Methodology: how out-of-stock rates were measured

A reading is what a retailer's website reported for one product at one specific store on one day: available or not. Readings were recorded daily at most chains. Nothing finer than a day is measured.

A day is the calendar day in the store's own time zone. A product at a store has one state per day, the last reading that day. Days with no reading have no state and are never filled in.

Counted product-store pairs. A product at a store enters the numbers on a day only if it was reported available there at least once in the previous 60 days. Products a store never carried are left out.

An out-of-stock spell is a run of days in the unavailable state, starting the first unavailable day after an available one. Days out are counted from that first day to the day the item is reported back. Spells still running at the end of the window are counted as unfinished.

A restock is the first available day after a spell, counted only when the item had an available reading before the spell, its first reading was more than 14 days before the spell, and its listing was not edited during the spell. Weekday counts use product-days: one product returning at many stores on one day counts once per product, per retailer, per day.

Nearby available asks, for a product reported unavailable at a store on a day, whether the same retailer reported it available at another store within 5, 10 and 25 miles that day, measured on store coordinates.

Horizons. Question 1 looks 1, 7 and 30 days ahead; question 4 looks at spells ended within 1, 3, 7, 14 and 30 days.

The window is the 90 days ending on the snapshot date. Products first seen inside the window count for question 1 and are left out of spell statistics.

Every number is computed per brand and retailer first, then combined. No brand contributes more than 10% of the pooled total; the excess is down-weighted. Per-brand medians are reported beside pooled rates. Every number carries a 95% range: a Wilson interval for a share, a bootstrap over brands for a median.

Categories are reported only with 5 or more brands.

Brands with more than six months of history, compared with all brands at the same 42 chains, so the comparison measures history length rather than chain mix: 58 brands over 96,301,701 product-store days. Every finding on the study page is shown with this subset beside it, and the table there marks any pair that differs by more than 5 points. A finding is published only if the two agree in direction.

A retailer page is published only when its data clears a bar. The bar is about data, not effort: pages appear on their own once a retailer crosses it, and are never ranked against each other.

No brand may make up more than half of a page's product-store pairs without its permission. Retailers whose availability signal could not be confirmed are excluded. Retailers whose website reports an Instacart catalog are labelled as such and kept out of the headline.