How Does the SPARLINE Model Work?

The SPARLINE model is the most sophisticated and accurate model for calculating a baseline and estimating incremental volume and profit from a trade promotion (the SPARLINE). The SPARline is what you would have sold in the absence of a promotion.  It is an iterative model using over 50 subroutines to calculate the individual impact of different marketing activities.  But the core of the model is the ability to use a multi-variate calculation to quantify the impact of all the marketing variables that impact sales.  The following is how it works.

Consider a simple situation where normal sales (baseline or SPARLINE) are 100.  Note the SPARLINE is a brand name to mean baseline.  Month 1 sales are 100.  In month 2 a promotion is run and sales are 150.  It is clear that the impact of the Promotion on sales is 50.  Mathematically we can show that as:

Sales in Month 1 (S(1)or 100) = Base sales (B).

Sales in Month 2 (S(2) or 150) = Base sales (B) + Incremental sales from the Promotion (P).

or

100 = B

150 = B+P

The SPARLINE (baseline) is 100 and incremental impact of the promotion is 50.

This can also be shown as two matrices to be solved of:

100
150

and

1 0
1 1

Clearly  the incremental impact of the Promotion is 50.

Now let’s add a third month of sales and introduce an extra variable (a coupon or C) and sales in month 3 of 175.

Sales in month 3 (S(3) or 175) = B + P + C

This gives the following equation to solve:

100 = B

150 = B+P

175 = B+P+C

Still fairly easy to solve using paper and pencil, algebra, or matrix algebra which show the baseline is 100, the incremental impact of a Promotion is 50, and the impact of a coupon on top of a Promotion is 25.  Note if you did not take into consideration the impact of the coupon you would average the impact of two promotions over the base and incorrectly conclude that the average impact of a Promotion is 62.5 and not 50.

Let us now use a slightly more complicated situation of 6 months of sales and 2 additional marketing factors of Weather (W) and Competitive Promotions (CP).

100 = B

150 = B+P

175 = B+P+C

200 = B+P+C+W+CP

175 = B+W

150 = B+C+W+CP

75 = B+C+CP

We can now see if we ignore the impact of certain marketing activities we can easily come up with a wrong answer for the incremental impact of a Promotion.  For example, if we ignored the impact of Competition we would come up with a baseline that is too low and overstate the incremental impact of a Promotion.

It can become almost impossible to solve for a real-world situations with years of sales data and numerous factors impacting sales.  The SPARLINE allows for 24 different marketing factors with a Base to be calculated with 60 months of data.  While not limited to 60 months or 24 variables, we have found no noticeable impact on accuracy when using more than 60 months of data and 24 variables.  The SPARLINE model does not pre-select the variables to be used and selects from many more than 24 but the model never uses more than the most impactful 24.  For example weather may be important for products such as beer and soda but have no impact on baby food or toilet tissue.

The actual equations in the SPARLINE model are as follows:

Monthly Sales (I)  (where I = 1 to 60)  = Base + Variable  (I,J) (where J = 1 to 24)

The equations would be:

Sales in month 1 = Base + Variable  (1,1) + Variable (1,2) + Variable (1,3) +...+ Variable (1,23) + Variable (1,24)

.

.

.
Sales in month 60 = Base + Variable (60,1) + Variable (60,2) + Variable (60,3) +...+Variable (60,23) + Variable (60,24)

This cannot be solved algebraically but can be by setting up a matrix   The two matrices would look as follows.

Sales in month 1

Sales in month 2
.

.

.
Sales in month 60

and

V1 (1) V2 (1) V3 (1)...V23 (1) V24 (1)

.

.

.
V1 (60) V2 (60) V3 (60)...V23 (60) V24 (60)

Using these matrices and inverting them (a proven mathematical technique for solving simultaneous equations) is the core calculation for generating the SPARline.  Hopefully this simplified explanation and example will give you an understanding of the complexities of developing an accurate baseline and the underlying theory of how the SPARLINE is calculated.  The Journal of Marketing Research Article in the Articles section shows how matrices can be used in combination with set theory and explains the use of matrices in more detail.