Every Now and Again, a Pie can be Good

It is hard to find anyone in visualization today with much time for pie charts. In fact it seems de rigueur to disdain them. And yet we see an awful lot of them. Now, I’m not going to claim that they are a good, general purpose chart, but I do always like to think of times when a chart will actually work well.

When Pie Charts Work At All

One well-known requirement for a pie to have a chance of working is that the data represent a fraction of a whole. That’s the big selling point of pie charts — each data row should represent a fraction of the overall data. So pies work best for percentages and fractions, and second-best for counts, populations, weights — things for which there is a natural feeling that summing them all up and saying “that represents 100%” is good.

On the side of evil is when the numbers must not be summed — if the data represent means (for different sized groups) or degrees Fahrenheit, then a pie representation is flat-out wrong. It’s not a bad rule to say:

Only Use a Pie if it makes sense to think of the data values as summing to 100%

The second rule I’d suggest is based on the inability for people accurately to judge angles. Pies do not work well for that, so if you need accurately to judge numbers, do not use a pie. Pies work well for “A is about twice as big as B” or “ C is definitely smaller in the second pie”. They are not good for “C is very slightly lower than D” or “B is just under 33%”. Stating it positively:

Use a Pie if the goal is to make broad comparisons, not detailed ones.

Finally, I’d offer a third suggestion, rather than a rule. It’s based on the observation that a bar chart (a natural competitor to a pie chart) is very often improved by ordering — high to low values, for example. Pies can often look radically different when categories are re-ordered, and although it is sometimes suggested that you do this ordering for pies, I think that a pie for categories that can be re-ordered would almost certainly look better in another form. Instead I would suggest the following:

Use a Pie when the categories have a natural order

When Pie Charts Work Well

Stephen Few (Save the pies for Dessert: http://www.perceptualedge.com/articles/08-21-07.pdf) quotes a study showing that when pies have been shown to be actively superior to bar charts — it is when it makes sense to want to compare sums of categories (e.g. the sum of the first two against the sum of the second two); the reason being that in a pie, you can compare angles for multiple segments easily, whereas in a bar chart that is not easy. 

Survey Data: Bar Chart and Pie Chart

Survey Data: Bar Chart and Pie Chart

The figure above shows some data where these three rules have been observed. It’s from the World Values Survey (http://www.worldvaluessurvey.org) and shows the response to the question “how much do you trust the press?” For this data:

  • Values are percentages — perfect for pies
  • Categories are strongly ordered
  • Qualitative insights are more important than quantitative ones

Ignoring the labels, the bar chart is much better at answering the question “How much more do people respond not very much more than quite a lot ?” In fact, on the pie chart, the initial impression we have is that

  • Not very much is answered about the same amount as quite a lot
  • About three-quarters of the time people respond either not very much or quite a lot

Ah, but the second observation is an interesting one. That information is very hard to see in the bar chart — We have to spatially sum the areas of the middle to bars and compare them to the spatial sum of all the bars. Very tricky. This is the area where pies work well, and the reason I argue they need naturally ordered data. For this data it makes a lot of sense to compare the first two categories (generally positive opinion) with the last two (generally negative), and it also makes sense to compare the ends (strong opinion) with the middle (weak opinion).

Few closes his article with the statement that “a comparison of two sets of summed parts is rare in the real world”, but that seems odd to me — survey data is very commonly comprised of this sort of data; and surveys are not exactly a rare art. This form of data is exactly the sort that Few states you should use a pie chart for, and I have to agree; it works well.

More Benefits

One major benefit of a pie chart, especially for dashboards and web-based presentations, is that pies are compact. Not only does the data take a higher proportion of the available area, but also the pie chart is better in terms of Tufte’s data-ink ratio. I’m not a huge fan of that measure, but hey, I’ll use what I can. Tufte also states “the only worse design than a pie chart is several of them” and if we are talking about aligned charts (as in a paneling of small multiples) a bar chart does win out, as comparing aligned bars is so natural and easy for us to do. But what about non-aligned bars? Or even worse, if the mini-charts overlap each other. When might this happen? Well, for the survey data above, if we drill-down to show data on a per-country basis, we see the following for bars and pies:  

Survey Responses By Country (as Bar Charts)

Survey Responses By Country (as Bar Charts)

Survey Responses By Country (as Pie Charts)

Survey Responses By Country (as Pie Charts)

Circles have the great characteristic that when they intersect, they are more easy to distinguish (which is why scatterplots use them as symbols for the point locations). In the above figures, not only are the pies easier for answering questions like “Does South Africa generally trust the press?” but when they start overlapping, it’s easier to see that there are three mini-charts for Scandinavian countries, and even though Europe is a mess (graphically, I mean), I think it is still easier to spot similarities and differences in the pie version.

Also, the pies are all the same symmetric shape, no matter what the data, and so it is much easier to work out which underlying country the pie chart refers to.

Summary

A Pie Chart is not my go-to chart. If I have categories and values, the bar chart is my default choice. But there are times when I’ll consider other charts, liked packed bubble charts, tag cloud and “Wordle” charts, and, yes, even pie charts