A Sold-Out Shoe Size Can Make Demand Look Smaller Than It Is

A shoe size can be popular and still look weak in a sales report.

Imagine that size 250 sells out on Tuesday. From Wednesday onward, the system records no more sales for that size—not because shoppers stopped wanting it, but because there was nothing left to buy. By Friday, a size that remained available all week may show a higher unit count. Comparing those totals at face value can lead a team to order too little of the fast-selling size again.

This is the central problem of censored demand: once inventory constrains a purchase, observed sales no longer reveal the full demand that might have existed.

Recorded sales are not the same as demand

A useful mental model is simple:

Observed sales = the smaller of latent demand and available inventory.

When inventory is sufficient, sales can be a reasonable proxy for demand. When a size stocks out, sales are capped. The missing portion is not automatically recoverable from the sales ledger.

That does not mean a team should invent a lost-sales number. It means the availability history must travel with the sales history. Without the time each size was actually buyable, the data cannot distinguish “nobody wanted it” from “nobody could buy it.”

This timeline is conceptual. It does not estimate how many purchases were lost.

What happens after the stockout?

A shopper who cannot buy the preferred size may leave, wait for a restock, try a neighboring size, switch to another color or model, or buy from another retailer. Those outcomes matter because they have different implications for assortment planning.

A neighboring-size purchase, for example, is not proof that the substitute was the shopper’s true preference. It may be a constrained choice. A return after substitution may add another signal, but it still does not reveal every shopper who left without ordering.

The discipline is to preserve the uncertainty. A strong analysis asks which behaviors are directly observed, which are inferred, and which remain unknown.

Size-level analysis should compare like-for-like products while keeping measurement, availability and purchase events distinct.

Four signals that should not be collapsed into one

For footwear, a more useful size-level dataset keeps at least four categories separate:

• Recorded sales: completed purchases by product, size, time and channel.

• Availability: when each size was in stock, low in stock or unavailable—and whether the page or store still exposed the option.

• Size intent: product views, size selections, measurement or recommendation interactions, and other consented signals that may indicate interest.

• Outcomes after constraint: substitutions, wait-list actions, restocks, cancellations and returns.

These signals are not interchangeable. A recommendation event is not a purchase order. A page view is not a unit of demand. A return may reflect fit, product expectations, delivery or another reason. The value comes from testing whether carefully defined signals improve a planning decision—not from renaming every interaction “demand.”

What the research contributes

Operations research has studied ordering decisions when demand observations are censored. Sachs and Minner describe how demand beyond available supply cannot be recorded and examine how stockout timing can help infer unsatisfied demand. Jain, Rudi and Wang likewise show why stockout timing contains important information for demand estimation under censoring.

More recent work such as FreshRetailNet-50K provides a stockout-annotated dataset for fresh retail forecasting. It is not a footwear study, so its results should not be transferred directly. Its relevance here is methodological: models need explicit availability information when stockouts make observed demand incomplete.

The shared lesson is practical. A weekly sales total without size-level availability history is not enough to identify latent demand.

A testable footwear workflow

A responsible pilot should be designed around a decision and a future validation period.

1. Choose a narrow scope. Start with a defined category, channel and set of models where size-level stock status is reliable.

2. Create an event dictionary. Define a recommendation, size selection, stockout, substitution and return before analyzing them.

3. Match the right entities. Product, color, market, gender and size system must align. Poor SKU or size normalization can create false patterns.

4. Preserve privacy and consent. Use only permitted data, aggregate where appropriate and limit access to what the test requires.

5. Establish a baseline. Compare any additional signal against the current sales-and-inventory planning method.

6. Validate forward. Evaluate the next decision period under known availability instead of declaring success from a retrospective fit alone.

7. Document human overrides. Merchandising context—launch timing, distribution, promotion and lifecycle—still matters.

The output should be a measurable recommendation with confidence and limitations, not a black-box forecast presented as certainty.

An empty shelf is evidence about availability. It is not, by itself, a complete count of unmet demand.

Where Perfitt fits—and where it does not yet

PerfittSize currently uses foot data and product-specific shoe measurements to recommend a size. PerfittOnsite brings measurement and recommendation into an offline environment. These interactions can create fit-related signals when the appropriate consent, governance and product matching are in place.

Using aggregated fit signals to improve size-level assortment planning is a direction for PerfittMerchandiser to test through pilots and the product roadmap. It is not a claim that Perfitt currently provides an end-to-end production-planning system, nor is it proof of a specific customer outcome.

The longer-term 3-Zero Vision—reducing fit-related returns, size-specific inventory loss and overproduction—is an aspiration. Reaching it requires evidence: well-defined data, careful pilots and measured operational decisions.

Questions worth asking before the next buy

• For how long was every size genuinely available?

• Did the shopper see an unavailable size, or was it hidden?

• Can substitution and return behavior be linked without overstating intent?

• Which fit interactions are consented, comparable and sufficiently aggregated?

• What future outcome would prove that an additional signal improved the buy?

If those questions are unanswered, last season’s units may still be useful—but they should not be mistaken for the whole demand picture.

Discuss size-level fit demand intelligence

Perfitt is exploring how fit interactions can complement sales and inventory history in controlled, measurable pilots. If your team is evaluating size-level demand signals, we would be glad to compare assumptions, data requirements and validation plans.

Sources

• Sachs & Minner, “The data-driven newsvendor with censored demand observations”

• Jain, Rudi & Wang, “Demand Estimation and Ordering under Censoring: Stock-out Timing Is (Almost) All You Need”

• FreshRetailNet-50K: A Stockout-Annotated Censored Demand Dataset