Attribution Models — The Math, Worked

Six standard models, one journey scored six ways, and data-driven attribution explained without the black box. Use this when the user wants to understand why two models disagree, or needs to pick one defensibly.

The worked journey

A single B2B buyer's path to a $12,000 annual deal, five touches over 38 days:

#	Day	Touch	Role in the story
T1	0	LinkedIn ad (paid social)	First discovered you — created awareness
T2	5	Organic blog post (organic search)	Came back to learn — built interest
T3	12	Retargeting ad (paid social)	Nudged back mid-consideration
T4	30	Branded search (paid search, branded)	Ready to act — searched your name
T5	38	Direct → demo request (direct)	Converted

The whole point: the touch that gets credit depends entirely on the model, and each model tells a different story about where your $12k came from.

The six models, applied

Credit for the $12,000 deal under each model:

Touch	Channel	First-touch	Last-touch	Last non-direct	Linear	Time-decay	Position (U)
T1	Paid social	$12,000	$0	$0	$2,400	$175	$4,800
T2	Organic	$0	$0	$0	$2,400	$290	$800
T3	Paid social	$0	$0	$0	$2,400	$575	$800
T4	Paid search (branded)	$0	$0	$12,000	$2,400	$3,415	$800
T5	Direct	$0	$12,000	$0	$2,400	$7,545	$4,800

(Time-decay uses a 7-day half-life — weight = 0.5^(days-before-conversion / 7), normalized: shares of ~1.5% / 2.4% / 4.8% / 28.5% / 62.9% (dollars rounded to sum to $12,000). With a 38-day journey the credit concentrates hard on the last two touches — which is exactly why time-decay behaves almost like last-touch on long cycles. Position-based is 40/40/20, the 20% split evenly across T2–T4.)

Read the disagreement:

• First-touch hands everything to the LinkedIn ad — great for arguing paid social's demand-gen value, blind to what closed it.
• Last-touch hands everything to Direct — which is really "we don't know," the junk-drawer channel (see SKILL.md §6). This is how top-of-funnel gets defunded.
• Last non-direct hands it to branded search — but branded search only happened because the LinkedIn ad and blog created the demand. Crediting the closing branded click is crediting your own brand for demand someone else's channel created.
• Linear spreads it evenly — honest that all five mattered, useless for deciding what to cut (everything looks equally important).
• Time-decay favors the recent — reasonable for short cycles, but here it under-credits the LinkedIn ad that started everything.
• Position-based credits the bookends (discovered + closed) — usually the most defensible single model for B2B, because "what created this deal" and "what closed it" are the two decisions you actually make.

The takeaway to give the user: report first-touch and last-touch side by side. The LinkedIn-vs-Direct gap is the insight — it tells you paid social creates demand that later shows up as direct/branded. No single number captures that; the spread does.

Data-driven / algorithmic attribution (Shapley), plainly

Data-driven attribution (Google's DDA, most MTA tools) doesn't use a fixed rule. It asks a counterfactual: how much does each touch actually change the probability of conversion? The formal engine is the Shapley value from cooperative game theory.

The plain-English version:

• Treat each touch as a "player" on a team that produced the conversion.
• Look across all your journeys — converting and non-converting.
• For a given touch, compare conversion rates of journeys that had it vs. otherwise-similar journeys that didn't, across every possible combination of the other touches.
• A touch's credit = its average marginal lift to conversion probability across all those combinations.

So if journeys with a retargeting touch convert meaningfully more often than identical journeys without it, retargeting earns real credit. If adding a channel changes nothing, it earns ~zero — even if it appears on every path.

When it's worth it:

• You have volume — the counterfactuals need enough conversions to be stable. (Google Ads historically gated data-driven attribution behind ~3,000 ad interactions and ~300 conversions in 30 days; it has since relaxed the hard minimums and made data-driven the default model, but the underlying reality is unchanged: below real volume, DDA is noise dressed as science.) Use position-based instead when you're thin.
• Your journeys are mostly digital and tracked — Shapley can only weigh touches it was fed. Offline events, dark social, and cookie-lost touches are invisible to it, so a high-word-of-mouth B2B motion will get a confidently-wrong DDA. Pair it with self-reported (SKILL.md §4).

Its honest limitations:

• Black box — you can't easily explain to a CFO why LinkedIn got 23%. "The model says so" is a weak budget argument on its own.
• Correlation, not causation — it models what co-occurs with conversion, not what causes it. That's why incrementality testing (see measurement-paradigms.md) exists: to validate what DDA claims.
• Garbage in — inherits every blind spot in your tracking. If half your journeys are "direct," DDA is confidently splitting credit on half-blind data.

Choosing — a short decision guide

• Short cycle, few touches, small volume → last non-direct, plus a self-reported survey. Don't over-model.
• Long B2B cycle, clear created/closed moments → position-based as the primary, first-touch + last-touch shown alongside.
• High volume, mostly-digital, need day-to-day allocation → data-driven, validated periodically by incrementality.
• Offline + brand-heavy, real budget → don't rely on any user-level model; go MMM + incrementality (see measurement-paradigms.md).

In every case: pick one model, stay consistent, and pair it with an out-of-model check. Model-switching to make a channel look good is the fastest way to lose trust in the whole attribution program.