Adstock and Diminishing Returns: non-linear advertising effects

Adstock is an important concept in marketing effectiveness. It was first quantified by Simon Broadbent in the 1970s. Its value lies in helping make marketing and media mix models more accurate by recognising that advertising and media investments have non-linear “carryover” response effects.

These non-linear effects are normally grouped into two areas:

1. the delayed effect of advertising and
2.  diminishing returns in advertising.

Let’s look at each one in turn:

1 – Adstock or Carryover

The first type of non-linear effect we see in media investment is the carryover effect. When we advertise, we know that the effects are not always seen immediately. This is because advertising, well good advertising, gets remembered and the memory effect on consumer behaviour may be felt some time after the ad is seen.

So, for example if an advertiser buys 100 GRPs in a week, the full effects of that investment are not confined to that week. What happens in practice is that the effect of that advertising tends to “carryover” into the next week and the week after that. How do we know this? We know because when we build models (e.g. MMM) to quantify response to media investment, they tend to be much more accurate when we carry-over the effect of advertising into the following weeks.  We call this carryover effect Adstock.

You might ask “how much do we carry over?” The answer to this is found by testing different Adstock carry-over levels and analysing how they correlate with sales response over time.  The most commonly used analogy here is borrowed from nuclear physics (don’t worry it’s not as complicated as it sounds). In nuclear physics radioactive substances have a half-life, that’s the time it takes for their radioactivity to decay by exactly half.  Marketers borrow this thinking and use half-life decay rates to model lagged advertising effects. We refer to the length of time required for advertising Adstock to fall by half as the ‘half-life’.

So, as an example, if in week 1, 100 GRPs create 1000 sales, a one week half-life might see that effect carry-over to 500 sales in the second week, 250 sales in the third week and 125 sales in the fourth week.    Any model that counts only the 1000 sales in the first week underestimates the lagged ROI of those first 100 GRPs. That’s because over the four weeks those 100 GRPs delivered 1,875 sales (1000+500+250+125) rather than the 1,000 sales originally reported. We can see that by considering Adstock, the ROI of the first week’s 100 GRPs almost doubles.

Here is an example of adstock applied to raw media spend (BVOD, 60% decay)

2  – Diminishing Returns

The second type of non-linear effect we see in media investment is diminishing returns. The law of diminishing returns states that as more of something is bought, the less utility is gained from it.   A frequently quoted example is agriculture – as more resources are invested into an acre of land, the yield of corn does not increase proportionally.  A more day to day example I like to use is buying coffee. The first coffee of the day is wonderful and hugely satisfying. The second is less satisfying and by the time I venture to more than three cups I’m not getting much satisfaction at all. These are both examples of diminishing returns and the same patterns can be seen in media investment.

Let’s assume we are investing in media to drive web traffic. If we buy 100 GRPs in a week we might see 100,000 visits.  But if we invest in an additional 100 GRPs in the same week we might see these incremental GRPs deliver only 50k visits. And if we invest in a further 100 GRPs in the same week we might only see 25k additional visits generated. We can see the visits we are generating fall by half for every 100 incremental GRPs we buy. This is a diminishing return and it applies to all channels from TV to PPC.

What’s the cost of this diminishing return? Given that 100 GRPs might cost £350k we can see how  taking the spend over a certain level in a specific time frame starts to reduce ROI significantly.   Whereas the first 100 GRPs generated 100,000 visits, 300 GRPs only generated 175,000 visits (100k+50k+25k). Our CPV has increased four times from £3.50 on the first 100 GRPs to £14.00 on the third 100 GRPs. When we apply these examples to large scale media budgets, we can see how diminishing returns can have a dramatic effect on media effectiveness. In the worst case scenarios budgets are set at levels so high that they risk producing no additional sales response at all.

What causes diminishing returns?  Diminishing returns are usually caused by market size constraints. If a brand has a consideration pool size of 5m consumers, with ten percent actively in market in a week or  a month, over-spending excessively against this group will not change purchase behaviour sufficiently enough to match your increased spend, you will simply spend more, sales will not grow at a proportionate rate and your media ROI will fall.

Here is an example of some advertising response curves

Note linear response =1, non-linear response = less than 1.

What does this mean for media planning and investment?

The challenge for media planners is to arrange media investment to leverage the carry-over effects produced by Adstock whilst reducing the impact of diminishing returns.

The main implications for media planning are around setting budget weights and phasing to leverage these two effects to maximise media effectiveness. Budget weights have to be contained within acceptable diminishing return limits while Adstock carry-overs can be used to fill gaps in a pulsing media strategy.

Further reading

Broadbent, S. (1979) “One Way TV Advertisements Work”, Journal of the Market Research Society Vol. 23 no.3

Joy Joseph, 2006, “Understanding Advertising Adstock Transformations” (independent)

Fry, T.R.L., Broadbent, S. and Dixon, J.M. (2000), “Estimating Advertising Half-life and the Data Interval Bias”, Journal of Targeting, Measurement & Analysis in Marketing, 8, 314-334

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