Free Advertising Adstock & Media Saturation Lab

Step 1: Media Spend, Decay Lambda, Saturation Half-Point (K) & Market Ceiling

Adstock & Saturation Inputs

📢 Weekly Media Budget & Memory Decay

Weekly Ad Spend ($)

Direct weekly media budget ($).

Decay Rate Lambda (λ)

Carryover retention (0.1 to 0.9).

Product Gross Margin (%)

Gross margin before ad spend.

🏔️ Hill Saturation & Market Capacity

Saturation Half-Point (K $)

Adstock for 50% saturation.

Max Revenue Ceiling ($/wk)

Theoretical 100% capacity.

Blended ROAS

3.24x ROAS

Marginal ROAS: 1.12x vs 1.54x breakeven hurdle (65% margin)

Generated Weekly Revenue

$162K/wk

64.8% of $250K max market capacity

Cumulative Adstock

$90.9K

Steady-state adstock (0.45 decay rate, 0.9 wk half-life)

Weekly Net Profit After Ads

$55.4K/wk

$105.4K gross profit minus $50.0K ad spend

Adstock Matrix: Weekly Spend vs. Decay Rate (λ)

Simulates realized Blended ROAS, generated weekly revenue ($), and weekly net profit after ads across media spend and ad memory carryover variations.

Weekly Ad Spend	Decay 0.25	Decay 0.35	Decay 0.45 (Base)	Decay 0.55	Decay 0.65

Marketing Science & Econometrics

Understanding Adstock & Saturation Traps

Key Media Mix Modeling (MMM) principles governing ad spend:

The Adstock Carryover Effect: Marketing does not convert 100% in the week it runs. Memory carryover ($lambda$) builds cumulative brand momentum over time.
The Marginal Saturation Trap: Marketers often look at blended ROAS (e.g. 3.5x) and believe they can double their budget profitably. As adstock climbs, the Hill saturation curve flattens, causing marginal ROAS on the next dollar to collapse below breakeven.
Share of Voice & ESOV: Explore excess share of voice market share gains in the Share of Voice & ESOV Lab.
Marketing Efficiency Ratio (MER): Model blended e-commerce ROAS in the Marketing Efficiency Ratio Lab.

Explore multi-channel attribution in the Multi-Touch Attribution Lab.

Mathematical Formulation

Media mix modeling equations

ext{Adstock}_t = ext{Spend}_t + lambda imes ext{Adstock}_{t-1}

ext{Steady-State Adstock} = rac{ ext{Weekly Spend}}{1 - lambda}

ext{Advertising Half-Life} = rac{-ln(2)}{ln(lambda)}

ext{Generated Revenue} = left(rac{ ext{Adstock}^S}{K^S + ext{Adstock}^S} ight) imes ext{Max Revenue}

ext{Marginal ROAS} = rac{Delta ext{Revenue}}{Delta ext{Spend}} quad ext{vs.} quad ext{Breakeven Hurdle} = rac{1}{ ext{Margin %}}

Evaluate channel acquisition costs in the CAC by Channel Lab.

FAQ

Adstock & media saturation questions

What is Advertising Adstock?

Advertising Adstock (invented by Simon Broadbent) models the cumulative carryover and lingering memory effect of past advertising campaigns over time: Adstock_t = Spend_t + Lambda x Adstock_{t-1}.

What is advertising half-life?

Advertising half-life is the duration required for the impact of an ad spend to decay by 50%: Half-Life = -ln(2) ÷ ln(Lambda). A decay rate of 0.50 corresponds to a 1.0-week half-life.

Why is Marginal ROAS more important than Blended ROAS?

Blended ROAS looks at total revenue divided by total spend, which conceals diminishing returns. Marginal ROAS measures the revenue generated by the *next* incremental dollar spent. Spending beyond the saturation point results in marginal ROAS falling below breakeven.

What is the Hill function in Media Mix Modeling (MMM)?

The Hill equation is an S-shaped saturation function that models diminishing marginal returns in marketing: Response = [Adstock^S ÷ (K^S + Adstock^S)] x MaxRevenue.

Can I export adstock and media saturation simulations to CSV?

Yes. You can export complete steady-state adstocks, saturation ratios, marginal ROAS metrics, and 5x5 spend-decay sensitivity heatmaps as a UTF-8 CSV spreadsheet with formula defense.

Continue Exploring Marketing & Demand Tools

Explore our Marketing & Demand Hub, calculate market share growth in the Share of Voice Lab, model blended e-commerce returns in the Marketing Efficiency Ratio Lab, evaluate sales quotas in the Sales Quota Lab, or calculate attribution in the Multi-Touch Attribution Lab.