Time-Decay Attribution Explained

How the weighting actually works

Time-decay attribution uses an exponential half-life: pick a half-life period — seven days is a common default — and each touch's credit halves for every half-life it sits further back from the purchase. A touch on the day of purchase gets full weight; a touch seven days earlier gets half; a touch fourteen days earlier gets a quarter; and so on, until the earliest touches carry a small enough weight that they barely register in the total.

The half-life you choose matters as much as the model itself. A seven-day half-life makes sense for a fast-consideration category where most decisions happen within a couple of weeks. A 21-day half-life suits a considered purchase — furniture, electronics, anything with a longer research phase — because a seven-day half-life would nearly zero out touches that, in that category, are still genuinely influential.

It sits deliberately between the two single-touch extremes and linear attribution's flat split. Last-touch is time-decay with an infinitely short half-life — everything but the final touch effectively rounds to zero. Linear attribution is time-decay with an infinitely long half-life — nothing ever decays, so every touch stays equal. Seeing time-decay as a dial between those two poles, rather than a wholly separate model, makes the half-life choice easier to reason about: shorter half-life pulls you toward last-touch's bias, longer pulls you toward linear's.

A worked example

Take a $150 order with three touches: a DSP display impression 12 days before purchase, a Sponsored Brands click 4 days before, and a branded search click on the day of purchase. Using a 7-day half-life, weight = 0.5^(days back / 7). The display impression scores 0.5^(12/7) ≈ 0.297. The Sponsored Brands click scores 0.5^(4/7) ≈ 0.674. The branded search click, at zero days back, scores 1.0. Total weight = 0.297 + 0.674 + 1.0 = 1.971. Normalising each to a share of the $150: display gets $150 × (0.297/1.971) ≈ $22.60; Sponsored Brands gets ≈ $51.30; branded search gets ≈ $76.10.

Compare that to last-touch, which would give the full $150 to branded search alone, and to linear, which would split it three ways at $50 each. Time-decay lands between the two — it acknowledges the display touch happened, unlike last-touch, but weights it far less than the touches closer to the sale, unlike linear.

When the recency assumption actually holds

Time-decay is the most defensible model for categories where buying decisions genuinely compress toward the purchase moment — fast-moving consumer goods, impulse-adjacent categories, anything where the gap between "aware" and "ready to buy" is short. In those categories, a touch from three weeks ago realistically had less influence on today's decision than one from yesterday, and the model's core assumption matches how the funnel actually behaves.

When it quietly gets the answer wrong

The assumption breaks for considered purchases and for exactly the awareness-building media this measurement territory is built around. In our own DSP book, streaming and connected-TV inventory carries the highest new-to-brand rate of any placement, 56.3%, precisely because it's introducing people to a brand who then go on to research and buy weeks later. A time-decay model with a short half-life will near-zero out that streaming touch by the time the sale happens, understating exactly the channel that started the journey — the same structural problem last-touch has, just softened rather than solved. Choosing too short a half-life for a considered-purchase category reproduces last-touch's blind spot under a more sophisticated-sounding name.

The common mistake, including ours

The mistake is adopting a default half-life — seven days is the number that shows up in most marketing textbooks and dashboard defaults — without checking whether it matches the actual path length in your own category. We've run a time-decay analysis with a stock seven-day half-life on an account selling a considered, higher-price item, and the output looked almost identical to plain last-touch, because nearly every touch older than two weeks had decayed to functional zero before we noticed the half-life was miscalibrated for that funnel. The fix wasn't switching models — it was recomputing the actual median path length from the account's own AMC data and setting the half-life to match it, rather than trusting the textbook default.

The same mistake is easy to make in the other direction too. Set the half-life too long for a genuinely fast-decision category and time-decay starts to behave like linear attribution, quietly re-crediting old, stale touches that had no realistic bearing on a purchase decided within days. A miscalibrated half-life in either direction produces a model that looks sophisticated and answers the wrong question, which is arguably worse than a simple model everyone knows is crude — at least a crude model's limitations are visible.

How to pick and check your half-life

Pull your own median time-to-purchase from path data — Amazon Marketing Cloud can surface this directly — and set the half-life somewhere near that median, not at a generic default. Then sanity-check the output against what you already know about the account: if a channel you're confident is doing real upper-funnel work is scoring near-zero under your chosen half-life, that's a sign the half-life is too short for your funnel, not that the channel is failing.

What to do when a time-decay result contradicts what you expected

If a channel you'd normally call top-of-funnel scores unexpectedly high, or one you'd expect to close scores unexpectedly low, resist the instinct to immediately recalibrate the half-life until the model agrees with your prior. Check the raw path data first — a shift in touch timing, a change in creative that moved when in the journey a channel typically fires, or a seasonal shift in path length can all produce a genuine change in the right answer, not a broken model. Only adjust the half-life once you've confirmed the underlying path data, not just the output, has actually changed. And treat any single time-decay read as descriptive, not causal — if a result is surprising enough to change a budget decision, that's exactly the point to run a holdout test rather than trust the credit-split model further.