Aurora 00: The Trap

Aurora Coffee Co. is a fast-growing direct-to-consumer coffee brand with two product lines — Original (ground & whole bean) and Cold Brew (ready-to-drink) — and four paid channels: TV, Search, Social, Display. It's planning season. The CMO has to defend the budget to the CFO and answer one deceptively simple question: what is each channel actually worth, and how should we reallocate? A normal dashboard answers with correlations. This page — the hook of the six-part Aurora showcase, mirroring nbs/aurora/00_overview.ipynb — shows why that answer is wrong in a way that costs real money. Because Aurora's world is synthetic with a sealed answer key, every claim here can be graded against ground truth.

Meet the business

Two years (104 weeks) of weekly data: revenue in $000s by product, spend by channel, plus a few business drivers (a category demand index, average price, and a brand-awareness survey with gaps). Average revenue is $839k/week, and media truly drives 26% of revenue — there is real money on the table either way.

Measured — the actual weekly series from the shared Aurora world (nbs/builders/aurora.py, seeded; the same dataset every notebook in the series fits). Top: revenue stacked by product — notice Cold Brew surging each summer exactly as Original dips. Bottom: media spend by channel — notice Search and Social swelling into the winter peaks. Both of those rhythms are about to matter.

The trap

The fastest way to "value" a channel is to correlate its spend with sales — that is what most dashboards quietly do. Do exactly that for Aurora, and put the result next to the true ROAS, which we know because we built this world.

Measured — left panel: Pearson correlation of weekly spend with total sales, computed on the seeded Aurora dataset (TV 0.29, Search 0.85, Social 0.69, Display 0.52). Right panel: the generative ground-truth ROAS — revenue per $1 of spend (TV 2.14, Search 0.66, Social 0.49, Display 2.11). The dashed line is breakeven. The ranking doesn't just shift — it inverts.

The sealed answer key

The key says: Search is a demand-chasing mirage. Aurora's team bids harder on Search when demand is already high, so Search spend rides the same wave as sales — the latent demand signal and Search spend correlate at 0.94. The credit belongs to demand, not the channel. In notebook 1, an MMM reads Search at 2.51 demand-blind (still 1.04 even after a demand control); folding a geo-lift experiment into the likelihood collapses it to 0.66 — right on top of the true 0.66.

Meanwhile TV and Display are Aurora's brand engines — true ROAS 2.14 and 2.11 — but their effect flows almost entirely through awareness (98.8% and 96.7% of their true effect is mediated). They barely sell anything directly, which is why correlation — and, as notebook 3 shows, even a well-specified base MMM — underrates them.

Over the two years, the true incremental revenue ledger reads: TV $13.0M, Display $6.0M, Search $2.2M, Social $1.5M. The dashboard's ranking is that ledger upside down.

Three seeded pathologies

Three things are breaking the correlation, and each was deliberately seeded into the world so the framework has something real to find. Toggle between them:

Measured — z-scored latent demand against z-scored Search spend from the seeded Aurora world. They are nearly the same curve (correlation 0.94): the team bids on Search when demand is already high, so Search inherits demand's credit.

How chasing inflates a channel

Why exactly does demand-chasing manufacture correlation? Suppose sales are \( y_t = \alpha + \gamma\, d_t + \beta\, s_t + \varepsilon_t \) where \(d_t\) is latent demand and \(s_t\) is spend — but the team sets spend as \( s_t = \mu + \kappa\, d_t + u_t \), chasing demand with intensity \(\kappa\). A naive regression of sales on spend then recovers not \(\beta\) but \( \beta + \gamma\,\mathrm{cov}(d_t, s_t)/\mathrm{var}(s_t) \): the channel inherits demand's effect in proportion to how hard it chases. Drag the slider and watch a money-losing channel (true ROAS fixed at 0.66, Aurora's Search) turn into a dashboard hero:

Illustrative simulation (seeded) — not the Aurora dataset. 104 simulated weeks where latent demand moves sales, spend chases demand with the intensity you set, and the channel's true effect never changes. The red line is the naive spend–sales fit; the dashed dark line is the true incremental effect (slope 0.66). At \(\kappa = 0\) they nearly coincide; near \(\kappa = 0.85\) — Aurora's actual Search chasing intensity in the generator — the naive line is several times too steep and the correlation reads like a hero channel.

The tour: notebooks 01–05

The rest of the series undoes the trap one pathology at a time, on this same dataset, and ends with a reallocation worth real money. Read in order — the story builds — but each chapter regenerates the data and fits what it needs, so any one stands alone.

What to take away