Regression to the Mean: What is it and Why Does it Matter for TV Advertising?

By September 17, 2018 clypd Blog, Research

What can Magic Johnson teach us about advanced TV advertising? He has appeared in many commercials over the years (including AT&T, Coca Cola and MasterCard), but it is his sporting career that gives us important insights into how performances vary and how even hall of famers struggle to maintain the same level of results year after year. And this struggle to maintain performance applies to many things, including TV shows.

Earvin ‘Magic’ Johnson burst onto the scene in 1979, becoming the first and only rookie to win the NBA Finals MVP award. He also holds the NBA record for assists per game (APG), averaging 11.2 across his career in regular season play. When we look at his APG stats by year, we see he improved through the first few years of his career, then hit a high point, culminating in a league-leading 13.1 APG in 1983-4. Heading into 1984-5 it would have been natural to think that he might continue improving, with an APG of 14 or even 15 as the logical next step. But it didn’t happen like that: Magic performed well in the following years, but he never got above 13 again.

Why not? Magic himself is not really to blame, nor the Lakers. What we see here is a naturally occurring statistical phenomenon known as regression to the mean. Higher than average performers will tend to remain higher than average but will typically move closer to the average over time, especially after an exceptional “outlier” performance like Magic’s in 1983-4. Equally, lower than average performances often even out and increase. Another example of this is the tendency for tall parents to have tall children who are nonetheless often slightly shorter than their parents, and for shorter parents to have short children who are nonetheless slightly taller than their parents (imagine how humans would vary in height if this regression to the mean didn’t happen…)

So what has this got to do with advanced audiences? One of the key considerations in creating campaigns is the accuracy of audience forecasts. Invariably, audience forecasts consider the historical performance of programs, networks and dayparts, while also looking at trends, seasonality and other factors. Advertising schedules are then created by selecting advantageous units within agreed constraints of network/dayparts/programs and in terms of expected audience delivery and unit price. Because we are selecting the high performing units to meet the campaign requirements as efficiently as possible, there will inevitably be some regression to the mean – not all of these units will perform as well as predicted. In effect, Magic’s 83-84 highpoint of 13.1 would be forecast, but what would be delivered would be the 12.6 of 84-85 – not bad, but an under-delivery.

A simple illustration is given here. We have seven units of inventory, all priced the same for simplicity. Our budget allows us to buy two units and our objective is to deliver the maximum impressions. Clearly the first two units promise the most impressions, and in fact deliver the most, but the delivery is less than the forecast…due to regression to the mean.

The inevitable question then is: how do we account for this phenomenon when forecasting audiences and selecting units? The answer is that regression to the mean can be estimated via the inherent statistical variability of the audience forecast. Considering a standard bell curve of performance for the forecasts, we select the high performing units at the right end of the distribution

Audience Forecasts

Then some of those high forecast units regress to the mean due to natural variability in the estimates.

Audience Delivery

Because regression to the mean reflects sampling variability, we reduce the effect by using more stable data, for example by using selling title estimates rather than individual programs or hours. We also assess the likely delivery of the campaign by calculating confidence intervals around the estimates.

In the extract below, the forecast of 72.4 TRPs has a lower 99% confidence interval of 67.7 TRPs. This tells us that, assuming there is no change in the schedule or unexpected shifts in viewing between planning and the running of the campaign, we can be 99% confident that the schedule will deliver at least 67.7 TRPs. Note that these estimates typically include media owner sales bumps to prevent inadvertent wasteful over-delivery, with Audience Deficiency Units being employed to deliver the agreed Impressions.

It can be seen then that statistical principles underpin both sporting and advertising statistics, but how does this knowledge translate into actual advertising outcomes? The chart below shows results for sixteen actual campaigns, optimized for advanced audience delivery. In each case the forecast and delivered TRPs are shown, as well as an un-optimized benchmark estimate. The delivery of advanced audience impressions across these campaigns is 97% of the forecast and 45% higher than a standard deal created without advanced audience optimization. An important point to note is that these deals were guaranteed on demographics rather than the advanced targets, so the 97% delivery of the advanced target is an excellent performance in that context.

Postscript: Magic and The Sports Illustrated Cover Jinx

Some readers may be familiar with the Sports Illustrated Cover Jinx. Leaving aside some of the more tragic examples, much of the supposed jinx is actually evidence of regression to the mean, and Magic Johnson again provides an example, though this time as one of the owners of the Los Angeles Dodgers baseball team.

On the May 28, 2012 SI issue, the Dodgers (represented by Matt Kemp and Magic Johnson) were featured on the cover. At the time, the Dodgers were at the top, with the best record in baseball (30-13). They were heavy favorites to sweep the Arizona Diamondbacks (19-25). Instead, the Dodgers lost to the Diamondbacks in an 11-4 blowout game, with Matt Kemp getting reinjured. The Dodgers went on to lose the next 8 of 11 games. Their previous outlier performance had regressed to the mean…

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