Thomas H. Lenhard Data Mining: Measuring the Success of Advertisement

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1 Thomas H. Lenhard Data Mining: Measuring the Success of Advertisement This article is printed in "in Podium der Wirtschaft Band 17, Verlag Harald Kupfer, Altdorf, 2009, ISBN Indroduction Today no one would deny that advertisement is essential for several kinds of businesses. But how can we evaluate advertisement and the amortisation of advertising activities? Before this question can be answered, we need to think of the after-effect of advertisement. If we promote one product, we want to know, - if the sales of it are changing - if other products are substituted - if the sales of other products are increasing - if there are additional sales - what happens about our profits - if there is a time-lag between advertising and any changes 2. The Time-Lag First we will look at the sales of the product which is promoted by advertisement. There are three possible effects of the advertisement. The first effect is that nothing will happen. If there are no other/further effects, then there was much ado about nothing, which means that the activity, normally causing costs, failed. The standard case we normally expect, is, that a product which is promoted has higher sales than without advertisement. There can also be the opposite case, especially if a product is advertised for, so that customers come into the store and buy another substitute product. In order to analyse if one of the effects is caused by a marketing activity, we need a forecast which amount of sales of an advertised product is expected. We are using in this example the most simple method of forecasting. Supposing that the sales of our product do not have big amplitudes, we use a deductive approach by calculating an average of a past period and come to the conclusion that we are expecting the calculated values. The following graph will explain what can happen to the sales if a 1

2 product is promoted. Normally the graph will include points. Here the points are connected by a evened-out curve, for easier reading. The left vertical line marks the point in time where the marketing activity starts. The right vertical line marks the end of it. The horizontal line at the value 1000 shows the expected sales without advertisement Day Real value Expected value Picture1: Sales-Curve Between the start of the activity and the first value which is apparently out of the normal range there is a time-lag of one day. This example of a time-lag explains that if relations between product promotion and changing amounts of sales are searched for, it is necessary to think about this time-lag, which can be shorter or longer than in the example. Depending on the kind of advertisement, the marketing mix, the product and other parameters, it is imaginable, that this time-lag is a period of a some days. To search for correlations between a marketing activity and the sales of a product, it is possible to use a flag to mark the day which is included in the period of special advertisement. The following example will explain how important the knowledge about a time-lag can be. Imaging that we want to analyse the data of the table for the described correlation and that we have a time-lag of two days, the first calculation shows what happens if it is ignored (table 1). The marked fields are used for this first analysis. The number one, tell us, that the marketing activity is active, while Zero says, that it is inactive. 2

3 Day Sales of Product x Promotion Day Sales of Product x Promotion Table 1 Table 2 If we calculate the correlation between the two rows of numbers, thinking of parallelism, we get a value of It s a value outside any range interesting for us. If we use the same table and take into consideration the time-lag of two days, so that the analysed sales start on the third day, like shown in the second table, we get a result of It may be that the second value is a bit unrealistic, but as an example it demonstrates the danger of getting a totally unusable result if the time-lag is neglected. This method can be described by modifying the formula of the correlation analysis as follows while x stands for the activity and y for the sales. s xy 1 n 1 n i 1 ( x i _ x)( y i t ( m n t j 1 t n y i t )) It is possible to use the amount or turnover for sales but this formula can also be used with the profit, considering that it is possible that the profit is decreasing at the same time the number of sales is increasing. This can happen, especially if the price for a product is lowered as a instrument of promotion. 3

4 3. Substitution In many cases we can estimate - or we know by experience - which product can be substituted by another, especially equivalent products of competitors in the market are potential candidates for substitution. Other substitutions can be found by methods shown in this work. So, if we advertise for example a detergent of a special brand, we can expect, that increasing sales of this product are potentially substitutions of other brands of detergents. To prove what happens to this brands, we calculate the difference between the expected values of sales and the real sales. If we find a negative correlation between the advertised product and the alternative brand, we can define the hypothesis, that a part of the sales of this product is substituted by the promoted one. In general, we can expect that the cheaper the substitute product is sold the higher the degree of substitution of other brands will be. One Problem of advertisement is the danger that a product is substituted by itself. How this can happen explains the example of a photo-shop where cameras and films and other stuff is sold. This shop sold several brands of 35mm films like Agfa, Konica, Kodak or Fuji and a own brand. The highest margin was reached with the own brand; so they decided to substitute other brands by their own to make a higher profit. The strategy was to sell the own films at a very low price so that the customers should buy these films instead of other brands. While the marketing activity was running, 5 times as many films of the own brand were sold, but there was no substitution of other films. After the period of promotion was over there was no change in the sales of the other brands but the sales of the own brand went down seriously. What happened? Each film has slightly different colours and some customers prefer a film with a higher degree of the colour blue while other customers prefer a green film. It was a failure to think, that someone buys a film only because of the low price. The promoted product substituted its own future sales. How can such a self-substitution be detected? For example: the national economy does not consume more detergent only because of a special price in one market. That means it normally results in kind of a substitution. And if there is no substitution the same time we find high correlations between promotion of a product and its sales, it is probable that the substitution has a time lag and perhaps the product substitutes itself. If we analyse a scenario to find the effects of advertising and we find no other 4

5 information than the increasing sales of the product which is advertised for, there can be three reasons for. It can be a really increased consumption, there can be a timelag in substitution which also includes self-substitution of a product, or customers who buy normally a product in another store come into our shop to buy the promoted product. Analysing actual data can only give a clue that it might be useful thinking of these reasons. A self-substitution can only be avoided by experience. If there is a substitution of sales at a competitor s shop, it can be guessed by looking at the number of customers or bons/receipts. This can also be a indicator, which helps interpreting what happens due to advertisement. 4. How can the Time-Lag Been Found? In the previous chapter, there was a example explaining that ignoring a potential time-lag can cause unusable information. Perhaps information is the wrong word to describe it, because it seems to be information but it might be totally unusable for decision making based on it. Even a difference of one day which is not detected can produce another result, or - staying in the frame of the context - there is the danger of creating an absolute different hypothesis. It might be helpful to modify the delay between the period of a marketing activity and a period of measured sales and to look for the highest correlation coefficient between the two periods. This calculation can give a clue about the time-lag. It has to be checked critically and it needs experience to conclude if it is realistic or if other parameters influence the result. Therefore we come to a hypothesis which opposes experience and knowledge. The following pseudo-code gives an example how this analysis can be implemented. It is not feasible by the exclusive use of SQL, because it must include an iteration. Step1 Building an array of correlation coefficients define LAG 10 // what is the highest value which is analysed for the lag - 10 days int i; // counter int start; // date as int int end; // date as int float *flparray[lag+2]; long lstartingday; // need a value! lstartingday = 36982; // int-conversion (ms-access) of the 1 st April 01 5

6 for (i=0; i!= (LAG+1); i++) { EXECSQL: SELECT ((1/(COUNT(*)-1)) * SUM( (SELECT activity.promotion - (SELECT AVG(activity.promotion) WHERE day BETWEEN :start AND :end ) WHERE day BETWEEN :start AND :end ) * (SELECT activity.sales - (SELECT AVG (activity.sales) WHERE day BETWEEN (:start + :i) AND (:end + :i)) WHERE day BETWEEN (:start + :i) AND (:end + :i) ))) / ((SQR( SUM( (SELECT activity.promotion- (SELECT AVG(activity.promotion) WHERE day BETWEEN :start AND :end) WHERE day BETWEEN :start AND :end) * (select activity.promotion- (SELECT AVG(activity.promotion) WHERE day BETWEEN :start AND :end) WHERE day BETWEEN :start and :end)) / ((SELECT COUNT(*) WHERE day BETWEEN :start AND :end) -1))) * (SQR( SUM( (SELECT activity.sales - (SELECT AVG(activity.sales) WHERE day BETWEEN (:start + :i) AND (:end + :i)) WHERE day BETWEEN (:start + :i) AND (:end + :i)) * (SELECT activity.sales- 6

7 / (SELECT AVG(activity.sales) WHERE day BETWEEN (:start + :i) AND (:end + :i)) WHERE day BETWEEN (:start + :i) AND (:end + :i)) ) ((SELECT COUNT(*) WHERE day BETWEEN :start and :end) -1)))) INTO :flparray[i]; } Step 2 Selecting the highest value out of the array of step 1 float flhighestvalue; /definitions related to step 2 float flcheck; int idays = 0; int counter = 1; int mode; flhighestvalue = flparray[0] For (j=1; j!=(lag+2);j++) { flcheck = flparray[j]; if (flcheck > flhighestvalue) { counter = 1; flhighestvalue = flcheck idays = j; } if (flcheck == flparray[i]) counter = counter + 1; } if (counter > 1) { mode = 0; } else mode = 1; 7

8 The array flparray is used because of the iteration which is necessary to calculate the correlation coefficient for each day and to store it. The mode at the end of the demo-code explains if there is a unique result. If the mode is 1, it is unique. In this case the highest correlation coefficient is stored in the variable flhighestvalue and the supposed time-lag is stored in idays. If the mode is finally set to 0, there is no base to define a hypothesis, because the highest value is not unique. In this case, the variable idays includes the last day for which this correlation coefficient, which is not unique, is calculated. No matter how the final result looks, it will be only a hypothesis. 8