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Technical methodology
How MixPilot moves from weekly business data to contribution, ROI, uncertainty, diagnostics, and budget recommendations.
sales_t, spend_channel_t, controls_t, geo_t
Each row represents one time period, usually a week. Sales or revenue is the outcome. Media spend, pricing, promotions, holidays, distribution, stockouts, geo, and population become explanatory variables.
adstock_t = spend_t + decay * adstock_(t-1)
Adstock captures carryover. A channel with higher decay keeps influencing future weeks for longer. Search may decay quickly; TV or video may decay more slowly.
response = x^alpha / (x^alpha + gamma^alpha)
Saturation captures diminishing returns. After spend reaches a high level, each extra euro produces less incremental outcome than the euro before it.
log(1 + sales) = intercept + media_effects + controls
The local preview model fits transformed media and business controls using positive ridge regression. It is fast and directional, not the final production truth.
loss = prediction_error + lambda * sum(beta^2)
The penalty stabilizes coefficients when channels move together. It reduces extreme estimates caused by noisy or correlated marketing data.
sales_t ~ baseline_t + media_t + controls_t + error_t
Meridian and PyMC-Marketing estimate distributions, not just one coefficient. Priors and observed data combine into posterior estimates for contribution, ROI, and uncertainty.
contribution = prediction_with_channel - prediction_without_channel
The model compares expected outcome with the channel active against a counterfactual where that channel is set to zero.
ROI = incremental_outcome / spend
Average ROI explains what the channel returned historically. It should not be the only number used for future budget movement.
mROI = delta_outcome / delta_spend
Marginal ROI estimates the return from the next euro. Budget decisions should prioritize marginal ROI because saturated channels may have strong average ROI but weak next-euro returns.
CI = posterior quantiles, usually 5% to 95%
Credible intervals show uncertainty around contribution, ROI, and marginal ROI. Wider intervals mean recommendations need more caution or validation.
calibrated_roi = model_roi * (1 - w) + experiment_roi * w
Lift tests, geo experiments, and platform incrementality studies can pull model estimates toward observed causal evidence. The weight depends on confidence and test quality.
recommended_spend = current_spend * (1 + shift)
Spend shifts are based on marginal ROI, channel constraints, minimums, maximums, fixed commitments, and whether the channel can realistically scale.
MAPE = mean(abs(actual - predicted) / actual)
Holdout validation tests whether the model predicts unseen weeks well enough to trust planning outputs.
baseline = expected outcome without paid media
Baseline includes demand that would likely happen without paid marketing, such as brand equity, seasonality, distribution, pricing, and organic demand.
P(baseline < 0)
A high probability of negative baseline is a warning sign. It usually means the model is over-crediting media or missing important controls.
compare outputs across model candidates
Robust recommendations should remain directionally stable across reasonable adstock, saturation, prior, control, and geo specifications.