Treatment Cost
Treatment cost is what it takes to apply an intervention to one unit: sending one email, serving one impression, honoring one discount, administering one course of a drug. Multiplied by the number of units treated it becomes the campaign’s total cost, and set against the campaign’s effect it turns a measurement into a decision.
Radcliffe and Surry use it exactly that way. Taking the cost of treating each 1 percent of a population as \$1,000 and the contribution from each incremental sale as \$150, they convert an evaluation chart into a profit chart and read the best volume off it: “Given cost and value information, we can determine the optimal cutoff for each model and choose the one that leads to the highest predicted campaign profit.” On their figures one model peaks at 40 percent volume with 680 incremental sales and about \$62,000 of profit, and another at 60 percent with 870 sales and about \$70,500.
What the cost includes
The invoice is the easy part and usually the smaller part.
| Component | Example | Where it shows up |
|---|---|---|
| Cost per contact | \$2 of postage, list rental and production | On the invoice, scaling with volume |
| Fixed cost of running it | Creative, build, analysis time | On the invoice, not scaling with volume |
| Margin surrendered | A 20 percent discount taken by customers who would have bought at full price | Nowhere, until someone computes it |
| Value destroyed | Customers whose response to the treatment is negative | Already inside a net uplift estimate, which is a difference of group means and nets negative responders against positive ones. Add it as a cost only if the effect figure you are using excludes it, or it is counted twice |
The third row is the one Radcliffe and Surry single out. A customer who has already decided to buy receives a coupon and uses it, so the campaign has both spent the contact cost and reduced the revenue it would have collected anyway — “not only were marketing costs increased by including the customer, but incremental revenue was reduced—from some perspectives, almost the worst possible outcome”. The fourth row is worse still, because a treatment that suppresses a purchase costs the whole sale rather than the discount on it, and nothing in an attribution report will show it.
Both are reasons the cost side and the effect side cannot be estimated separately and then bolted together. A discount’s cost depends on who takes it, which depends on who was targeted, which is the thing being decided.
The rule it feeds
Treat a customer when the value their treatment is expected to create exceeds the cost of treating them. With \(s\) for the predicted uplift score, \(v\) for the contribution a conversion carries and \(c\) for the cost per contact, the rule is \(s \cdot v > c\), which rearranges to a threshold on the score itself, \(s > c/v\).
That rearrangement has a consequence worth stating plainly: the rule uses the predicted values, not their order. Most uplift evaluation measures only the ranking — the Qini coefficient and AUUC both throw the values away after sorting — so a model can rank perfectly and still put the threshold in the wrong place if its predictions are systematically too large or too small. Radcliffe and Surry draw the same line: a rank-based measure is enough when a fixed volume is to be treated, but “for some purposes, however, calibration matters, especially when picking cut-off points”.
A worked calculation
The figures are illustrative, and the accounting boundary is fixed first so that nothing is counted twice. A retailer mails 2,000 customers at \$5 each in postage, production and list rental — an outlay that leaves the business whatever the customer does, and one that is nowhere in the revenue figures. The campaign produces \$15,000 of incremental revenue at a 40 percent contribution margin.
There is deliberately no coupon in this example. A discount is the awkward case: it reduces the revenue the business records, so a revenue figure taken from the sales system already carries it, and subtracting it again as a cost double-counts. If a discount is to appear on the cost line, the revenue has to be measured at list price, and only actual redemptions count — mailing 2,000 coupons does not by itself surrender 2,000 discounts.
| Line | Value |
|---|---|
| Total treatment cost, 2,000 × \$5 in postage and production | \$10,000 |
| Incremental revenue | \$15,000 |
| Incremental contribution, at 40 percent | \$6,000 |
| Net | -\$4,000 |
Subtracting the cost from the revenue would have reported a \$5,000 gain. Subtracting it from the contribution reports a \$4,000 loss, and that is the number the decision needs, because the \$15,000 of revenue arrived with \$9,000 of cost of goods attached. The same correction applies to the return figure: dividing net contribution by spend gives -0.4 here, where dividing net revenue by spend would have claimed +0.5.
Cost per contact and cost in total
Whether a cost scales with volume decides how it enters the choice of depth. A per-contact cost raises the threshold every customer must clear, so it shifts the profitable cut-off up the ranking. A fixed cost does not change which customers are worth treating; it only decides whether the campaign is worth running at all. Mixing the two into a single average cost per customer blurs a distinction the decision depends on, because the average falls as volume rises and makes deep targeting look better than it is.
Where the cost sits relative to the effect is the subject of revenue net of treatment cost, and how the effect itself is estimated — with an interval that is usually far wider than any uncertainty in the cost — is covered under incremental revenue and total incremental benefit.
References
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