Lost sales are not all demand
If a SKU sells 30 units a day and is out for five days, 150 units of demand pass through the store. Some of that demand is fulfilled by another SKU, some waits, some is backordered and some is lost.
The substitution rate captures everything that is not lost. A 20% substitution rate means 80% of the demand becomes lost orders. Treating 100% of demand as lost overstates the cost; treating none as lost understates it.
The formula
Lost orders = daily demand × stockout days × (1 − substitution rate). Lost contribution = lost orders × contribution per order. Lost revenue = lost orders × average order value.
Daily contribution at risk = daily demand × (1 − substitution rate) × contribution per order. It answers “what does each additional day out of stock cost?” and is useful for deciding whether to expedite a replenishment.
Worked example
Daily demand 30, stockout 5 days, substitution 20%, contribution $15, AOV $60. Lost orders are 30 × 5 × 0.8 = 120. Lost contribution is $1,800 and lost revenue is $7,200. Daily contribution at risk is $360.
The range at 0% substitution is 150 lost orders and $2,250; at 20% it is 120 and $1,800; at 40% it is 90 and $1,350. The entered assumption is the middle of a plausible band, not a precise measurement.
Reading the range
The ±20 point band is a stress test. It shows how much the answer moves when customers are more or less willing to substitute. If the range is wide, invest in better substitution data before treating the midpoint as a budget number.
A high-substitution SKU is less exposed to stockout cost because demand has somewhere else to go. A unique SKU with no substitute sits closer to the low-substitution end.
What is not counted
Brand damage, customer lifetime value loss, expedited freight, support tickets, lost marketplace ranking and future price concessions are excluded. These can be larger than the immediate contribution loss, but they are hard to measure credibly.
The model also assumes demand is stable during the stockout. A launch, promotion or seasonal peak needs its own daily demand assumption.
How to use it
Estimate daily demand from a recent normal week, not from the stockout period itself. Then test a few substitution rates to see the range.
Use the daily risk number to decide whether expedited freight or a transfer is worth paying for. Pair the result with safety stock and reorder point so the next stockout is less likely.