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Plus Report - By Thomas Baekdal - May 2013

Measuring Results: Don't be Fooled By Math

In my report about "Making Sense of Social Media Monitoring and Sentiment Analysis", I very briefly mentioned the problem with using averages. But a number of people commented on just that one thing as being a constant problem they have every day.

There are many problems with averages. In fact, there are many problems with using math in the first place. As an analyst I use math every day. When I'm studying a brand or a publisher, I sometimes live inside a spreadsheet for a whole week. Here, for example, is one of the many spreadsheets I worked on for "Reverse Engineering Facebook EdgeRank - Beyond the Theory"

But math has one big shortcoming. It provides an extremely precise answer to what is often a vague question. For instance, 2+2+8 equals 12, with an average of 4. But if these people were buying products, nobody bought four products.

You get a precise answer to a vague question. Your question is, "what are people buying?" and math gives you four products on average. See the problem?

As an analyst, I very often find myself in conflict with math. When you are analysing vague concepts like user behaviors or future trends, math has a tendency to mislead you from seeing the real effect. And using averages is one of the worst elements of all.

So, let me give you a few simple examples of the problem and how to do it better:

The curse of averages

Using averages has long been a favorite of business analysts. It provides a simple straightforward number, without all the complexity involved in having to look at the details. If you are a sales manager, telling your CEO that 'on average' product A is doing 37% better than product B, is very effective.

But averages are also one of the main reasons why so many companies fail to understand what is really happening to their business.

One simple example is these two graphs. They are complete opposites, but have exactly the same average. And this is true not just for the vertical average (X-axis), but also for the horizontal axis.

But this is also largely useless, because no company would ever have a graph like this. The real world is far more complicated, which makes using averages even more misleading.

So let's look at some real world examples:

Different products

Here is one example showing the total for two different things (this could be sales, products or people). As you can see, the average is somewhere in the middle.

So, this graph could illustrate the difference between free-traffic and subscriber traffic, for example. Or customers versus non-customers. But if you take the average, you end up thinking that these two groups are the same.

Never calculate the average of two completely different things. People in one box might not the same as the people in another box.

 
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Thomas Baekdal

Founder, media analyst, author, and publisher. Follow on Twitter

"Thomas Baekdal is one of Scandinavia's most sought-after experts in the digitization of media companies. He has made ​​himself known for his analysis of how digitization has changed the way we consume media."
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