Pie charts and self-sufficiency

This graphic shows up in a recent issue of Princeton alumni magazine, which has a series of pie charts.

The story being depicted is clear: the school has been generously increasing the amount of financial aid given to students since 1998. The proportion receiving any aid went from 43% to 67% so about two out of three students who enrolled in 2023 are getting aid.

The key components of the story are the values in 1998 and 2023, and the growth trend over this period.

***

Here is an exercise worth doing. Think about how you figured out the story components.

Is it this?

Or is it this?

***

This is what I've been calling a "self-sufficiency test" (link). How much work are the visual elements doing in conveying the graph's message to you? If the visual elements aren't doing much, then the designer hasn't taken advantage of the visual medium.

Is this dataviz?

The message in this Visual Capitalist chart is simple - that big tech firms are spending a lot of cash buying back their own stock (which reduces the number of shares in the market, which pushes up their stock price - all without actually having improved their business results.)

But is this data visualization? How does the visual design reflect the data?

The chart form is a half-pie chart, composed of five sectors, of increasing radii. In a pie chart, the data are encoded in the sector areas. But when the sectors are of different radii, it's possible that the data are found in the angles.

The text along the perimeter, coupled with the bracketing, suggests that the angles convey information - specifically, the amount of shares repurchased as a proportion of outstanding share value (market cap). On inspection, the angles are the same for all five sectors, and each one is 180 degrees divided by five, the number of companies depicted on the chart, so they convey no information, unless the company tally is deemed informative.

Each slice of the pie represents a proportion but these proportions don't add up. So the chart isn't even a half-pie chart. (Speaking of which, should the proportions in a half-pie add up to 100% or 50%?)

What about the sector areas? Since the angles are fixed, the sector areas are directly proportional to the radii. It took me a bit of time to figure this one out. The radius actually encodes the amount spent by each company on the buyback transaction. Take the ratio of Microsoft to Meta: 20 over 25 is 80%. To obtain a ratio of areas of 80%, the ratio of radii is roughly 90%; and the radius of Microsoft's sector is indeed about 90% of that of Meta. The ratio between Alphabet and Apple is similar.

The sector areas represent the dollar value of these share buybacks, although these transactions range from 0.6% to 2.9% as a proportion of outstanding share value.

Here is a more straightforward presentation of the data:

I'm not suggesting using this display. The sector areas in the original chart depict the data in the red bars. It's not clear to me how the story is affected by the inclusion of the market value data (gray bars).

Neither the forest nor the trees

On the NYT's twitter feed, they featured an article titled "These Seven Tech Stocks are Driving the Market". The first sentence of the article reads: "The S&P 500 is at an all-time high, and investors have just a handful of stocks to thank for it."

Without having seen any data, I'd surmise from that line that (a) the S&P 500 index has gone up recently, and (b) most if not all of the gain in the index can be attributed to gains in the tech stocks mentioned in the headline. (For purists, a handful is five, not seven.)

The chart accompanying the tweet is a treemap:

The treemap is possibly the most overhyped chart type of the modern era. Its use here is tangential to the story of surging market value. That's because the treemap presents a snapshot of the composition of the index, but contains nothing about the trend (change over time) of the average index value or of its components.

***

Even in representing composition, the treemap is inferior to, gasp, a pie chart. Of course, we can only use a pie chart for small numbers of components. The following illustration takes the data from the NYT chart on the Magnificent Seven tech stocks, and compares a treemap versus a pie chart side by side:

The reason why the treemap is worse is that both the width and the height of the boxes are changing while only the radius (or angle) of the pie slices is varying. (Not saying use a pie chart, just saying the treemap is worse.)

There is a reason why the designer appended data labels to each of the seven boxes. The effect of not having those labels is readily felt when our eyes reach the next set of stocks – which carry company names but not their market values. What is the market value of Berkshire Hathaway?

Even more so, what proportion of the total is the market value of Berkshire Hathaway? Indeed, if the designer did not write down 29%, it would take a bit of work to figure out the aggregate value of yellow boxes relative to the entire box!

This design sucessfully draws our attention to the structural importance of various components of the whole. There are three layers - the yellow boxes (Magnificent Seven), the gray boxes with company names, and the other gray boxes. I also like how they positioned the text on the right column.

***

Going inside the NYT article itself, we find two line charts that convey the story as told.

Here's the first one:

They are comparing the most recent stock prices with those from October 12 2022, which is identified as the previous "low". (I'm actually confused by how the most recent "low" is defined, but that's a different subject.)

This chart carries a lot of good information, even though it does not plot "all the data", as in each of the 500 S&P components individually. Over the period under analysis, the average index value has gone up about 35% while the Magnificent Seven's value have skyrocketed by 65% in aggregate. The latter accounted for 30% of the total value at the most recent time point.

If we set the S&P 500 index value in 2024 as 100, then the M7 value in 2024 is 30. After unwinding the 65% growth, the M7 value in October 2022 was 18; the S&P 500 in October 2022 was 74. Thus, the weight of M7 was 24% (18/74) in October 2022, compared to 30% now. Consequently, the weight of the other 473 stocks declined from 76% to 70%.

This isn't even the full story because most of the action within the M7 is in Nvidia, the stock most tightly associated with the current AI hype, as shown in the other line chart.

Nvidia's value jumped by 430% in that time window. From the treemap, the total current value of M7 is $12.3 b while Nvidia's value is $1.4 b, thus Nvidia is 11.4% of M7 currently. Since M7 is 29% of the total S&P 500, Nvidia is 11.4%*29% = 3% of the S&P. Thus, in 2024, against 100 for the S&P, Nvidia's share is 3. After unwinding the 430% growth, Nvidia's share in October 2022 was 0.6, about 0.8% of 74. Its weight tripled during this period of time.

Chartjunk as marketing copy

I got some spam marketing message last week. How exciting. They even use a subject line that has absolutely nothing to do with its content, baiting me to open it. And open I did, to some data graphics horrors.

The marketer promises a whole series of charts to prove that art is a great asset class for investment returns.

The very first chart already caught my full attention. It's this one:

It's a simple bar chart, with four values. Looks innocuous.

I'm unable to appreciate the recent trend to align bars in the middle, rather than at their bases. So I converted it to the canonical form:

Do you see the problem?

The second value ($1.7 trillion) is exactly half the size of the first value ($3.4 trillion) and yet the second bar is two-thirds of the length of the first bar. So, the size of the second bar is exaggerated relative to its label – and that’s the bar displaying the market size for “art,” which is what the spammer is pitching.

The bottom pair of values share the same relationship: $0.8 trillion is exactly half of $1.6 trillion. Again, the relative lengths of those two bars are not 50% but slightly over 60%.

Did the designer think that the bar lengths could be customized to whatever s/he desires? This one is hard to crack.

***

The sixth chart in the series is a different kind of puzzle:

All three lines have the exact same labels but show different values over time.

***

And they have pie charts, of course. Take a look:

Something went wrong here too. I'll leave it to my readers who can certainly figure it out :)

***

These charts were probably spammed to at least thousands.

 

Accounting app advertises that it doesn't understand fractions

I captured the following image of an ad at the airport at the wrong moment, so you can only see the dataviz but not the text that came with it. The dataviz is animated with blue section circling around and then coming to a halt.

The text read something like "75% of the people who saw this ad subsequently purchased something". I think the advertiser was TripActions. It is an app for accounting. Too bad their numbers people don't know 75% is three-quarters and their donut chart showed a number larger than 75%.

***

Browsing around the TripActions website, I also found this pie chart.

The radius of successive sectors is decreasing as the size of the proportions shrinks. As a result, the same two sectors labeled 12% at the bottom have differently-sized areas. The only way this dataviz can work is if the reader decodes the angles sustained at the center, and ignores the areas of the sectors. However, the visual cues all point readers to the areas rather than the angles.

In this sense, the weakness of this pie chart is the same as that of the racetrack chart, discussed recently here.

In addition, the color dimension is not used wisely. Color can be used to group the expenses into categories, or it can be used to group them by proportion of total (20%+, 10-19%, 5-9%, 1-4%, <1%).

 

 

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!

A German obstacle course

A twitter user sent me this chart from Germany.

It came with a translation:

"Explanation: The chart says how many car drivers plan to purchase a new state-sponsored ticket for public transport. And of those who do, how many plan to use their car less often."

Because visual language should be universal, we shouldn't be deterred by not knowing German.

The structure of the data can be readily understood: we expect three values that add up to 100% from the pie chart. The largest category accounts for 58% of the data, followed by the blue category (40%). The last and smallest category therefore has 2% of the data.

The blue category is of the most interest, and the designer breaks that up into four sub-groups, three of which are roughly similarly popular.

The puzzle is the identities of these categories.

The sub-categories are directly labeled so these are easy for German speakers. From a handy online translator, these labels mean "definitely", "probably", "rather not", "definitely not". Well, that's not too helpful when we don't know what the survey question is.

According to our correspondent, the question should be "of those who plan to buy the new ticket, how many plan to use their car less often?"

I suppose the question is found above the column chart under the car icon. The translator dutifully outputs "Thus rarer (i.e. less) car use". There is no visual cue to let readers know we are supposed to read the right hand side as a single column. In fact, for this reader, I was reading horizontally from top to bottom.

Now, the two icons on the left and the middle of the top row should map to not buying and buying the ticket. The check mark and cross convey that message. But... what do these icons map to on the chart below? We get no clue.

In fact, the will-buy ticket group is the 40% blue category while the will-not group is the 58% light gray category.

What about the dark gray thin sector? Well, one needs to read the fine print. The footnote says "I don't know/ no response".

Since this group is small and uninformative, it's fine to push it into the footnote. However, the choice of a dark color, and placing it at the 12-o'clock angle of the pie chart run counter to de-emphasizing this category!

Another twitter user visually depicts the journey we take to understand this chart:

The structure of the data is revealed better with something like this:

The chart doesn't need this many colors but why not? It's summer.

 

 

 

 

Multicultural, multicolor, manufactured outrage

Twitter users were incensed by this chart:

It's being slammed as one of the most outrageous charts ever.

***

An image search reveals this chart form has international appeal.

In Kazakh:

In Turkish:

In Arabic, but the image source is a Spanish company:

In English, from an Indian source:

In Russian:

***

Some people are calling this a pie chart.

But it isn't a pie chart since the slices clearly add up to more than one full circle.

It may be a graph template from an infographics website. You see people are applying data labels without changing the sizes or orientation or even colors of the slices. So the chart form is used as a container for data, rather than an encoder.

***

The Twitter user who called this "outrageous" appears to want to protect the designer, as the words have been deliberately snipped from the chart.

Nevertheless, Molly White coughed up the source in a subsequent tweet.

A bit strange, if you stop and think a little. Why would Molly shame the designer 20 hours later after she decided not to?

 

 

According to Molly, the chart appeared on the website of an NFT company. [P.S. See note below]

Here's the top of the page that Molly White linked to:

Notice the author of this page. That's "Molly White",  who is the owner of this NFT company! [See note below: she's the owner of a satire website who was calling out the owner of this company.]

Who's more outrageous?

Someone creating the most outrageous chart in order to get clout from outraged Twitter users and drive traffic to her new NFT venture? Or someone creating the template for the outrageous chart form, spawning an international collection?

 

[P.S. 3/17/2022 The answer is provided by other Twitter users, and the commentors. The people spreading this chart form is more ourageous. I now realized that Molly runs a sarcastic site. When she linked to the "source", she linked to her own website, which I interpreted as the source of the image. The page did contain that image, which added to the confusion. I must also add her work looks valuable, as it assesses some of the wild claims in Web3 land.

]

[P.S. 3/17/2022 Molly also pointed out that her second tweet about the source came around 45 minutes after the first tweet. Twitter showed "20 hours" because it was 20 hours from the time I read the tweet.]

Graphing highly structured data

The following sankey diagram appeared in my Linkedin feed the other day, and I agree with the poster that this is an excellent example.

It's an unusual use of a flow chart to show the P&L (profit and loss) statement of a business. It makes sense since these are flows of money. The graph explains how Spotify makes money - or how little profit it claims to have earned on over 2.5 billion of revenues.

What makes this chart work so well?

The first thing to notice is how they handled negative flows (costs). They turned the negative numbers into positive numbers, and encoded the signs of the numbers as colors. This doesn't come as naturally as one might think. The raw data are financial tables with revenues shown as positive numbers and costs shown as negative numbers, perhaps in parentheses. Like this:

Now, some readers are sure to have an issue with using the red-green color scheme. I suppose gray-red can be a substitute.

The second smart decision is to pare down the details. There are only four cost categories shown in the entire chart. The cost of revenue represents more than two-thirds of all revenues, and we know nothing about sub-categories of this cost.

The third feature is where the Spotify logo is placed. This directs our attention to the middle of the diagram. This is important because typically on a sankey diagram you read from left to right. Here, the starting point is really the column labeled "total Spotify revenue". The first column just splits the total revenue between subscription revenue and advertising revenue.

Putting the labels of the last column inside the flows improves readability as well.

On the whole, a job well done.

***

Sankey diagrams have limitations. The charts need to be simple enough to work their magic.

It's difficult to add a time element to the above chart, for example. The next question a business analyst might want to ask is how the revenue/cost/profit structure at Spotify have changed over time.

Another question a business analyst might ask is the revenue/cost/profit structure of premium vs ad-supported users. We have a third of the answer - the revenue split. Depending on relative usage, and content preference, the mix of royalties is likely not to replicate the revenue split.

Yet another business analyst might be interested in comparing Spotify's business model to a competitor. It's also not simple to handle this on a sankey diagram.

***

I searched for alternative charts, and when you look at what's out there, you appreciate the sankey version more.

Here is a waterfall chart, which is quite popular:

Here is a stacked column chart, rooted at zero:

Of course, someone has to make a pie chart - in this case, two pie charts:

 

 

 

 

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.