 under first click is a model choice, not a measurement.
3. Comparing reports with different windows or channel groupings. Align them before comparing.
4. Believing "data-driven" means causal. Data-driven models learn from observed paths and inherit their selection bias.
5. Ignoring non-converting paths. Path-only models cannot tell whether a channel raises conversion rates; Shapley and Markov models need the non-converters too.
6. Forgetting what is not tracked: views without clicks, offline media, other devices and users who decline tracking.
7. Rewarding brand search for demand created elsewhere. Brand search is often the last step of a journey started by TV, social or word of mouth.
8. Letting each platform grade itself. Platforms count conversions on their own terms; the sum of platform-reported conversions often exceeds actual sales.
9. Treating tool settings as permanent. Available models and privacy rules change; date every report.

Self-test questions

1. In one sentence, what is the difference between attribution and incrementality?
2. Under which rules-based model does Northfield's social get the most credit, and why?
3. Write the time-decay weight for a touch 14 days before purchase with a 7-day half-life, before normalising.
4. State the four properties that characterise the Shapley value.
5. In example A, what is search's marginal contribution when it joins social, and where does it come from?
6. Why do Shapley values computed from observed conversion rates still carry selection bias?
7. Define the removal effect in a Markov attribution model.
8. Which attribution models does Google Analytics 4 offer as of October 2026, according to Google's help page?
9. Why does App Tracking Transparency make user-level attribution harder on iOS?
10. Which experiment would you run first after reading example A, and why?

My notes and next steps

Sources and further reading

• Shapley, L. S. (1953). A value for n-person games. In H. W. Kuhn and A. W. Tucker (eds.), Contributions to the Theory of Games, Volume II (Annals of Mathematics Studies 28), 307-317. Princeton University Press.
• Shao, X., and Li, L. (2011). Data-driven multi-touch attribution models. Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 258-264.
• Dalessandro, B., Perlich, C., Stitelman, O., and Provost, F. (2012). Causally motivated attribution for online advertising. Proceedings of the Sixth International Workshop on Data Mining for Online Advertising and Internet Economy (ADKDD), 1-9.
• Li, H., and Kannan, P. K. (2014). Attributing conversions in a multichannel online marketing environment: an empirical model and a field experiment. Journal of Marketing Research, 51(1), 40-56.
• Anderl, E., Becker, I., von Wangenheim, F., and Schumann, J. H. (2016). Mapping the customer journey: lessons learned from graph-based online attribution modeling. International Journal of Research in Marketing, 33(3), 457-474.
• Berman, R. (2018). Beyond the last touch: attribution in online advertising. Marketing Science, 37(5), 771-792.
• Gordon, B. R., Zettelmeyer, F., Bhargava, N., and Chapsky, D. (2019). A comparison of approaches to advertising measurement: evidence from big field experiments at Facebook. Marketing Science, 38(2), 193-225.
• Gordon, B. R., Moakler, R., and Zettelmeyer, F. (2023). Close enough? A large-scale exploration of non-experimental approaches to advertising measurement. Marketing Science, 42(4), 768-793.
• Official pages (checked 28 October 2026): Google Analytics help, "Select attribution settings" (support.google.com/analytics/answer/10596866); Apple, "User privacy and data use" (developer.apple.com/app-store/user-privacy-and-data-use); Google Privacy Sandbox blog, "Update on plans for Privacy Sandbox technologies" (17 October 2025) and "Next steps for Privacy Sandbox and tracking protections in Chrome" (22 April 2025).
• Textbooks (further reading, by name only): Kotler and Keller, Marketing Management; Chaffey and Ellis-Chadwick, Digital Marketing; Kohavi, Tang and Xu, Trustworthy Online Controlled Experiments.

Answer key

Worked example B. (1) $v(AB) - v(B) = 2.1 - 0.9 = 1.2$; $\phi_A = 0.4 + 0.6 = 1.00$ pp. (2) $\phi_B = \tfrac{1}{2}(0.4) + \tfrac{1}{2}(0.8) = 0.60$ pp; sum 1.60 pp = 2.1 - 0.5. (3) Base $0.005 \times 12{,}000 = 60$; A $0.010 \times 12{,}000 = 120$; B $0.006 \times 12{,}000 = 72$; total 252. (4) 0.8203; sum 2.1251; normalised 0.1434, 0.3860, 0.4706. (5) Last click: search. Position-based: social 40%, email 20%, search 40%. (6) The rates come from users who chose or were targeted into each exposure, so the difference between groups mixes the ads' effect with who the users are; only random assignment separates the two.

Exercise C. (1) From Start: social 0.6250, search 0.3125, email 0.0625. From social: search 0.3000, email 0.2000, purchase 0.0050, null 0.4950. From email: search 0.3333, purchase 0.0333, null 0.6333. From search: purchase 0.1111, null 0.8889. (2) $P$ = 0.07187 = 115/1,600. (3) Without search 0.00937 (removal effect 0.8696); without social 0.03912 (0.4557); without email 0.05868 (0.1836). (4) Shares 57.6%, 30.2%, 12.2%: search 66.3, social 34.7, email 14.0 purchases; last click gives search 100, social 5, email 10. (5) Social, from 5 to 34.7, because it starts many journeys that end in search; last click ignores openers.

Self-test.

1. Attribution divides the credit for observed conversions among touchpoints; incrementality measures how many conversions would not have happened without the channel.
2. First click (750 purchases), because social opens most multi-touch journeys (P1, P3, P6, P8).
3. $2^{-14/7} = 0.25$.
4. Efficiency, symmetry, null player (zero for a channel that never adds anything) and additivity.
5. 1.50 pp: the "search and social" rate (2.00%) minus the "social only" rate (0.50%).
6. Users self-select or are targeted into channels (email goes to existing customers), so their conversion rates differ for reasons other than the ads.
7. The share of conversions lost when the channel is removed from the journey graph and its visits go to null.
8. Data-driven attribution, paid and organic last click, and Google paid channels last click (first click, linear, time decay and position-based were removed in November 2023, per Google's help page).
9. Apps need the user's permission to track across other companies' apps and websites or to read the advertising identifier; without it, cross-app user-level paths cannot be joined, so fewer journeys are visible.
10. A social holdout (widest disagreement between models, large spend) or an email holdout (largest likely gap between credit and increment); either turns a model argument into a measurement.

Revision history

Standard and licence note

Based on cooperative game theory (Shapley 1953) and the attribution and advertising measurement literature (Shao and Li 2011; Dalessandro et al. 2012; Li and Kannan 2014; Anderl et al. 2016; Berman 2018; Gordon et al. 2019, 2023), with tool and privacy facts from the official Google and Apple pages checked on 28 October 2026. The text, data and exercises are original and fictional; no textbook, published case or course material was copied or paraphrased. This template is not affiliated with or endorsed by any business school, publisher, author, analytics vendor, platform or browser maker. Check the current official pages before you rely on a tool setting or privacy rule. Template licence: MIT.