The blue mist

The New York Times printed several charts about Twitter "blue checks," and they aren't one of their best efforts (link).

Blue checks used to be credentials given to legitimate accounts, typically associated with media outlets, celebrities, brands, professors, etc. They are free but must be approved by Twitter. Since Elon Musk acquired Twitter, he turned blue checks into a revenue generator. Yet another subscription service (but you're buying "freedom"!). Anyone can get a blue check for US$8 per month.

[The charts shown here are scanned from the printed edition.]


The first chart is a scatter plot showing the day of joining Twitter and the total number of followers the account has as of early November, 2022. Those are very strange things to pair up on a scatter plot but I get it: the designer could only work with the data that can be pulled down from Twitter's API.

What's wrong with the data? It would seem the interesting question is whether blue checks are associated with number of followers. The chart shows only Twitter Blue users so there is nothing to compare to. The day of joining Twitter is not the day of becoming "Twitter Blue", almost surely not for any user (Nevetheless, the former is not a standard data element released by Twitter). The chart has a built-in time bias since the longer an account exists, one would assume the higher the number of followers (assuming all else equal). Some kind of follower rate (e.g. number of followers per year of existence) might be more informative.

Still, it's hard to know what the chart is saying. That most Blue accounts have fewer than 5,000 followers? I also suspect that they chopped off the top of the chart (outliers) and forgot to mention it. Surely, some of the celebrity accounts have way over 150,000 followers. Another sign that the top of the chart was removed is that an expected funnel effect is not seen. Given the follower count is cumulative from the day of registration, we'd expect the accounts that started in the last few months should have markedly lower counts than those created years ago. (This is even more true if there is a survivorship bias - less successful accounts are more likely to be deleted over time.)

The designer arbitrarily labelled six specific accounts ("Crypto influencer", "HBO fan", etc.) but this feature risks sending readers the wrong message. There might be one HBO fan account that quickly grew to 150,000 followers in just a few months but does the data label suggest to readers that HBO fan accounts as a group tend to quickly attain high number of followers?


The second chart, which is an inset of the first, attempts to quantify the effect of the Musk acquisition on the number of "registrations and subscriptions". In the first chart, the story was described as "Elon Musk buys Twitter sparking waves of new users who later sign up for Twitter Blue".


The second chart confuses me. I was trying to figure out what is counted in the vertical axis. This was before I noticed the inset in the first chart, easy to miss as it is tucked into the lower right corner. I had presumed that the axis would be the same as in the first chart since there weren't any specific labels. In that case, I am looking at accounts with 0 to 500 followers, pretty inconsequential accounts. Then, the chart title uses the words "registrations and subscriptions." If the blue dots on this chart also refer to blue-check accounts as in the first chart, then I fail to see how this chart conveys any information about registrations (wbich presumably would include free accounts). As before, new accounts that aren't blue checks won't appear.

Further, to the extent that this chart shows a surge in subscriptions, we are restricted to accounts with fewer than 500 followers, and it's really unclear what proportion of total subscribers is depicted. Nor is it possible to estimate the magnitude of this surge.

Besides, I'm seeing similar densities of the dots across the entire time window between October 2021 and 2022. Perhaps the entire surge is hidden behind the black lines indicating the specific days when Musk announced and completed the acquisition, respectively. If the surge is hiding behind the black vertical lines, then this design manages to block the precise spots readers are supposed to notice.

Here is where we can use the self-sufficiency test. Imagine the same chart without the text. What story would you have learned from the graphical elements themselves? Not much, in my view.


The third chart isn't more insightful. This chart purportedly shows suspended accounts, only among blue-check accounts.


From what I could gather (and what I know about Twitter's API), the chart shows any Twitter Blue account that got suspended at any time. For example, all the black open circles occurring prior to October 27, 2022 represent suspensions by the previous management, and presumably have nothing to do with Elon Musk, or his decision to turn blue checks into a subscription product.

There appears to be a cluster of suspensions since Musk took over. I am not sure what that means. Certainly, it says he's not about "total freedom". Most of these suspended accounts have fewer than 50 followers, and only been around for a few weeks. And as before, I'm not sure why the analyst decided to focus on accounts with fewer than 500 followers.

What could have been? Given the number of suspended accounts are relatively small, an interesting analysis would be to form clusters of suspended accounts, and report on the change in what types of accounts got suspended before and after the change of management.


The online article (link) is longer, filling in some details missing from the printed edition.

There is one view that shows the larger accounts:


While more complete, this view isn't very helpful as the biggest accounts are located in the sparsest area of the chart. The data labels again pick out strange accounts like those of adult film stars and an Arabic news site. It's not clear if the designer is trying to tell us that most of Twitter Blue accounts belong to those categories.

See here for commentary on other New York Times graphics.





Finding the right context to interpret household energy data

Bloomberg_energybillBloomberg's recent article on surging UK household energy costs, projected over this winter, contains data about which I have long been intrigued: how much energy does different household items consume?

A twitter follower alerted me to this chart, and she found it informative.

If the goal is to pick out the appliances and estimate the cost of running them, the chart serves its purpose. Because the entire set of data is printed, a data table would have done equally well.

I learned that the mobile phone costs almost nothing to charge: 1 pence for six hours of charging, which is deemed a "single use" which seems double what a full charge requires. The games console costs 14 pence for a "single use" of two hours. That might be an underestimate of how much time gamers spend gaming each day.


Understanding the design of the chart needs a bit more effort. Each appliance is measured by two metrics: the number of hours considered to be "single use", and a currency value.

It took me a while to figure out how to interpret these currency values. Each cost is associated with a single use, and the duration of a single use increases as we move down the list of appliances. Since the designer assumes a fixed cost of electicity (shown in the footnote as 34p per kWh), at first, it seems like the costs should just increase from top to bottom. That's not the case, though.

Something else is driving these numbers behind the scene, namely, the intensity of energy use by appliance. The wifi router listed at the bottom is turned on 24 hours a day, and the daily cost of running it is just 6p. Meanwhile, running the fridge and freezer the whole day costs 41p. Thus, the fridge&freezer consumes electricity at a rate that is almost 7 times higher than the router.

The chart uses a split axis, which artificially reduces the gap between 8 hours and 24 hours. Here is another look at the bottom of the chart:



Let's examine the choice of "single use" as a common basis for comparing appliances. Consider this:

  • Continuous appliances (wifi router, refrigerator, etc.) are denoted as 24 hours, so a daily time window is also implied
  • Repeated-use appliances (e.g. coffee maker, kettle) may be run multiple times a day
  • Infrequent use appliances may be used less than once a day

I prefer standardizing to a "per day" metric. If I use the microwave three times a day, the daily cost is 3 x 3p = 9 p, which is more than I'd spend on the wifi router, run 24 hours. On the other hand, I use the washing machine once a week, so the frequency is 1/7, and the effective daily cost is 1/7 x 36 p = 5p, notably lower than using the microwave.

The choice of metric has key implications on the appearance of the chart. The bubble size encodes the relative energy costs. The biggest bubbles are in the heating category, which is no surprise. The next largest bubbles are tumble dryer, dishwasher, and electric oven. These are generally not used every day so the "per day" calculation would push them lower in rank.


Another noteworthy feature of the Bloomberg chart is the split legend. The colors divide appliances into five groups based on usage category (e.g. cleaning, food, utility). Instead of the usual color legend printed on a corner or side of the chart, the designer spreads the category labels around the chart. Each label is shown the first time a specific usage category appears on the chart. There is a presumption that the reader scans from top to bottom, which is probably true on average.

I like this arrangement as it delivers information to the reader when it's needed.




Modern design meets dataviz

This chart was submitted via Twitter (thanks John G.).


Perhaps the designer is inspired by this:


That's the Royal Ontario Museum, one of the beautiful landmarks in Toronto.


The chart addresses an interesting question - how much do home buyers over or under-estimate home value?  That said, gathering data to answer this question is challenging. I won't delve into this issue in this post.

Let's ask where readers are looking for data on the chart. It appears that we should use the right edge of each triangle. While the left edge of the red triangle might be useful, the left edges of the other triangles definitely would not contain data.

Note that, like modern architecture, the designer is playing with edges. None of the four right edges is properly vertical - none of the lines cuts the horizontal axis at a right angle. So the data actually reside in the imaginary vertical lines from the apexes to the horizontal baseline.

Where is the horizontal baseline? It's not where it is drawn either. The last number in the series is a negative number and so the real baseline is in the middle of the plot area, where the 0% value is.

The following chart shows (left side) the misleading signals sent to readers and (right side) the proper way to consume the data.


The degree of distortion is quite extreme. Only the fourth value is somewhat accurate, albeit by accident.

The design does not merely perturb the chart; it causes a severe adverse reaction.


P.S. [9/19/2022] Added submitter name.




Speedometer charts: love or hate

Pie chart hate is tired. In this post, I explain my speedometer hate. (Also called gauges,  dials)

Next to pie charts, speedometers are perhaps the second most beloved chart species found on business dashboards. Here is a typical example:



For this post, I found one on Reuters about natural gas in Europe. (Thanks to long-time contributor Antonio R. for the tip.)


The reason for my dislike is the inefficiency of this chart form. In classic Tufte-speak, the speedometer chart has a very poor data-to-ink ratio. The entire chart above contains just one datum (73%). Most of the ink are spilled over non-data things.

This single number has a large entourage:

- the curved axis
- ticks on the axis
- labels on the scale
- the dial
- the color segments
- the reference level "EU target"

These are not mere decorations. Taking these elements away makes it harder to understand what's on the chart.

Here is the chart without the curved axis:


Here is the chart without axis labels:


Here is the chart without ticks:


When the tick labels are present, the chart still functions.

Here is the chart without the dial:


The datum is redundantly encoded in the color segments of the "axis".

Here is the chart without the dial or the color segments:


If you find yourself stealing a peek at the chart title below, you're not alone.

All versions except one increases our cognitive load. This means the entourage is largely necessary if one encodes the single number in a speedometer chart.

The problem with the entourage is that readers may resort to reading the text rather than the chart.


The following is a minimalist version of the Reuters chart:


I removed the axis labels and the color segments. The number 73% is shown using the dial angle.

The next chart adds back the secondary message about the EU target, as an axis label, and uses color segments to show the 73% number.


Like pie charts, there are limited situations in which speedometer charts are acceptable. But most of the ones we see out there are just not right.


One acceptable situation is to illustrate percentages or proportions, which is what the EU gas chart does. Of course, in that situation, one can alo use a pie chart without shame.

For illustrating proportions, I prefer to use a full semicircle, instead of the circular sector of arbitrary angle as Reuters did. The semicircle lends itself to easy marks of 25%, 50%, 75%, etc, eliminating the need to print those tick labels.


One use case to avoid is numeric data.

Take the regional sales chart pulled randomly from a Web search above:


These charts are completely useless without the axis labels.

Besides, because the span of the axis isn't 0% to 100%, every tick mark must be labelled with the numeric value. That's a lot of extra ink used to display a single value!

Dataviz is good at comparisons if we make the right comparisons

In an article about gas prices around the world, the Washington Post uses the following bar chart (link):


There are a few wrinkles in this one compared to the most generic bar chart one can produce:


(The numbers on my chart are not the same as Washington Post's. That's because the data vendor charges for data, except for the most recent week. So, my data is from a different week.)

_trifectacheckup_imageThe gas prices are not expressed in dollars but a transformation turns prices into a cost-effectiveness metric: miles per dollar, or more precisely, miles per $40 dollars of gas. The metric has a reverse direction - the higher the price, the lower the miles. The data transformation belongs to the D corner of the Trifecta Checkup framework (link). Depending on how one poses the Q(uestion) of the chart, the shift from dollars to miles can bring the Q and the D in sync.

In the V(isual) corner, the designer embellishes the bars. A car icon is placed at the tip of each bar while the bar itself is turned into a wavy path, symbolizing a dirt path. The driving metaphor is in full play. In fact, the video makes the most out of it. There is no doubt that the embellishment has turned a mere scientific presentation into a form of entertainment.


Did the embellishment harm visual clarity? For the most part, no.

The worst it can get is when they compared U.S. and India/South Africa:


The left column shows the original charts from the article. In  both charts, the two cars are so close together that it is impossible to learn the scale of the difference. The amount of difference is a fraction of the width of a car icon.

The right column shows the "self-sufficiency test". Imagine the data labels are not on the chart. What we learn is that if we wanted to know how big of a gap is between the two countries, when reading the charts on the left, we are relying on the data labels, not the visual elements. On the right side, if we really want to learn the gaps, we have to look through the car icons to find the tips of the bars!

This discussion does not necessarily doom the appealing chart. If the message one wants to send with the India/South Afrcia charts is that there is negligible difference between them, then it is not crucial to present the precise differences in prices.


The real problem with this dataviz is in the D corner. Comparing countries is hard.

As shown above, by the miles per $40 spend metric, U.S. and India are rated essentially the same. So is the average American and the average Indian suffering equally?

Far from it. The clue comes from the aggregate chart, in which countries are divided into three tiers: high income, upper middle income and lower middle income. The U.S. belongs to the high-income tier while India falls into the lower-middle-income tier.

The cost of living in India is much lower than in the US. Forty dollars is a much bigger chunk of an Indian paycheck than an American one.

To adjust for cost of living, economists use a PPP (purchasing power parity) value. The following chart shows the difference:


The right graph contains cost-of-living adjustments. It shows a completely different picture. Nominally (left chart), the price of gas in about the same in dollar terms between U.S. and India. In terms of cost of living, gas is actually 5 times more expensive in India. Thus, the adjusted miles per $40 gas number is much smaller for India than the unadjusted. (Because PPP is relative to U.S. prices, the U.S. numbers are not affected.)

PPP is not the end-all here. According to the Economic Times (India), only 22 out of 1,000 Indians own cars, compared to 980 out of 1,000 Americans. Think about the implication of using any statistic that averages the entire population!


Why is gas more expensive in California than the U.S. average? The talking point I keep hearing is environmental regulations. Gas prices may be higher in Europe for a similar reason. Residents in those places may be willing to pay higher prices because they get satisfaction from playing their part in preserving the planet for future generations.

The footnote discloses this not-trivial issue.


When converting from dollars per gallon/liter into miles per $40, we need data on miles per gallon/liter. Americans notoriously drive cars (trucks, SUVs, etc.) that have much lower mileage than those driven by other countries. However, this factor is artificially removed by assuming the same car with 32 mpg on all countries. A quick hop to the BTS website tells us that the average mpg of American cars is a third of that assumption. [See note below.]

Ignoring cross-country comparisons for the time being, the true number for U.S. is not 247 miles per $40 spent on gas as claimed. It is a third of that value: 82 miles per $40 spent.

It's tough to find data on fuel economy of all passenger cars, not just new passenger cars. I found Australia's number, which is 21 mpg. So this brings the miles per $40 number down from about 230 to 115. These are not small adjustments.

Washington Post's analysis paints a simplistic picture that presupposes that price is the only thing people care about. I call this issue xyopia. It's when the analyst frames the problem as factor x explaining outcome y, and when factor x is not the only, and frequently not even the most important, factor affecting y.

More on xyopia.

More discussion of Washington Post graphics.


[P.S. 7-25-2022. Reader Cody Curtis pointed out in the comments that the Bureau of Transportation Statistics report was using km/liter as units, not miles per gallon. The 10 km/liter number for average cars is roughly 23 mpg. I'll leave the text as is in the post as the larger point is valid: that there is variation in average fuel economy between nations - partly due to environemental regulation and consumer behavior - and thus, a proper comparison requires adjusting for this factor.]

Ringing in the data

There is a lot of great stuff at Visual Capitalist.

This circular design isn't one of their best.



A self-sufficiency test helps diagnose the problem. Notice that every data point is printed on the diagram. If the data labels were removed, there isn't much one can learn from the chart other than the ranking of countries from most indebted to least. It would be impossible to know the difference in debt levels between any pair of countries.

In other words, the data labels rather than visual elements are doing most of the work. In a good dataviz, we like the visual elements to carry the weight.


The concentric rings embed a visual hierarchy: Japan is singled out, then the next tier of countries include Sudan, Greece, Eritrea, Cape Verde, Italy, Suriname, and Barbados; and so on.

What is the clustering algorithm? What determines which countries fall into the same group?

It's implicitly determined by how many countries can fit inside the next ring. The designer carefully computed the number of rings, the widths of the rings, the density of the circles, etc. in such a way that there is no unsightly white space on the outer ring. Score a 10/10 for effort!

So the clustering of countries is not data-driven but constrained by the chart form. This limitation is similar to that found on maps used to illustrate spatial data.



Asymmetry and orientation

An author in Significance claims that a single season of Premier League football without live spectators is enough to prove that the so-called home field advantage is really a live-spectator advantage.

The following chart depicts the data going back many seasons:


I find this bar chart challenging.

It plots the ratio of home wins to away wins using an odds scale, which is not intuitive. The odds scale (probability of success divided by probability of failure) runs from 0 to positive infinity, with 1 being a special value indicating equal odds. But all the values for which away wins exceed home wins are squeezed into the interval between 0 and 1 while the values for which home wins exceed away wins are laid out between 1 and infinity. So it's an inherently asymmetric graphic for a symmetric formula.

The section labeled "more away wins than home wins" are filled with red bars for all those seasons with positive home field advantage while the most recent season, the outlier, has a shorter bar in that section than the rest.

Here's an alternative view:


I have incorporated dual axes here - but both axes are different only by scaling. There are 380 games in a Premier League season so the percentage scale is just a re-expression of the counts.



One of the most frequently produced maps is also one of the worst

Summer is here, many Americans are putting the pandemic in their rear-view mirrors, and gas prices are soaring. Business Insider told the story using this map:


What do we want to learn about gas prices this summer?

Which region has the highest / lowest prices?

How much higher / lower than the national average are the regional prices?

How much has prices risen, compared to last year, or compared to the last few weeks?


How much work did you have to do to get answers to those questions from the above map?

Unfortunately, this type of map continues to dominate the popular press. It merely delivers a geography lesson and not much else. Its dominant feature tells readers how to classify the 50 states into regions. Its color encodes no data.

Not surprisingly, this map fails the self-sufficiency test (link). The entire dataset is printed on the map, and if those numbers were removed, we would be left with a map of the regions of the U.S. The graphical elements of the chart are not doing much work.


In the following chart, I used the map as a color legend. Also, an additional plot shows each region's price level against the national average.


One can certainly ditch the map altogether, which makes having seven colors unnecessary. To address other questions, just stack on other charts, for example, showing the price increase versus last year.


_trifectacheckup_imageFrom a Trifecta Checkup perspective, we find that the trouble starts with the Q corner. There are several important questions not addressed by the graphic. In the D corner, no context is provided to interpret the data. Are these prices abnormal? How do they compare to the national average or to a year ago? In the V corner, the chart takes too much effort to comprehend a basic fact, such as which region has the highest average price.

For more on the Trifecta Checkup, see this guide.


Come si dice donut in italiano

One of my Italian readers sent me the following "horror chart". (Last I checked, it's not Halloween.)


I mean, people are selling these rainbow sunglasses.


The dataset behind the chart is the market share of steel production by country in 1992 and in 2014. The presumed story is how steel production has shifted from country to country over those 22 years.

Before anything else, readers must decipher the colors. This takes their eyes off the data and on to the color legend placed on the right column. The order of the color legend is different from that found in the nearest object, the 2014 donut. The following shows how our eyes roll while making sense of the donut chart.


It's easier to read the 1992 donut because of the order but now, our eyes must leapfrog the 2014 donut.


This is another example of a visualization that fails the self-sufficiency test. The entire dataset is actually printed around the two circles. If we delete the data labels, it becomes clear that readers are consuming the data labels, not the visual elements of the chart.


The chart is aimed at an Italian audience so they may have a patriotic interest in the data for Italia. What they find is disappointing. Italy apparently completely dropped out of steel production. It produced 3% of the world's steel in 1992 but zero in 2014.

Now I don't know if that is true because while reproducing the chart, I noticed that in the 2014 donut, there is a dark orange color that is not found in the legend. Is that Italy or a mysterious new entrant to steel production?

One alternative is a dot plot. This design accommodates arrows between the dots indicating growth versus decline.



Pies, bars and self-sufficiency

Andy Cotgreave asked Twitter followers to pick between pie charts and bar charts:


The underlying data are proportions of people who say they won't get the coronavirus vaccine.

I noticed two somewhat unusual features: the use of pies to show single proportions, and the aspect ratio of the bars (taller than typical). Which version is easier to understand?

To answer this question, I like to apply a self-sufficiency test. This test is used to determine whether the readers are using the visual elements of the chart to udnerstand the data, or are they bypassing the visual elements and just reading the data labels? So, let's remove the printed data from the chart and take another look:


For me, these charts are comparable. Each is moderately hard to read. That's because the percentages fall into a narrow range at one end of the range. For both charts, many readers are likely to be looking for the data labels.

Here's a sketch of a design that is self-sufficient.


The data do not appear on this chart.


My first reaction to Andy's tweet turned out to be a misreading of the charts. I thought he was disaggregating the pie chart, like we can unstack a stacked bar chart.


Looking at the data more carefully, I realize that the "proportions" are not part to the whole. Or rather, the whole isn't "all races" or "all education levels". The whole is all respondents of a particular type.