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Budget allocation, bid optimization, channel-mix solver inputs, saturation curves, pacing strategy, budget-cap gate criteria. Includes a worked $100k example.
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Based on SOC occupation classification
| name | media-mix-modeling |
| description | Budget allocation, bid optimization, channel-mix solver inputs, saturation curves, pacing strategy, budget-cap gate criteria. Includes a worked $100k example. |
| user-invocable | true |
| allowed-tools | ["Read","Glob","Grep","Write"] |
Owned by media-buyer-bidder. Operationalizes the MMM outputs from marketing-attribution into budget decisions, bid strategies, and pacing plans. Deterministic where possible; surfaces budget-cap breaches for HITL.
Objective: allocate budget B across channels c=1..C to maximize total expected KPI.
maximize Sigma_c f_c(x_c)
subject to Sigma_c x_c = B
x_c >= 0
L_c <= x_c <= U_c # min/max guardrails per channel
Where f_c(x_c) is the saturation-adjusted response curve for channel c.
Per Lagrangian: at optimum, marginal return is equal across all funded channels:
df_c/dx_c | x_c=x*_c = lambda (for all c with x*_c > L_c)
If channel c has higher mROI than channel c', shift dollars from c' to c until they equalize (subject to guardrails).
Two canonical forms (from MMM):
f(x) = K * x^alpha / (k^alpha + x^alpha)
f(x) = K * log(1 + x / k)
Smoother, no inflection, easier to fit when data is sparse.
Operational rule: do not exceed 80% of K on any single channel — diminishing returns dominate; reallocate to next-best channel.
Practical heuristics (when full MMM is not available):
| Signal | Interpretation |
|---|---|
| CPA rising >25% over 4 weeks at flat creative | Saturation approaching |
| Frequency >7 per user / 28 days on social | Audience exhausted |
| Auction win-rate <30% at current bid | Inventory saturation |
| Branded search CTR climbs while non-brand CTR drops | Demand cannibalization |
When any 2 of 4 fire on the same channel, propose reallocation in next planning cycle.
| Strategy | When to use | Risk |
|---|---|---|
| Manual CPC / CPM | Early test, learning phase, brand reach | High oversight cost |
| Maximize clicks | Awareness, top-funnel | Quality variance |
| tCPA (target CPA) | Mature campaign with conversion volume | Needs >=30 conv/wk per ad set |
| tROAS (target ROAS) | DTC, value-known | Volatile if value signal noisy |
| Value-based / max conversion value | DTC, varied AOV | Requires server-side value upload |
| Max conversions (no target) | Volume-first, when CPA tolerance wide | Spend volatility |
Below the floor, fall back to manual or max-conversions and revisit weekly.
media-buyer-bidder requires these inputs to run the channel-mix solver:
solver_inputs:
budget_usd: 100000
horizon_weeks: 6
objective: "maximize_kpi" # or maximize_kpi_capped_cpa
kpi: "qualified_leads"
cap:
cpa_usd_max: 250 # guardrail
channels:
- id: meta_paid_social
response_K: 400 # max leads achievable
response_k: 25000 # half-saturation spend
response_alpha: 1.3
min_spend: 5000
max_spend: 50000
- id: google_search
response_K: 250
response_k: 15000
response_alpha: 1.0
min_spend: 8000
max_spend: 30000
- id: linkedin_ads
response_K: 180
response_k: 20000
response_alpha: 1.1
min_spend: 0
max_spend: 25000
- id: youtube_video
response_K: 220
response_k: 35000
response_alpha: 1.5
min_spend: 0
max_spend: 30000
audience_overlap_matrix: <CxC overlap %>
attribution_coefficients: <from latest MMM>
Using the inputs above and a numerical solver (scipy.optimize.minimize with SLSQP):
| Channel | Allocated $ | Predicted leads | Predicted CPA |
|---|---|---|---|
| Meta paid social | $42,000 | 251 | $167 |
| Google search | $26,000 | 174 | $149 |
| LinkedIn ads | $18,000 | 88 | $205 |
| YouTube video | $14,000 | 75 | $187 |
| Total | $100,000 | 588 | $170 |
Notes on solution:
If business adds $25k mid-flight: solver reallocates marginal $ to whichever channel has highest df/dx at current solution — typically Meta or YouTube (S-curve channels).
| Strategy | Pacing curve | When |
|---|---|---|
| Level | Uniform daily spend | Always-on, mature campaign |
| Front-load | Heavy weeks 1-2 | New product launch, time-sensitive promo |
| Accelerate-to-end | Heavy weeks N-1, N | Tentpole (Black Friday), event-driven |
| Pulse | On / off weeks | Brand-build with paid-search always-on |
| Adaptive | Based on weekly performance | Mature campaigns with weekly review |
Default: level pacing with 10% reserve for in-flight reallocation.
The budget-cap gate fires when:
| Condition | Action |
|---|---|
| Proposed spend exceeds approved cap by >=5% | Fail + HITL |
| Pacing trajectory will exceed cap before flight-end | Auto-throttle + warn |
| Reallocation shifts >25% of budget between channels mid-flight | HITL (re-approval) |
| New channel added with >10% of total budget | HITL (re-approval) |
| CPA guardrail breached for 2 consecutive weeks | Pause channel + HITL |
Verdict schema follows brand-safety skill's verdict structure with gate_id: "budget-cap".
media-buyer-bidder produces:
output/campaigns/<id>/media-plan.md — channel allocation + pacingoutput/campaigns/<id>/measurement/weekly-pacing.md — actuals vs planoutput/campaigns/<id>/measurement/reallocation-proposals.md — when triggeredmarketing-attribution)marketing-attribution (response curves, MMM coefficients)experimentation-design (calibration via geo-lift)campaign-playbook (channel-mix starting defaults per profile)Five named aesthetic bundles (Ethereal Glass, Editorial Luxury, Soft Structuralism, Minimalist Editorial, Industrial Brutalist) with surface / typography / motion / texture specs and a profile-to-archetype decision matrix.
Canonical CreativeBrief markdown + JSON schema, aligned 1:1 with Hydra CreativeBrief envelope. Sections cover vision, references, aesthetic, technical approach, key shots/messages, production, guardrails, approvals.
HITL gate catalog, audit-log shape, DecisionRecord schema, three-lines-of-defense mapping, v1 gate IDs (brand-consistency, regulated-claims-review, budget-cap, attribution-soundness, ip-clearance).
Audience segmentation toolkit — RFM, behavioral cohorts, JTBD, ICP for B2B, CDP/CRM integration patterns, persona archetype templates.
Brand safety and regulated-claims rulebook — toxicity/bias categories, FDA/FTC/FCA/GDPR rules, prohibited-content registry, brand-guideline enforcement, HITL escalation matrix, verdict schema.
Six industry-specific campaign playbooks — funnel stages, KPI targets, channel mix, cadence, critical gates, failure modes, blueprint examples.