Diminishing Returns, The Square Root Rule, and Page Counts

One of the least understood issues in cataloging is knowing how many pages to have in each catalog. Let's apply the square root rule to this concept.

Assume that last year you mailed a 100 page catalog to 1,000,000 customers, generating $5,000,000 demand via phone, mail and website. Demand was converted to profit at a rate of 35%, and the catalog cost $800,000 to mail. Profit = $5,000,000 * 0.35 - $800,000 = $950,000. Mmmmm .... profit!

The table below simulates what might have happened at different page counts.

Circulation = 1,000,000 Customers
	Square
Pages	Root	Demand	Profit
60	0.775	$3,872,983	$875,544
80	0.894	$4,472,136	$925,248
100	1.000	$5,000,000	$950,000
120	1.095	$5,477,226	$957,029
140	1.183	$5,916,080	$950,628

If you're wondering, the square root function is calculated as (simulated pages / actual pages) ^ 0.5. At 60 pages, the value is 0.775.

Notice that peak profit occurs at a simulated page count of 120. If enough merchandise is available, at an appropriate presentation density, your page count could increase.

Folks, this stuff is about to become really important. In a few years, the ecological pressures (i.e. cutting down too many trees) on catalogers will be significant enough that intimate knowledge of appropriate page counts will have to be standard knowledge.

As you can see, this isn't rocket science. Combining page counts with circ depth (which can also be simulated in a similar manner), one can develop a circ plan for a catalog in about ninety seconds. An entire year's worth of catalogs can be "simulated" in a half our or an hour. Historically, our industry chose not to take the "simulation" route in figuring out how to configure a catalog.

Of course, you'll want to do the real work required to manage a circulation plan, including file forecasting, housefile vs. acquisition, and RFM profitability. But this is where your work starts.

Next up: A worksheet for combining circ depth and page count.

Diminishing Returns, The Square Root Rule and Peak Profit

We've previously talked about diminishing returns in marketing.

Understanding how diminishing returns impact profit is something that anybody can do.

You don't have to be accountable for paid search or online marketing or catalog marketing to understand how effective your strategy is at a macro level.

And the level of science is irrelevant. Most statisticians would become paralyzed by all of the assumptions being violated here. You're not trying to be a perfect statistician. You're trying to approximately understand where marketing spend is optimized.

Here's Example #1:

• Your paid search marketing budget is forecast to be $1,000,000 this year. You also expect to generate $4,000,000 demand. You convert demand to profit at a rate of 40%.

• Profit = $4,000,000 * 0.40 - $1,000,000 = $600,000.

• Using the square root rule, we can measure where "peak profit" occurs.

	Square
Spend Levels	Root	Demand	Profit
$500,000	0.707	$2,828,427	$631,371
$600,000	0.775	$3,098,387	$639,355
$700,000	0.837	$3,346,640	$638,656
$800,000	0.894	$3,577,709	$631,084
$900,000	0.949	$3,794,733	$617,893
$1,000,000	1.000	$4,000,000	$600,000
$1,100,000	1.049	$4,195,235	$578,094
$1,200,000	1.095	$4,381,780	$552,712
$1,300,000	1.140	$4,560,702	$524,281
$1,400,000	1.183	$4,732,864	$493,146
$1,500,000	1.225	$4,898,979	$459,592

Here's where you have a series of choices. You are generating $600,000 of profit at $1,000,000 of paid search spend. However, "peak profit" occurs at $600,000 of spend. If you want to achieve better profitability, you spend $400,000 less, and give up nearly a million dollars of demand.

Folks who measure lifetime value combine short-term and long-term profit, and probably end up spending more than a million dollars based on those findings. Notice how diminishing returns occur, especially after a million dollars of spend.

Also notice how few online marketers measure anything beyond "cost per order" --- there's an opportunity for online marketers to improve their "tool box" with this style of analysis.


Example #2:

• You spend $40,000,000 on catalog marketing. Although your productivity has been in decline for several years, your catalogs are still profitable. You generate $170,000,000 of demand across channels, with 40% converted to profit.

• Where does "peak profit" occur?

	Square
Spend Levels	Root	Demand	Profit
$20,000,000	0.707	$120,208,153	$28,083,261
$24,000,000	0.775	$131,681,434	$28,672,574
$28,000,000	0.837	$142,232,205	$28,892,882
$32,000,000	0.894	$152,052,622	$28,821,049
$36,000,000	0.949	$161,276,161	$28,510,464
$40,000,000	1.000	$170,000,000	$28,000,000
$44,000,000	1.049	$178,297,504	$27,319,002
$48,000,000	1.095	$186,225,670	$26,490,268
$52,000,000	1.140	$193,829,822	$25,531,929
$56,000,000	1.183	$201,146,713	$24,458,685
$60,000,000	1.225	$208,206,628	$23,282,651

Here, we see that "peak profit" occurs at $28,000,000 of catalog spend. However, the amount of profit difference between $28,000,000 of spend and $40,000,000 of spend is not significant. Most marketers would err on the side of spending more, in this instance, due to the obvious benefits of growing the customer file.

Again, you don't have to be responsible for online marketing, catalog marketing, or e-mail marketing to do this type of analysis. Take the initiative to get your hands on some data, partner with your finance team if necessary, and analyze where "peak profit" occurs in your marketing efforts. Find out where diminishing returns take a bite out of profit.