Bubble charts, ratios and proportionality

A recent article in the Wall Street Journal about a challenger to the dominant weedkiller, Roundup, contains a nice selection of graphics. (Dicamba is the up-and-comer.)


The change in usage of three brands of weedkillers is rendered as a small-multiples of choropleth maps. This graphic displays geographical and time changes simultaneously.

The staircase chart shows weeds have become resistant to Roundup over time. This is considered a weakness in the Roundup business.


In this post, my focus is on the chart at the bottom, which shows complaints about Dicamba by state in 2019. This is a bubble chart, with the bubbles sorted along the horizontal axis by the acreage of farmland by state.


Below left is a more standard version of such a chart, in which the bubbles are allowed to overlap. (I only included the bubbles that were labeled in the original chart).


The WSJ’s twist is to use the vertical spacing to avoid overlapping bubbles. The vertical axis serves a design perogative and does not encode data.  

I’m going to stick with the more traditional overlapping bubbles here – I’m getting to a different matter.


The question being addressed by this chart is: which states have the most serious Dicamba problem, as revealed by the frequency of complaints? The designer recognizes that the amount of farmland matters. One should expect the more acres, the more complaints.

Let's consider computing directly the number of complaints per million acres.

The resulting chart (shown below right) – while retaining the design – gives a wholly different feeling. Arkansas now owns the largest bubble even though it has the least acreage among the included states. The huge Illinois bubble is still large but is no longer a loner.


Now return to the original design for a moment (the chart on the left). In theory, this should work in the following manner: if complaints grow purely as a function of acreage, then the bubbles should grow proportionally from left to right. The trouble is that proportional areas are not as easily detected as proportional lengths.

The pair of charts below depict made-up data in which all states have 30 complaints for each million acres of farmland. It’s not intuitive that the bubbles on the left chart are growing proportionally.


Now if you look at the right chart, which shows the relative metric of complaints per million acres, it’s impossible not to notice that all bubbles are the same size.

Taking small steps to bring out the message

Happy new year! Good luck and best wishes!


We'll start 2020 with something lighter. On a recent flight, I saw a chart in The Economist that shows the proportion of operating income derived from overseas markets by major grocery chains - the headline said that some of these chains are withdrawing from international markets.


The designer used one color for each grocery chain, and two shades within each color. The legend describes the shades as "total" and "of which: overseas". As with all stacked bar charts, it's a bit confusing where to find the data. The "total" is actually the entire bar, not just the darker shaded part. The darker shaded part is better labeled "home market" as shown below:


The designer's instinct to bring out the importance of international markets to each company's income is well placed. A second small edit helps: plot the international income amounts first, so they line up with the vertical zero axis. Like this:


This is essentially the same chart. The order of international and home market is reversed. I also reversed the shading, so that the international share of income is displayed darker. This shading draws the readers' attention to the key message of the chart.

A stacked bar chart of the absolute dollar amounts is not ideal for showing proportions, because each bar is a different length. Sometimes, plotting relative values summing to 100% for each company may work better.

As it stands, the chart above calls attention to a different message: that Walmart dwarfs the other three global chains. Just the international income of Walmart is larger than the total income of Costco.


Please comment below or write me directly if you have ideas for this blog as we enter a new decade. What do you want to see more of? less of?

All these charts lament the high prices charged by U.S. hospitals


A former student asked me about this chart from the New York Times that highlights much higher prices of hospital procedures in the U.S. relative to a comparison group of seven countries.

The dot plot is clearly thought through. It is not a default chart that pops out of software.

Based on its design, we surmise that the designer has the following intentions:

  1. The names of the medical procedures are printed to be read, thus the long text is placed horizontally.

  2. The actual price is not as important as the relative price, expressed as an index with the U.S. price at 100%. These reference values are printed in glaring red, unignorable.

  3. Notwithstanding the above point, the actual price is still of secondary importance, and the values are provided as a supplement to the row labels. Getting to the actual prices in the comparison countries requires further effort, and a calculator.

  4. The primary comparison is between the U.S. and the rest of the world (or the group of seven countries included). It is less important to distinguish specific countries in the comparison group, and thus the non-U.S. dots are given pastels that take some effort to differentiate.

  5. Probably due to reader feedback, the font size is subject to a minimum so that some labels are split into two lines to prevent the text from dominating the plotting region.


In the Trifecta Checkup view of the world, there is no single best design. The best design depends on the intended message and what’s in the available data.

To illustate this, I will present a few variants of the above design, and discuss how these alternative designs reflect the designer's intentions.

Note that in all my charts, I expressed the relative price in terms of discounts, which is the mirror image of premiums. Instead of saying Country A's price is 80% of the U.S. price, I prefer to say Country A's price is a 20% saving (or discount) off the U.S. price.

First up is the following chart that emphasizes countries instead of hospital procedures:


This chart encourages readers to draw conclusions such as "Hospital prices are 60-80 percent cheaper in Holland relative to the U.S." But it is more taxing to compare the cost of a specific procedure across countries.

The indexing strategy already creates a barrier to understanding relative costs of a specific procedure. For example, the value for angioplasty in Australia is about 55% and in Switzerland, about 75%. The difference 75%-55% is meaningless because both numbers are relative savings from the U.S. baseline. Comparing Australia and Switzerland requires a ratio (0.75/0.55 = 1.36): Australia's prices are 36% above Swiss prices, or alternatively, Swiss prices are a 64% 26% discount off Australia's prices.

The following design takes it even further, excluding details of individual procedures:


For some readers, less is more. It’s even easier to get a rough estimate of how much cheaper prices are in the comparison countries, for now, except for two “outliers”, the chart does not display individual values.

The widths of these bars reveal that in some countries, the amount of savings depends on the specific procedures.

The bar design releases the designer from a horizontal orientation. The country labels are shorter and can be placed at the bottom in a vertical design:


It's not that one design is obviously superior to the others. Each version does some things better. A good designer recognizes the strengths and weaknesses of each design, and selects one to fulfil his/her intentions.


P.S. [1/3/20] Corrected a computation, explained in Ken's comment.

Conceptualizing a chart using Trifecta: a practical example

In response to the reader who left a comment asking for ideas for improving the "marginal abatements chart" that was discussed here, I thought it might be helpful to lay out the process I go through when conceptualizing a chart. (Just a reminder, here is the chart we're dealing with.)


First, I'm very concerned about the long program names. I see their proper placement in a horizontal orientation as a hard constraint on the design. I'd reject every design that displays the text vertically, at an angle, or hides it behind some hover effect, or abbreviates or abridges the text.

Second, I strongly suggest re-thinking the "cost-effectiveness" metric on the vertical axis. Flipping the sign of this metric makes a return-on-investment-type metric, which is much more intuitive. Just to reiterate a prior point, it feels odd to be selecting more negative projects before more positive projects.

Third, I'd like to decide what metrics to place on the two axes. There are three main possibilities: a) benefits (that is, the average annual emissions abatement shown on the horizontal axis currently), b) costs, and c) some function that ties together costs and benefits (currently, this design uses cost per unit benefit, and calls it cost effectivness but there are a variety of similar metrics that can be defined).

For each of these metrics, there is a secondary choice. I can use the by-project value or the cumulative value. The cumulative value is dependent on a selection order, in this case, determined by the criterion of selecting from the most cost-effective program to the least (regardless of project size or any other criteria).

This is where I'd bring in the Trifecta Checkup framework (see here for a guide).

The decision of which metrics to use on the axes means I'm operating in the "D" corner. But this decision must be made with respect to the "Q" corner, thus the green arrow between the two. Which two metrics are the most relevant depends on what we want the chart to accomplish. That in turn depends on the audience and what specific question we are addressing for them.

Fourth, if the purpose of the chart is exploratory - that is to say, we use it to guide decision-makers in choosing a subset of programs, then I would want to introduce an element of interactivity. Imagine an interface that allows the user to move programs in and out of the chart, while the chart updates itself to compute the total costs and total benefits.

This last point ties together the entire Trifacta Checkup framework (link). The Question being exploratory in nature suggests a certain way of organizing and analyzing the Data as well as a Visual form that facilitates interacting with the information.