We go back to 1991 for the origin of The Square Root rule.
"Back in the day", catalogers were experimenting with statistical models. At Lands' End, statistical models had been used to decide who received catalog mailings since at least the mid 1980s.
But statistical models can make deciding how much a segment of customers might spend a real headache.
Consider this example.
- A segment has 10,000 customers.
- Only 8,000 customers were selected by the statistical model to receive the mailing.
- The segment of 8,000 customers spent $3.00 per customer, $24,000 total, when mailed the catalog.
It would take nearly seven years to find a simple solution to this problem.
Honestly, one can use "rules of thumb", or statisticians can create unique models for every catalog to solve this problem.
After witnessing the results of maybe 300 catalog mailings over a seven year period of time, a simple solution was created. In 1998 at Eddie Bauer, we developed "The Square Root Rule".
- The 8,000 customers above spent $3.00 per catalog, $24,000 total.
- If 10,000 customers would have been mailed, total spend would increase by the following factor:
- (10,000 / 8,000) ^ 0.5 = 1.25 ^ 0.5 = 1.118.
- In other words, 10,000 customers would have spent $24,000 * 1.118 = $26,832.
- Dollar per catalog for 10,000 customers = $26,832 / 10,000 = $2.68.
- The remaining 2,000 customers would have spent $2,832 / 2,000 = $1.42 each.
The Square Root Rule applies to advertising budgets and page counts and items offered per e-mail campaign ... basically any situation where you have limited information and no good history to estimate what might happen.
Of course, the approximation has numerous limitations. Don't use it to extrapolate too far ... if you only mail 10% of the customers in a segment, the equation might fail. If you want to mail 3x as many customers as were mailed last year, the equation will fail.
But for many instances, this equation solves problems, especially if you have limited data and you don't have a statistician sitting next to you, awaiting your beckon call!