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.