Diffuser Methodology Sensitivity

1. Background

The Fall 2026 production forecast covers the 114-day window from August 14 through December 5. The forecast engine generates unit demand by fragrance and package format using a five-layer pipeline. The first three layers are calibrated against multi-year history; the fourth — diffuser overlay — is a recently-added treatment with no historical analog because diffusers are a new product. The question this report answers is how that fourth layer should behave, and what is at stake.

Definitions used throughout: Decay rate — the year-over-year percentage change in unit demand for a fragrance at the same point in its lifecycle (e.g., second-year vs. first-year). A negative number means demand is contracting. Elasticity weight — a multiplier applied to a fragrance's demand based on its age tier; intended to reflect that newer fragrances accelerate faster than mature ones. Cannibalization — when a new product captures demand that would otherwise have gone to an existing product, rather than adding incremental demand. Overlay — adding new-product units on top of the existing forecast. In-distribution — placing new-product units inside the existing forecast (no new total, the mix shifts). Hybrid — splitting the new-product demand between the two treatments.

2. Decomposition: how the headline growth is built up

Two fragrances dominate the question. Flannel + Leaves (F+L) is in its first year of repeat (Y1→Y2). Autumn Heirloom (AH) is in its second-to-third year (Y2→Y3). Both anchor decay rates were re-derived this week using a same-lifecycle proxy methodology and the narrowed Aug 14 – Dec 5 window. The re-anchored rates are F+L +4.79% and AH −6.85%. Yet the workbook reports F+L at +115.3% and AH at +36.1% growth on the prior year. The gap is explained by three additional multiplicative layers stacked on top of the decay rate.

The mechanical reading: of the F+L +115% headline, only roughly 5 percentage points are attributable to the empirical decay rate (a same-lifecycle Y1→Y2 behavior anchored on Autumn Heirloom's own Y1→Y2 history). The rest comes from two assumption-heavy layers — the age-tier elasticity weight (1.5× for Y2 fragrances), and the diffuser overlay (a second category of inventory layered additively on top of fragrance). Of those two, the diffuser overlay is the younger and the more easily switched.

3. Sensitivity to the two free knobs

If the Flannel + Leaves elasticity weight or the diffuser multiplier were calibrated differently, the headline growth changes substantially. The grid below shows the F+L total under a 5×4 sweep of the two free knobs. The current production setting is highlighted.

Two observations. First, the diffuser knob alone moves F+L by roughly 2,400 units between off and on at current settings — meaningful but not the dominant driver. Second, the elasticity weight knob moves F+L by roughly 7,300 units between 0.9 and 1.5 — the larger lever. This report focuses on the diffuser knob because diffusers are new product with no in-lake history, while the elasticity weights are an open calibration item under separate review.

4. Three methodology choices

Three internally-consistent treatments of diffuser demand are available without further data collection.

Approach A — Overlay (current production setting)

Diffuser units are added on top of the fragrance forecast, with diffuser volume mirroring the Car Freshener slot one-for-one. The implicit assumption is that diffusers expand the category — every diffuser sold represents a household that would not otherwise have bought a Grow product. Risk: if even part of the diffuser demand is in fact substitution for Car Freshener (or for the 5 oz spray), the lineup over-produces.

Approach B — In-distribution

Diffuser units are inserted into the existing fragrance forecast, with the total held constant — diffusers take volume from the other formats inside the fragrance lane. The implicit assumption is full cannibalization: diffusers are a form-factor switch for an existing buyer. Risk: if diffusers do drive net new demand, the lineup under-produces.

Approach C — Hybrid (50/50)

Diffuser demand is treated as 50% incremental and 50% in-distribution. Half the diffuser units add to the total; the other half pull volume from existing formats. This is a deliberate hedge between the two extreme assumptions. It is the most defensible setting in the absence of category-level demand evidence (SKU-level lift studies, search query incrementality, retailer reorder behavior), because it carries no claim about which extreme is true.

5. Production cost comparison

The choice of methodology has direct production-cost implications. To size the difference, the table below applies current bill-of-materials cost estimates to each approach. Diffuser unit cost is a placeholder; the methodology decision can be evaluated under a sensitivity range to confirm that the conclusion is not driven by that single estimate.

The cost gap is approximately $14,866 — Approach A commits the business to roughly that amount of additional production cost compared with Approach C. A useful sensitivity check: if the diffuser unit cost is in fact $11 rather than $7.36, the gap rises to approximately $18,000. If diffuser unit cost were $5, the gap is approximately $11,500. The methodology decision matters at the $11K–$18K level under any reasonable cost assumption — not at the $50K level, but not negligible.

6. Risk asymmetry

The three approaches do not carry equal cost-of-being-wrong. Approach A overcommits production if diffusers cannibalize. Approach B undercommits production if diffusers expand the category. Both errors are real; they are not symmetric.

The asymmetric piece: a leftover diffuser unit at year-end carries write-off risk (raw material, finished-goods labor, warehousing). A stocked-out diffuser unit at year-end represents lost revenue at full margin, plus the soft cost of disappointing a high-intent customer who searched for diffusers and found nothing. At a first approximation, the cost of one unit overproduced is roughly the BOM unit cost (≈$7); the cost of one unit unmet at the peak is roughly the lost margin (≈$15–20 for a Grow direct-channel sale). The asymmetry favors slight overproduction over slight underproduction — but only slightly, and only against a backdrop of historical sell-through.

The hybrid approach minimizes the maximum regret. If diffusers turn out to be fully cannibalizing, the hybrid is over by 1,000 units rather than 2,000. If diffusers turn out to be fully incremental, the hybrid is under by 1,000 units rather than 2,000. The hybrid keeps the worst-case error half the size of the worst case under either pure assumption.

7. Recommendation

Adopt Approach C — Hybrid 50/50 as the interim diffuser methodology. Document the treatment as: "Diffuser units treated as 50% incremental and 50% in-distribution against Car Freshener volume, in absence of category-level demand evidence." Plan to revisit the assumption when one of the following becomes available: (1) diffuser-specific search-query incrementality data, (2) early sell-in/sell-through data from a launch wave, (3) a controlled SKU-substitution test in the Shopify channel. Until then, the hybrid is the most defensible setting and the cheapest decision to revise.

Implementation: extend the engine's apply_diffuser_overlay() function to support a diffuser_mode switch with values overlay, distribute, and hybrid; default to hybrid. Re-run all three scenarios. Update the workbook and the run summary. The change is mechanical and reversible.

8. Caveats and open assumptions

Several inputs to this analysis remain calibration items:

Diffuser unit cost is a placeholder. No diffuser bill of materials exists in finance_bom_channel. The $7.36 figure used here is the F+L Car Freshener unit cost, applied as a proxy. Real diffuser cost will differ — most likely upward, given the housing component. If diffuser cost is $11 instead of $7.36, the production-cost gap between A and C widens to approximately $18,000. The directional finding (A > C) is robust to that range.

3-Wick Candle cost is estimated. Treated at $14.50 across all three fragrances based on category average. Once Nikita's BOM extends to the 3-Wick SKUs, this will firm up.

Elasticity weights have never been backtested. The Y2 weight of 1.5 is the dominant lever in F+L's growth trajectory. Whether 1.5 is the right number is an open assumption flagged separately in the open-items list. This report holds elasticity weight constant at 1.5 to isolate the diffuser question.

The +4.79% F+L decay rate uses Autumn Heirloom Y1→Y2 as the proxy. F+L's first-year volume (9,725) was approximately 13% larger than AH's first-year volume (8,603). If the F+L launch reflects breakout-fatigue dynamics that AH did not, the +4.79% may understate Y2 regression to the mean. This is an open assumption affecting all three approaches equally — methodology choice does not depend on it.

The diffuser overlay rule that mirrors Car Freshener is itself an assumption. Diffuser demand could plausibly be more like the 5 oz spray slot (longer-duration purchase) than the Car Freshener slot (multi-pack impulse). The overlay rule was set at the request of leadership on 2026-04-21; this report does not relitigate that choice, but flags that the mirror could be re-anchored to a different format if data warrants.

9. Methodology appendix

9.1 Source data and queries

All unit costs were pulled from the finance_bom_channel parquet table on 2026-04-27. The relevant query is:

SELECT fragrance, format, package_size,
       rm_cost, labor_cost, total_unit_cost
FROM   read_parquet('data/parquet/finance_bom_channel.parquet')
WHERE  fragrance IN ('Flannel + Leaves','Autumn Heirloom','Ginger Pumpkin')
  AND  status = 'active'
ORDER BY fragrance, format;

The five-layer engine pipeline is documented in analytics/david/forecast/Fall_2026_Config.md, Sections 3 (rationale) and 5 (decay overrides). The diffuser overlay logic lives in forecasting/forecast_engine.py, apply_diffuser_overlay().

9.2 How the three approaches were computed

Approach A is the production engine output, post-diffuser overlay. Approach B was computed by setting diffuser_multiplier = 0 in the engine config and re-running the base scenario; the resulting grand total is 34,711. Approach C is the arithmetic midpoint between A and B per fragrance. Because the diffuser overlay is a simple additive layer, the midpoint of "fully additive" and "zero diffuser overlay" is mathematically equivalent to applying half of the additive overlay — both expressions of the hybrid yield the same per-fragrance numbers (F+L 19,728; AH 11,449).

9.3 Reconciliation note

The grand totals reconcile to the workbook (Grow_Fall2026_Forecast_v2.xlsx, build 2026-04-27 16:38) and to the forecast run summary (forecast_run_summary_20260427.md). Bear/Base/Bull post-diffuser totals in the engine are 37,340 / 38,791 / 40,240 — the figures in this report draw from the base scenario.

9.4 Window

All forecasts are over the Fall 2026 sell-through window of August 14 through December 5, 2026 (114 days). This is the realistic Fall sell-through cutoff, narrower than the original December 31 fiscal-close window. The narrower window reduces all forecast totals proportionally; the methodology choice does not interact with the window.