One bubble is a tragedy, and a bag of bubbles is...

From Kathleen Tyson's twitter account, I came across a graphic showing the destinations of Ukraine's grain exports since 2022 under the auspices of a UN deal. This graphic, made by AFP, uses one of the chart forms that baffle me - the bag of bubbles.

The first trouble with a bag of bubbles is the single bubble. The human brain is just not fit for comparing bubble sizes. The self-sufficiency test is my favorite device for demonstrating this weakness. The following is the European section of the above chart, with the data labels removed.

How much bigger is Spain than the Netherlands? What's the difference between Italy and the Netherlands? The answers don't come easily to mind. (The Netherlands is about 40% the size of Spain, and Italy is about 20% larger than the Netherlands.)

While comparing relative circular areas is a struggle, figuring out the relative ranks is not. Sure, it gets tougher with small differences (Germany vs S. Korea, Belgium vs Portugal) but saying those pairs are tied isn't a tragedy.

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Another issue with bubble charts is how difficult it is to assess absolute values. A circle on its own has no reference point. The designer needs to add data labels or a legend. Adding data labels is an act of giving up. The data labels become the primary instrument for communicating the data, not the visual construct. Adding one data label is not enough, as the following shows:

Being told that Spain's value is 4.1 does little to help estimate the values for the non-labelled bubbles.

The chart does come with the following legend:

For this legend to work, the sample bubble sizes should span the range of the data. Notice that it's difficult to extrapolate from the size of the 1-million-ton bubble to 2-million, 4-million, etc. The analogy is a column chart in which the vertical axis does not extend through the full range of the dataset.

The designer totally gets this. The chart therefore contains both selected data labels and the partial legend. Every bubble larger than 1 million tons has an explicit data label. That's one solution for the above problem.

Nevertheless, why not use another chart form that avoids these problems altogether?

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In Tyson's tweet, she showed another chart that pretty much contains the same information, this one from TASS.

This chart uses the flow diagram concept - in an abstract way, as I explained in previous post.

This chart form imposes structure on the data. The relative ranks of the countries within each region are listed from top to bottom. The relative amounts of grains are shown in black columns (and also in the thickness of the flows).

The aggregate value of movements within each region is called out in that middle section. It is impossible to learn this from the bag of bubbles version.

The designer did print the entire dataset onto this chart (except for the smallest countries grouped together as "other"). This decision takes away from the power of the underlying flow chart. Instead of thinking about the proportional representation of each country within its respective region, or the distribution of grains among regions, our eyes hone in on the data labels.

This brings me back to the principle of self-sufficiency: if we expect readers to consume the data labels - which comprise the entire dataset, why not just print a data table? If we decide to visualize, make the visual elements count!

When words speak louder than pictures

I've been staring at this chart from the Wall Street Journal (link) about U.S. workers working remotely:

It's one of those offerings I think on which the designer spent a lot of effort, but ultimately didn't realize that the reader would spend equal if not more effort deciphering.

However, the following paragraph lifted straight from the article says exactly what needs to be said:

Workers overall spent an average of 5 hours and 25 minutes a day working from home in 2022. That is about two hours more than in 2019, the year before Covid-19 sent millions of workers scrambling to set up home oces, and down just 12 minutes from 2021, according to the Labor Department’s American Time Use Survey.

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Why is the chart so hard to read?

It's mostly because the visual is fighting the message. In the Trifecta Checkup (link), this is represented by a disconnect between the Q(uestion) and the V(isual) corners - note the green arrow between these two corners.

The message concentrates on two comparisons: first, the increase in amount of remote work after the pandemic; and second, the mild decrease in 2022 relative to 2021.

On the chart, the elements that grab my attention are (a) the green and orange columns (b) the shading in the bottom part of those green and orange columns (c) the thick black line that runs across the chart (d) the indication on the left side that tells me one unit is an hour.

None of those visual elements directly addresses the comparisons. The first comparison - before and after the pandemic - is found by how much the green column spikes above the thick black line. Our comprehension is retarded by the decision to forego the typical axis labels in favor of chopping columns into one-hour blocks.

The second comparison - between 2022 and 2021 - is found in the white space above the top of the orange column.

So, in reality, the text labels that say exactly what needs to be said are carrying a lot of weight. A slight edit to the pointers helps connect those descriptions to the visual depiction, like this:

I've essentially flipped the tactics used in the various pointers. For the average level of remote work pre-pandemic, I dispense of any pointers while I'm using double-headed arrows to indicate differences across time.

Nevertheless, this modified chart is still too complex.

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Here is a version that aligns the visual to the message:

It's a bit awkward because the 2 hour 48 minutes calculation is the 2021 number minus the average of 2015-19, skipping the 2020 year.

 

Redundancy is great

I have been watching some tennis recently, and noticed that some venues (or broadcasters) have adopted a more streamlined way of showing tiebreak results.

(This is an old example I found online. Can't seem to find more recent ones. Will take a screenshot next time I see this on my TV.)

For those not familiar with tennis scoring, the match is best-of-three sets (for Grand Slam men's tournaments, it's best-of-five sets); each set is first to six games, but if the scoreline reaches 5-5, a player must win two consecutive games to win the set at 7-5, or else, the scoreline reaches 6-6, and a tiebreak is played. The tiebreak is first to seven points, or if 6-6 is reached, it's first player to get two points clear. Thus, the possible tiebreak scores are 7-0, 7-1, ..., 7-5, 8-6, 9-7, etc.

A tiebreak score is usually represented in two parts, e.g., 7-6 (7-2).

At some point, some smart person discovered that the score 7-2 contains redundant information. In fact, it is sufficient to show just the score of the losing side in a tiebreak - because the winner's points can be inferred from it.

The rule can be stated as: if the displayed number is 5 or below, then the winner of the tiebreak scored exactly 7 points; and if the displayed number is 6 or above, then the winner scored two points more than that number.

For example, in the attached image, Djokovic won a tiebreak 7-6 (2) which means 7-6 (7-2) while Del Potro won a tiebreak 7-6 (6) which means 7-6 (8-6).

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While this discovery satisfies my mathematical side - we always like to find the most concise way to do a proof or computation - it is bad for data communications!

It's just bad practice to make readers do calculations in their heads when the information can be displayed visually.

I found where I saw this single-digit display. It's on the official ATP Tour website.

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Just for fun, if we applied the same principle to the display of the entire scoreline, we would arrive at something even more succinct :)

4-6, 7-6(6), 6-4 can simply be written as 4-, -6(6), -4

6-3, 7-6(4), 6-3 is -3, -6(4), -3

6-1, 6-4 is -1, -4

7-5, 4-6, 6-1 is -5, 4-, -1

The shortened display contains the minimal information needed to recover the long-form scoreline. But it fails at communications.

In this case, redundancy is great.

 

Tile maps on a trip

My friend Ray sent me to a recent blog about tile maps. Typical tile maps use squares or hexagons, although in theory many other shapes will do. Unsurprisingly, the field follows the latest development of math researchers who study the space packing problem. The space packing problem concerns how to pack a space with objects. The study of tesselations is to pack space with one or a few shapes.

It was an open question until recently whether there exists an "aperiodic monotile," that is to say, a single shape that can cover space in a non-repeating manner. We all know that we can use squares to cover a space, which creates the familiar grid of squares, but in that case, a pattern repeats itself all over the space.

Now, some researchers have found an elusive aperiodic monotile, which they dubbed the Einstein monotile. Below is a tesselation using these tiles:

Within this design, one cannot find a set of contiguous tiles that repeats itself.

The blogger then made a tile map using this new tesselation. Here's one:

It doesn't matter what this is illustrating. The blog author cites a coworker, who said: "I can think of no proper cartographic use for Penrose binning, but it’s fun to look at, and so that’s good enough for me." Penrose tiles is another mathematical invention that can be used in a tesselation. The story is still the same: there is no benefit from using these strange-looking shapes. Other than the curiosity factor.

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Let's review the pros and cons of using tile maps.

Compare a typical choropleth map of the United States (by state) and a tile map by state. The former has the well-known problem that states with the largest areas usually have the lowest population densities, and thus, if we plot demographic data on such maps, the states that catch the most attention are the ones that don't weigh as much - by contrast, the densely populated states in New England barely show up.

The tile map removes this area bias, thus resolving this problem. Every state is represented by equal area.

While the tesselated design is frequently better, it's not always. In many data visualization, we do intend to convey the message that not all states are equal!

The grid arrangement of the state tiles also makes it easier to find regional patterns. A regional pattern is defined here as a set of neighboring states that share similar data (encoded in the color of the tiles). Note that the area of each state is of zero interest here, and thus, the accurate descriptions of relative areas found on the usual map is a distractor.

However, on the tile map, these regional patterns are conceptual. One must not read anything into the shape of the aggregated region, or its boundaries. Indeed, if we use strange-looking shapes like Einstein tiles, the boundaries are completely meaningless, and even misleading.

There also usually is some distortion of the spatial coordinates on a tile map because we'd like to pack the squares or hexagons into a lattice-like structure.

Lastly, the tile map is not scalable. We haven't seen a tile map of the U.S. by county or precinct but we have enjoyed many choropleth maps displaying county- or precinct-level data, e.g. the famous Purple Map of America. There is a reason for this.

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Here is an old post that contains links to various other posts I've written about tile maps.