BOGO Margin Math: When Unit Two Loses

A buy one get one free offer has a bogo profit margin on paper and a different one in your bank account, and the gap between them is one question: how many of the shoppers who take the offer would have bought a single unit at full price anyway? Every one of them costs you the free unit and adds nothing. Margin-per-pair tables, including the ones in BOGO vs 50% Off the Second Item, price the pair itself and do not ask whether the shopper would have bought anyway. This post adds the missing term, derives the break-even share step by step, gives a lookup table you can read by gross margin, and shows how to estimate that share from your own order history. All prices and shares below are assumptions chosen to show the method; replace them with your own cost per unit and your own orders.

Three kinds of shoppers take a BOGO

Say a product sells for price P and costs you c per unit, so the gross margin is m = (P − c) ÷ P. A shopper who takes the offer pays P and leaves with two units, so the pair costs you 2c. Profit on that order is P − 2c, which is P × (2m − 1). Everything else in this post follows from who that shopper was before the offer:

• A new order. This shopper would not have bought at all. You earn P × (2m − 1), which is positive only above a 50 percent margin.
• A single-unit order that was coming anyway. This shopper would have paid P for one unit and earned you P − c. Under the offer you earn P − 2c. The difference is exactly c: you gave away one unit at cost for nothing.
• A two-unit order that was coming anyway. This shopper would have paid 2P for two units. Under the offer they pay P. You lose a full P of revenue.

The second kind is the group this post isolates, so the main derivation uses two groups only: a share s who would have bought one unit anyway, and a share 1 − s who are new.

The break-even share, derived

Take 100 BOGO orders. Profit with the offer is 100 × P × (2m − 1). Without the offer, only the s share would have ordered, each earning P × m, so the counterfactual profit is 100 × s × P × m. The offer pays for itself when:

(2m − 1) ≥ s × m

Divide both sides by m:

s ≤ (2m − 1) ÷ m = 2 − 1 ÷ m

Check it with money. Assume a 40 dollar product with a 60 percent gross margin, so c = 16 dollars. A BOGO order earns 40 − 32 = 8 dollars. A shopper who would have bought one unit anyway earned you 24 dollars, so the offer cost you 16 dollars on that order. If one third of BOGO orders are of that kind, 33 orders lose 16 dollars each (528 dollars) while 67 new orders earn 8 dollars each (536 dollars). That nets about zero, and the formula says the break-even share at a 60 percent margin is 2 − 1 ÷ 0.6, or 33.3 percent. The two views agree.

The same condition can be read as a ratio: you need (1 − m) ÷ (2m − 1) new orders for every order that was coming anyway. At a 60 percent margin that is 0.4 ÷ 0.2, or 2 new BOGO orders per cannibalized one.

Below a 50 percent margin the pair itself loses money, so no mix of shoppers rescues the offer. At exactly 50 percent the pair earns nothing and any shopper who would have bought anyway makes it worse.

Lookup table: gross margin against cannibalized share

The table shows the change in profit per BOGO order, in dollars, on a 40 dollar product, for four margins and four cannibalized shares (s). Each cell is 40 × (2m − 1 − s × m). A negative number means the offer earns less than not running it.

Read the 60 percent row. If a fifth of your BOGO takers were coming anyway, every 100 orders add 320 dollars. If two fifths were, the same 100 orders lose 160 dollars. The offer did not change; the shoppers did. Shipping, packaging, payment fees and returns come out of these figures too, and a BOGO order ships two units, so check your own parcel cost before you trust a cell near zero.

Reading the share from your own orders

You cannot read s directly from a report, but your order history gives a ceiling to start from. Shopify's Help Center says that in an order export, additional line items appear on separate rows, and that exports of more than 50 orders, or by date, are emailed rather than downloaded. Run it for the last 90 days and count three numbers for the product you want to put on offer:

1. Orders containing the product.
2. Of those, orders where the quantity is one.
3. Of those, orders where the quantity is two or more.

If 70 percent of your recent orders for the product were single units at full price, most people who see a BOGO banner on it are people who were going to pay for one unit. That share is a prior, not a measurement: some of those shoppers would not have come back for it, and some new shoppers arrive because of the offer. A holdout test or a matched-weeks comparison gives the real number, and how to measure promotion results shows how to run one.

The third group matters if your catalog sells in pairs. Take the 60 percent margin product again, with 50 percent new orders, 30 percent single-unit orders and 20 percent shoppers who would have bought two. Per 100 orders, new orders add 50 × 8 = 400 dollars. Single-unit shoppers cost 30 × 16 = 480 dollars. Two-unit shoppers cost 20 × 40 = 800 dollars. The offer loses 880 dollars per 100 orders, even though half the shoppers are new.

Stock depth when every order ships two units

A BOGO doubles the units an order carries, so the reorder point changes before the sales do. Assume a product that moves 40 single-unit orders a week, a four-week lead time and one week of safety stock. The reorder point at the current pace is 40 × 5 = 200 units. If every one of those orders becomes a BOGO order, the same count of orders takes 80 units a week and the reorder point is 400. If the offer also lifts orders by half, it is 120 units a week and a reorder point of 600. Run the arithmetic with your own lead time before you schedule the offer, and set the end date to the stock you actually hold.

Setting it up with a per-order limit

Shopify's Buy X get Y discount lets you set the maximum number of times the offer applies to each order, and its Help Center says customers must add all items to their cart manually. For automatic discounts with the same product in both the buy and the get sections, the Help Center says the lower-priced item the customer chooses is the one discounted. A limit of one per order stops a shopper from getting six free units for twelve, and how to limit a BOGO per customer covers repeat use across orders. If you prefer to compare the offer with a three-unit version first, Buy 2 Get 1 Free vs 3 for 2 works through that case.

The app's Buy one, get one (BOGO) template is described as "Buy a product, get another copy free." Pick one product whose margin clears the table, set a limit of one use per order, schedule an end date tied to your stock, and compare orders and profit per order with the weeks before.