Metric Translation: Logarithmic Scale

This is part 2 of our series on Metric Translation. Previous segments are available on our archives page.

Logarithmic Scale

If your business is doing well, you might see very rapid growth in specific metrics. For example, the following is the revenue for a newly launched product line for a fictional e-commerce company:

raw data

The rapid growth at the end makes the rest of the chart impossible to see. Using the actual value of the metric makes little sense in this case since the last values are so much larger than the rest!

One way to better visualize data with such different magnitudes is using a logarithmic scale. In such a scale, instead of having the evenly spaced y-axis labels progress using counting numbers (1, 2, 3… ), the labels are powers of 10 (10⁰, 10¹, 10², 10³…). The result is that you can see movement in a metric that changes in significantly in magnitude over time. Below is the same data as above, but now on a logarithmic scale:

log_raw data

It’s now apparent that the cyclical patterns in the later data are present in the earlier data, meaning that the pattern has continued even as the magnitude has increased. This kind of detail is hidden on the actual value chart since the early data is so small, but can be seen on this logarithmic view.

Exponential growth is often talked about in businesses, because if that is happening then you are doing well. One of the added advantages of a logarithmic scale is that you can easily judge if a metric is growing exponentially, since an exponentially growing metric will appear as a straight line on a logarithmic scale. For example, it is hard to tell if the following data is growing exponentially:

log_data

But on a logarithmic scale it forms a straight line, showing that is is exponential:

logarithmic scale

Of course, if the people viewing your data don’t understand that the scale is logarithmic these charts can be more confusing than useful. It is critical to label your charts in a way that the scale is unavoidable to avoid such confusion.

Tomorrow we’ll look at a more complex scenario, when you need to translate insights including more than one metric.

Quote of the Day: Such is our pride, our folly, or our fate, That few but such as cannot write, translate.” – John Denham