Here's how many folks approach the subject.
Step 1: Review last year's mail and holdout results. Let's assume you had a holdout group of 100,000 (yup, I said a big number like 100,000 ... if your customer buy more than three times a year, you'll end up needing a big holdout group). Compare performance between the mailed group and the holdout group.
- Mailed Group: Total = $15.00. Retail = $9.00, Online = $4.00, Phone = $2.00.
- Control Group: Total = $12.00. Retail = $7.00, Online = $3.00, Phone = $2.00.
- Incremental Lift: Total = $3.00. Retail = $2.00, Online = $1.00, Phone = $0.00.
- Fractional Change = $15.00 / $12.00 = 1.25.
Step 2: Apply the fractional change to each segment. Now, you're likely to have a half dozen statisticians tell you the twenty-nine assumptions you're violating. And they're right. But we're not managing clinical trials for Vioxx, are we? No, we're dealing with something less serious. So, we jump into Excel, and we look at what each segment is expected to spend during the three weeks this retail catalog is active. Once we have the estimate, we apply the fractional change to each segment. Then, we subtract the difference, yielding our expectation for the mailing.
- Segment 1 Expected Spend = $20.00.
- Fractional Change = $20.00 * 1.25 = $25.00.
- Expected Catalog Performance = $25.00 - $20.00 = $5.00.
- Segment 2 Expected Spend = $12.00.
- Fractional Change = $12.00 * 1.25 = $15.00.
- Expected Catalog Performance = $15.00 - $12.00 = $3.00.
- Segment 3 Expected Spend = $4.00.
- Fractional Change = $4.00 * 1.25 = $5.00.
- Expected Catalog Performance = $5.00 - $4.00 = $1.00.
Step 3: Run a profit and loss statement against each segment. Depending upon the cost of the catalog, and your flow-through rate from sales to profit, it is likely that only segment one, and maybe segment two, will be profitable.
Step 4: Apply your file forecast to each segment. Multiply performance by file counts. Now, you have a sales and profit forecast for your retail catalog!
Step 5: You can use the relationships in Step 1 to allocate expected sales by channel.
Again, statisticians will have your hide for using such a sloppy sales forecasting process. They'll criticize your assumption that each segment performs at the same level of fractional change. If you and your statistician disagree, go ahead and test within individual segments --- though my experience suggests this strategy isn't fruitful.