How do I decide how deep to mail a scored list?

Mail each decile whose response rate is above the break-even rate, the cost per piece divided by what a responder is worth, and stop at the first decile below it. In the default example the break-even rate is about 0.17%, so the top seven deciles are mailed and the bottom three, which respond below it, are not.

What is top-decile lift?

How many times the list average the best-scored tenth of households responds. A lift of 1× means the scores do not separate households at all, so every decile looks alike and the depth decision is all or nothing. A stronger model raises the lift, puts more response at the top and makes it worth stopping sooner.

Why not mail everyone who might respond?

Low-scored households still respond sometimes, but below break-even each piece costs more than it returns. Stopping at the right decile can earn more than mailing the whole list while mailing fewer pieces; in the default example it earns about $18,000 more with 30% fewer pieces.

Should I use my real decile response rates?

Yes, where you have them. The calculator assumes response falls by the same ratio from decile to decile, which is a simplification. Response by decile from a past drop, ideally with a holdout group that was not mailed, gives the incremental rates the decision should rest on. The default inputs are an illustrative example, not a benchmark.

All frameworks

Mail Depth Calculator

How far down a response-scored prospect list should you mail before the next households cost more than they return?

Enter the size of a scored prospect list, its average response rate, how strongly your response model separates the best households from the rest, and the economics of a piece. The calculator ranks the list into ten deciles and shows how deep to mail. The starting values are an illustrative example, not a benchmark.

Households scored200,000Average response rate across the list0.50%Top-decile lift (best tenth vs list average)3.0×All-in cost per piece (print, postage, data)$0.75Responders who fund a loan30%Value per funded loan (revenue or margin)$1,500

Mail down to

Decile 7 of 10

Pieces mailed

140,000

Profit at that depth

$317,895

Profit mailing everyone

$300,000

Gain from stopping there

$17,895

Cost per funded loan

$372

Break-even response rate

0.17%

Blue deciles respond above the break-even rate and earn more than they cost; grey ones lose money on every piece. The calculator assumes response falls by the same ratio from each decile to the next; read your own decile response rates from a past drop where you have them. Enter margin per funded loan for profit you keep. Every response is counted as caused by the mail; a holdout group that is not mailed shows the incremental part.

How it works

A response model ranks households from most to least likely to respond, but it does not say where to stop. This calculator splits a scored list into ten deciles, estimates each decile's response from the list average and how strongly the model separates the best households, and mails down the list only while a decile responds above the break-even rate. Use it to see how deep to mail, what stopping there earns compared with mailing everyone, and how a stronger model changes the answer.

The list is split into ten equal deciles by response score. The top decile responds at the top-decile lift times the list average, and response falls by the same ratio from each decile to the next, chosen so the ten deciles average out to the list's response rate. Each decile earns its households times (response rate × share of responders who fund × value per funded loan − cost per piece). A decile is worth mailing when its response rate is above the break-even rate, the cost per piece divided by the value of a responder; because response only falls down the list, mailing every decile above break-even is also the depth with the highest total profit. Every response is counted as caused by the mail.

r^{*} = \frac{c}{f\,v}

r_1 = L\,\bar r, \qquad r_i = r_1\,q^{\,i-1}

\pi(d) = \sum_{i=1}^{d} n\,(r_i\,f\,v - c)

d^{*} = \max\{\,i : r_i > r^{*}\,\}

where

$n$: households per decile (list size ÷ 10)
$\bar r$: average response rate across the list
$L$: top-decile lift
$q$: ratio of each decile's response to the one above, set so the ten deciles average to the list response
$r_i$: response rate of decile i
$c,\ f,\ v$: cost per piece, share of responders who fund, value per funded loan
$r^{*},\ d^{*}$: break-even response rate, deepest decile worth mailing

What a real decision adds

Response does not fall smoothly down the list. Real deciles bunch and cross over, especially near the cutoff, so the depth is best set from measured response by decile rather than from a smooth curve.
A response score is not an incremental score. The households most likely to respond include many who would have applied anyway, so the deciles worth mailing are the ones where the mail changes the outcome, which only a holdout shows.
Value differs by household as well as response. A decile that responds less can still be worth mailing if its responders fund larger loans or are more likely to fund, so the cutoff should rest on expected value, not response alone.
Scores drift as the market and the list change. A model trained on last season's drops can rank households in the wrong order today, and the cutoff moves with it.

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Frequently asked questions

How do I decide how deep to mail a scored list?: Mail each decile whose response rate is above the break-even rate, the cost per piece divided by what a responder is worth, and stop at the first decile below it. In the default example the break-even rate is about 0.17%, so the top seven deciles are mailed and the bottom three, which respond below it, are not.
What is top-decile lift?: How many times the list average the best-scored tenth of households responds. A lift of 1× means the scores do not separate households at all, so every decile looks alike and the depth decision is all or nothing. A stronger model raises the lift, puts more response at the top and makes it worth stopping sooner.
Why not mail everyone who might respond?: Low-scored households still respond sometimes, but below break-even each piece costs more than it returns. Stopping at the right decile can earn more than mailing the whole list while mailing fewer pieces; in the default example it earns about $18,000 more with 30% fewer pieces.
Should I use my real decile response rates?: Yes, where you have them. The calculator assumes response falls by the same ratio from decile to decile, which is a simplification. Response by decile from a past drop, ideally with a holdout group that was not mailed, gives the incremental rates the decision should rest on. The default inputs are an illustrative example, not a benchmark.

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