Marketing Budget Allocation Model

Channel Scope:

Model: CPA = k × S^γ (Power-Law)

Each channel/country/device combination is fitted with a power-law model on weekly (spend, CPA) data over 52 weeks. The model is fitted in log-log space via linear regression with 5% outlier trimming (top 2.5% + bottom 2.5% of CPA observations removed).

Tab 1: CPA — Minimize Blended CPA

λ is the portfolio marginal CPA — the cost of acquiring one additional user from the most efficient next dollar across all optimized combos.

For each optimized combo, marginal CPA at spend S is:

Marginal_CPA(S) = k × Sγ / (1 − γ)

At the optimum, every optimized combo has the same marginal CPA = λ. This is the equal-marginal-returns condition. Binary search finds the λ where Σ S_i = Budget.

Target spend per combo: S_i = ((1−γ_i) × λ / k_i)^1/γ_i

Tab 2: CPHC — Minimize Cost Per Healthy Customer

CPHC (Cost Per Healthy Customer) = Spend ÷ Healthy Acquisitions, where a “healthy” customer is one who is both Prime and meets the D1_1500 threshold (uploaded ≥1500 photos in day 1).

Each combo has a measured health rate (fraction of acquisitions that are healthy). Since health rate is approximately constant per combo regardless of spend level (avg correlation = −0.05), the quality-adjusted model is:

CPHC = CPA / health_rate = (k / h) × Sγ
Marginal_CPHC(S) = (k / h) × Sγ / (1 − γ)

The optimization is identical to Tab 1 except λ is in CPHC units and allocation accounts for health rate:

Si = ((1−γi) × λ × hi / ki)1/γi

Effect: Combos with higher health rates receive proportionally more budget. A combo with 50% health rate gets treated as 2× more efficient than one with 25% health rate (at the same raw CPA).

Health rate data: 52-week aggregate % of customers acquired who are Prime + D1_1500. Ranges from 20.5% (Google/US/Android) to 58.2% (Meta/DE/Android).

Tab 3: Health Constrained — CPA Optimization with Health Floor

Same raw CPA optimization as Tab 1, but with an additional constraint: the portfolio blended health rate must be ≥ the floor set by the slider.

Algorithm:

1. Compute the unconstrained raw-CPA-optimal allocation (same as Tab 1)
2. Calculate blended health rate = Σ(acq_i × h_i) / Σ(acq_i)
3. If health ≥ floor → done (constraint satisfied naturally)
4. If health < floor → iteratively pause the lowest-health optimized combo (set its spend to $0) and reallocate that budget to remaining combos. Repeat until floor is met.

Paused combos are shown with ⏸️ in the allocation table. Their budget is redistributed to the remaining (healthier) combos via re-solved λ.

Trade-off: Higher floor = more combos paused = higher CPA (less efficient channels excluded) but better customer quality. The slider lets you explore this frontier.

Excluded Combos (R² < 0.3)

Combos with R² below 0.3 have unreliable spend→CPA relationships. Instead of curve-based optimization, they use the $10K milestone table:

• Reduce: If incremental CPA at current spend > λ → reduce to the spend level where incr_CPA ≤ λ
• Scale up: If incremental CPA at higher levels < λ × 0.8 → scale up (with 20% safety margin), capped at historical max
• Maintain: If current CPA ≤ λ but no further scaling passes the threshold

On the CPHC tab, incremental CPHC (= incr_CPA / health_rate) is compared against λ instead.

Confidence Zones

• • Tested: Recommended spend ≤ historical max. The model interpolates within observed data.
• • Extrapolating (1–2x): Beyond historical max but within 2x. Prediction interval widens. Proceed with weekly monitoring.
• • Uncharted (>2x): Beyond 2x historical max. Predictions are unreliable. Scale incrementally and validate.

Prediction intervals (80%) use each combo’s residual standard error, widened by an extrapolation factor proportional to distance beyond historical data.

Ramp-Rate Constraints

Large budget swings (e.g., +150% or -70%) cause platform algorithm instability — Meta and Google have algorithmic learning phases that reset when budgets change dramatically. The ramp-rate constraint limits weekly changes per combo:

S_this_week = clamp(S_optimal, S_current × (1 − maxDown), S_current × (1 + maxUp))

Defaults: maxUp = 25%, maxDown = 20% (asymmetric because cutting too fast destroys pixel/conversion signal permanently, while overspending is just temporarily expensive).

The allocation table shows both Target (unconstrained optimal) and Next Week (clamped) targets. A convergence indicator (Nwk) shows how many weeks at the ramp rate to reach target from current spend.

Channel-specific note: Apple Search Ads has no “learning phase” — you could ramp faster there. Consider setting higher limits for ASA combos (future enhancement).

CPA / CPHC Guardrail

On the CPA and Health Constrained tabs: when blended CPA would exceed the guardrail target, the model caps total deployment at the maximum budget where CPA ≤ target. Excess budget remains unspent.

On the CPHC tab: the guardrail operates on blended CPHC (cost per healthy customer). The slider range adjusts to $20–$60 to reflect the higher absolute CPHC values.

Data Source

Weekly aggregated data from quicksight.r_and_o (Redshift). Channels: Meta, Google App, Apple Search Ads. Devices: Android & iOS. Filter: is_raw_branch_log_data = 'N'. “Last 7d” metrics reflect the most recent complete week (Aug 10–16, 2026).

Health rate: SUM(CASE WHEN is_prime_acq='Y' THEN is_d1_1500 END) / SUM(customers_acquired) — constant per combo across 52-week history (correlation with spend ≈ −0.05).