Should we always account for all sales?
One thorny problem in multi-channel retail is the attribution of sales to one of several marketing programs. Imagine a retailer which uses infomercials and 800 numbers, an e-commerce page on the corporate site and an integrated online campaign. To keep the example simple, the productivity of each medium is the ratio of revenue to costs. The 800 number and on-line campaign are arguably easier to account for; but the e-commerce site has no good way of tracking back to spending -- just where was the impetus to purchase generated? Ultimately the business question is: Which medium is more efficient or productive in terms of generating sales?
A common approach is to assign the mystery sales to a channel based on some sort of allocation. Examples of the basis for such analysis include a) dollars spent, b) dollars received, or c) an arbitrary/benchmark/standard figure.
If the goal of the exercise is to understand the efficiency of different media, then the allocation should be excluded from the analysis. Any conclusion which includes such allocations is going to be distorted based on the assumptions about how to divide the unaccounted sales.
Two common analytic problems exist: 1) When using a productivity measure that is based on the ratio of revenue to costs then the 'law of large numbers' makes it harder to prove that the 800 pound guerilla is better than the 90-pound weakling because of the big denominator; 2) When allocating from the top down, the problem is one of algebra not of productivity. By definition there is one allocation figure at which the efficiency of the two media is equivalent making it possible to game the analysis and prove a desired conclusion.
In sum, if the question is about productivity and efficiency then avoid the allocation step altogether and keep it apples to apples.