### 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.