Digital channels (Paid Search, Paid Social) show the highest ROI with relatively narrow uncertainty bands, suggesting strong evidence of effectiveness. TV shows positive returns but with wider uncertainty— additional experimentation could sharpen this estimate.
All estimates include 80% credible intervals reflecting genuine uncertainty from limited data. Point estimates alone can be misleading—decisions should account for the full range of plausible values.
The model captures 94% of weekly revenue variance. The chart below shows actual vs. predicted revenue with the 80% prediction interval. The model performs well across seasons and promotional periods.
Replicated data from the posterior distribution matches key statistics of observed data: mean (within 2%), variance (within 5%), and autocorrelation structure. No systematic patterns remain in residuals.
ROI estimates with 80% credible intervals. The vertical line at ROI = 1.0 represents break-even. Channels with intervals crossing this line have uncertain profitability.
| Channel | Spend (2025) | ROI (Median) | 80% Credible Interval | Recommendation |
|---|---|---|---|---|
| Paid Search | $18.2M | 2.41 | [1.89 – 3.02] | Strong — Consider increasing |
| Paid Social | $12.5M | 1.87 | [1.42 – 2.38] | Positive — Maintain or increase |
| TV (National) | $42.0M | 1.24 | [0.78 – 1.74] | Uncertain — Recommend geo-test |
| Display | $8.3M | 1.15 | [0.71 – 1.62] | Uncertain — Wide interval |
| Radio | $6.8M | 0.82 | [0.41 – 1.28] | Likely unprofitable — Review |
| $4.2M | 0.54 | [0.22 – 0.91] | Reduce or eliminate |
Marketing channels exhibit diminishing returns at higher spend levels. The curves below show the relationship between spend and incremental revenue for each channel. Use the controls to explore how marginal ROI changes with spend level.
Paid Search and Paid Social operate below saturation—additional spend would yield positive marginal returns. TV is approaching saturation at current spend levels, suggesting reallocation opportunities.
Marketing investments create effects that persist beyond the week of spend. The visualization below shows how $1 of spend decays over time for each channel.
| Channel | Half-Life (weeks) | 80% CI | Peak Effect | Interpretation |
|---|---|---|---|---|
| TV (National) | 3.2 | [2.1 – 4.8] | Same week | Long-lasting brand effect |
| Paid Search | 0.4 | [0.2 – 0.7] | Same week | Immediate, short-lived |
| Paid Social | 1.1 | [0.6 – 1.8] | Same week | Moderate carryover |
| Display | 0.8 | [0.3 – 1.4] | Same week | Short carryover |
Comparing prior beliefs to posterior distributions shows how much the data informed our estimates. Narrow posteriors (relative to priors) indicate strong learning from data.
Digital channels show substantial posterior concentration, indicating the data strongly informs these estimates. TV effects have wider posteriors relative to priors—the data provides moderate but not decisive information.
Explore how different budget allocations affect expected revenue. The uncertainty bands show the range of outcomes across the posterior distribution.
"Optimal" allocations are sensitive to model uncertainty. The ranges shown reflect this uncertainty— treat point estimates as guides, not gospel. Consider experimentation before major reallocations.
How robust are our conclusions to different modeling assumptions? The chart below shows how key estimates vary across alternative specifications.
Paid Search ROI > 1.5 holds across all reasonable specifications. Print underperformance (ROI < 1.0) is consistent across sensitivity checks.
TV ROI varies from 0.9 to 1.6 depending on adstock assumptions— experimental validation is particularly valuable for this channel.
1. Increase Paid Search investment — Strong ROI evidence with narrow uncertainty.
Consider 15-25% budget increase.
2. Reduce Print spend — Consistently below break-even across model variations.
Reallocate to digital channels.
3. Maintain Paid Social — Solid ROI with moderate uncertainty. Current allocation appears efficient.
1. TV optimization — Before major reallocation, recommend geo-holdout test
to validate model-based ROI estimate.
2. Radio reduction — Model suggests underperformance, but consider qualitative
factors (reach, frequency) before elimination.
Q1 2026: TV geo-holdout in 3 test markets (10% of footprint) to validate MMM estimate.
Q2 2026: Incrementality test for Display to sharpen uncertain ROI estimate.
This analysis uses a Bayesian Marketing Mix Model with the following components:
Inference via MCMC (4 chains, 2000 samples each, 1000 warmup). All R-hat < 1.01, bulk ESS > 400 for all parameters.
This report follows principles of honest uncertainty quantification: