Suppose it is a sunny Sunday and we are watching a Cricket match. There are 2 new products launched in Indian market last week only i.e. ABC and XYZ. We watch one particular ad (ABC) for entire day every time a break comes up during the match and it came for only 1 day. On the other hand we watch another ad (XYZ) which doesn’t come every time but comes after every 3 hours and continuously for 1 week. Now if we go for shopping next Sunday to any super market like Big Bazaar and both products are available on the rack, which product has higher chance of getting sold? Considering you are not loyal to any previous brand and want to try something new. In my opinion XYZ has better chance. Why? Because you would recall XYZ easily than ABC. The reason behind this is decay in effect of the ads. No one will remember what they saw 1 week back and will quickly recall something which they watch daily. In technical term we call it AdStock. I will put more links to read about AdStock below.

Now while developing “Marketing Mix” model we need to take care of these things. Our sponsor may not run TV ads for each week but that doesn’t mean that following week will go blank and customers will forget about the brand. The effect of last week promotion will continue and we call it decay effect. So make better marketing decisions and formulating strategy, it is very necessary to understand this concept.
Let’s try to understand through this simple example first. Say we can measure the effect of ad and our sponsor runs TV ad only on 1st and 2nd weeks. So technically the effect of ad on 3rd and 4th week should be 0 but not. The effect of ads run on 1st and 2nd week will continue but will decay.

Week Number Ad published (effect) Actual effect
1 2.5 2.5
2 2.7 2.9
3 0 1.5
4 0 .5

So mathematically we can write:
A(t) = X(t) + AdStock Rate_Week1 * A(t-1) + AdStock Rate_Week2 * A (t-2) + …….
where,
A(t) = Cumulative effect
X(t) = Base effect
A(t-1) = Previous time period effect (last week)
A(t-2) = Last 2nd week’s effect
AdStock Rate_week1 = 1 week decay
AdStock Rate_week2 = 2 weeks decay