Visualizing composite ratings

A twitter reader submitted the following chart from Autoevolution (link):

This is not a successful chart for the simple reason that readers want to look away from it. It's too busy. There is so much going on that one doesn't know where to look.

The underlying dataset is quite common in the marketing world. Through surveys, people are asked to rate some product along a number of dimensions (here, seven). Each dimension has a weight, and combined, the weighted sum becomes a composite ranking (shown here in gray).

Nothing in the chart stands out as particularly offensive even though the overall effect is repelling. Adding the overall rating on top of each column is not the best idea as it distorts the perception of the column heights. But with all these ingredients, the food comes out bland.

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The key is editing. Find the stories you want to tell, and then deconstruct the chart to showcase them.

I start with a simple way to show the composite ranking, without any fuss:

[Since these are mockups, I have copied all of the data, just the top 11 items.]

Then, I want to know if individual products have particular strengths or weaknesses along specific dimensions. In a ranking like this, one should expect that some component ratings correlate highly with the overall rating while other components deviate from the overall average.

An example of correlated ratings is the Customers dimension.

The general pattern of the red dots clings closely to that of the gray bars. The gray bars are the overall composite ratings (re-scaled to the rating range for the Customers dimension). This dimension does not tell us more than what we know from the composite rating.

By contrast, the Developers Ecosystem dimension provides additional information.

Esri, AzureMaps and Mapbox performed much better on this dimension than on the average dimension. 

***

The following construction puts everything together in one package:

Visual design is hard, brought to you by NYC subway

This poster showed up in a NY subway train recently.

Visual design is hard!

What is the message? The intention is, of course, to say Rootine is better than others. (That's the Q corner, if you're following the Trifecta Checkup.)

What is the visual telling us (V corner)? It says Rootine is yellow while Others are purple. What do these color mean? There is no legend to help decipher it. And yellow-purple doesn't have a canonical interpretation (unlike say, red-green). In theory, purple can be better than yellow.

The other mystery is the black dot on the fifth item. (This is the NYC subway so the poster could have been vandalized.) It could mean "diet + lifestyle analyzed" is a unique feature of Rootine, not available on any other platform. That implies purple to mean available but not as effective, which significantly lessnes the impact of the chart.

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Finally, let's imagine the data that may exist to support this chart.

The aggregation of all competitors to "Others" imposes a major challenge. If yellow means yes, and purple means no, we'd expect few if any purple dots because across all competitors, there is a good chance that at least one of them has a particular feature.

Next, I'm dubious about the claim of "precision dosed, unique to you". I'm imagining they are selling some kind of medicine or health food, which can be "dosed". Predictive modelers like to market their models as "personalized," unique to each person but such a thing is impractical. Before you start using their products, they have no data on you, or your response to those products. How could the recommendation be "precision dosed, unique to you"?

Even if you've used the product for a while, it will be tough to achieve a good level of optimality with so little data. In fact, given that your past data are used to generate actions intended to improve your health - that is to say, to cause the future data to diverge from the past data, how do you know that any change you observe next period is caused by the actions you took? The pre-post difference is both affected by temporal shifts and the actions you've taken. If the next period's metric improves, you may want to believe that the actions worked. If the next period's metric declines, are you willing to conclude that the actions you took backfired?

"Formulas improve with you". This makes me more worried than relieved.

***

Problems like these can be solved by showing our work to others. Sometimes, we're too immersed in our own world we don't see we have left off key information.

 

 

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:

 

 

 

 

Surging gas prices

A reader finds this chart hard to parse:

The chart shows the trend in gas prices in New York in the past two years.

This is a case in which the simple line chart works very well.

I added annotations as the reasons behind the decline and rise in prices are reasonably clear. 

One should be careful when formatting dates. The legend of the original chart looks like this:

In the U.S., dates typically use a M/D/Y format. The above dates are ambiguous. "Aug 19" can be August 19th or August, xx19.

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?

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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.

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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.

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From 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.

 

Did prices go up or down? Depends on how one looks at the data

The U.S. media have been flooded with reports of runaway inflation recently, and it's refreshing to see a nice article in the Wall Street Journal that takes a second look at the data. Because as my readers know, raw data can be incredibly deceptive.

Inflation typically describes the change in price level relative to the prior year. The month-on-month change in price levels is a simple seasonal adjustment used to remove the effect of seasonality that masks the true change in price levels. (See this explainer of seasonal adjustment.)

As the pandemic enters the second year, this methodology is comparing 2021 price levels to pandemic-impacted price levels of 2020. This produces a very confusing picture. As the WSJ article explains, prices can be lower than they were in 2019 (pre-pandemic) and yet substantially higher than they were in 2020 (during the pandemic). This happens in industry sectors that were heavily affected by the economic shutdown, e.g. hotels, travel, entertainment.

Here is how they visualized this phenomenon. Amusingly, some algorithm estimated that it should take 5 minutes to read the entire article. It may take that much time to understand properly what this chart is showing.

Let me save you some time.

The chart shows monthly inflation rates of hotel price levels.

The pink horizontal stripes represent the official inflation numbers, which compare each month's hotel prices to those of a year prior. The most recent value for May of 2021 says hotel prices rose by 9% compared to May of 2020.

The blue horizontal stripes show an alternative calculation which compares each month's hotel prices to those of two years prior. Think of 2018-9 as "normal" years, pre-pandemic. Using this measure, we find that hotel prices for May of 2021 are about 4% lower than for May of 2019.

(This situation affects all of our economic statistics. We may see an expansion in employment levels from a year ago which still leaves us behind where we were before the pandemic.)

What confused me on the WSJ chart are the blocks of color. In a previous chart, the readers learn that solid colors mean inflation rose while diagonal lines mean inflation decreased. It turns out that these are month-over-month changes in inflation rates (notice that one end of the column for the previous month touches one end of the column of the next month).

The color patterns become the most dominant feature of this chart, and yet the month-over-month change in inflation rates isn't the crux of the story. The real star of the story should be the difference in inflation rates - for any given month - between two reference years.

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In the following chart, I focus attention on the within-month, between-reference-years comparisons.

Because hotel prices dropped drastically during the pandemic, and have recovered quite well in recent months as the U.S. reopens the economy, the inflation rate of hotel prices is almost 10%. Nevertheless, the current price level is still 7% below the pre-pandemic level.

 

 

Plotting the signal or the noise

Antonio alerted me to the following graphic that appeared in the Economist. This is a playful (?) attempt to draw attention to racism in the game of football (soccer).

The analyst proposed that non-white players have played better in stadiums without fans due to Covid19 in 2020 because they have not been distracted by racist abuse from fans, using Italy's Serie A as the case study.

The chart struggles to bring out this finding. There are many lines that criss-cross. The conclusion is primarily based on the two thick lines - which show the average performance with and without fans of white and non-white players. The blue line (non-white) inched to the right (better performance) while the red line (white) shifted slightly to the left.

If the reader wants to understand the chart fully, there's a lot to take in. All (presumably) players are ranked by the performance score from lowest to highest into ten equally sized tiers (known as "deciles"). They are sorted by the 2019 performance when fans were in the stadiums. Each tier is represented by the average performance score of its members. These are the values shown on the top axis labeled "with fans".

Then, with the tiers fixed, the players are rated in 2020 when stadiums were empty. For each tier, an average 2020 performance score is computed, and compared to the 2019 performance score.

The following chart reveals the structure of the data:

The players are lined up from left to right, from the worst performers to the best. Each decile is one tenth of the players, and is represented by the average score within the tier. The vertical axis is the actual score while the horizontal axis is a relative ranking - so we expect a positive correlation.

The blue line shows the 2019 (with fans) data, which are used to determine tier membership. The gray dotted line is the 2020 (no fans) data - because they don't decide the ranking, it's possible that the average score of a lower tier (e.g. tier 3 for non-whites) is higher than the average score of a higher tier (e.g. tier 4 for non-whites).

What do we learn from the graphic?

It's very hard to know if the blue and gray lines are different by chance or by whether fans were in the stadium. The maximum gap between the lines is not quite 0.2 on the raw score scale, which is roughly a one-decile shift. It'd be interesting to know the variability of the score of a given player across say 5 seasons prior to 2019. I suspect it could be more than 0.2. In any case, the tiny shifts in the averages (around 0.05) can't be distinguished from noise.

***

This type of analysis is tough to do. Like other observational studies, there are multiple problems of biases and confounding. Fan attendance was not the only thing that changed between 2019 and 2020. The score used to rank players is a "Fantacalcio algorithmic match-level fantasy-football score." It's odd that real-life players should be judged by their fantasy scores rather than their on-the-field performance.

The causal model appears to assume that every non-white player gets racially abused. At least, the analyst didn't look at the curves above and conclude, post-hoc, that players in the third decile are most affected by racial abuse - which is exactly what has happened with the observational studies I have featured on the book blog recently.

Being a Serie A fan, I happen to know non-white players are a small minority so the error bars are wider, which is another issue to think about. I wonder if this factor by itself explains the shifts in those curves. The curve for white players has a much higher sample size thus season-to-season fluctuations are much smaller (regardless of fans or no fans).

 

 

 

 

Losses trickle down while gains trickle up

In a rich dataset, it's hard to convey all the interesting insights on a single chart. Following up on the previous post, I looked further at the wealth distribution dataset. In the previous post, I showed this chart, which indicated that the relative wealth of the super-rich (top 1%) rose dramatically around 2011.

As a couple of commenters noticed, that's relative wealth. I indiced everything to the Bottom 50%.

In this next chart, I apply a different index. Each income segment is set to 100 at the start of the time period under study (2000), and I track how each segment evolved in the last two decades.

This chart offers many insights.

The Bottom 50% have been left far, far behind in the last 20 years. In fact, from 2000-2018, this segment's wealth never once reached the 2000 level. At its worst, around 2010, the Bottom 50% found themselves 80% poorer than they were 10 years ago!

In the meantime, the other half of the population has seen their wealth climb continuously through the 20 years. This is particularly odd because the major crisis of these two decades was the Too Big to Fail implosion of financial instruments, which the Bottom 50% almost surely did not play a part in. During that crisis, the top 50% were 30-60% better off than they were in 2000. Is this the "trickle-down" economy in which losses are passed down (but gains are passed up)?

The chart also shows how the recession hit the bottom 50% much deeper, and how the recovery took more than a decade. For the top half, the recovery came between 2-4 years.

It also appears that top 10% are further peeling off from the rest of the population. Since 2009, the top 11-49% have been steadily losing ground relative to the top 10%, while the gap between them and the Bottom 50% has narrowed.

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This second chart is not nearly as dramatic as the first one but it reveals much more about the data.

 

Atypical time order and bubble labeling

This chart appeared in a Charles Schwab magazine in Summer, 2019.

This bubble chart does not print any data labels. The bubbles take our attention but the designer realizes that the actual values of the volatility are not intuitive numbers. The same is true of any standard deviation numbers. If you're told SD of a data series is 3, it doesn't tell you much by itself.

I first transformed this chart into the equivalent column chart:

Two problems surface on the axes.

For the time axis, the years are jumbled. Readers experience vertigo, as we try to figure out how to read the chart. Our expectation that time moves left to right is thwarted. This ordering also requires every single year label to be present.

For the vertical axis, I could have left out the numbers completely. They are not really meaningful. These represent the areas of the bubbles but only relative to how I measured them.

***

In the next version, I sorted time in the conventional manner. Following Tufte's classic advice, only the tops of the columns are plotted.

What you see is that this ordering is much easier to comprehend. Figuring out that 2018 is an average year in terms of volatility is not any harder than in the original. In fact, we can reproduce the order of the previous chart just by letting our eyes sweep top to bottom.

To make it even easier to read the vertical axis, I converted the numbers into an index, with the average volatility as 100 %  (assigned to 0% on the chart) .

Now, you can see that 2018 is roughly at the average while 2008 is 400% above the average level. (How should we interpret this statement? That's a question I pose to my statistics students. It's not intuitive how one should interpret the statement that the standard deviation is 5 times higher.)

 

 

This holiday retailers hope it will snow dollars

According to the Conference Board, the pandemic will not deter U.S. consumers from emptying their wallets this holiday season. Here's a chart that shows their expectation (link):

 

A few little things make this chart work:

The "More" category is placed on the left, as English-speaking countries tend to be read Left-to-Right, and it is also given the deepest green, drawing our attention.

Only the "More" segments have data labels. I'd have omitted the decimals. I suspect they are added because financial analysts may be multiplying these percentages to yield dollar amounts, in which case the extra precision helps.

The categories are ordered by the decreasing propensity of increased spending this year relative to last year. (The business community has an optimism bias.)

The choice of three shades of one color instead of three different colors keeps the chart clean.

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The use of snowflakes surely infuriates a hardcore Tufte fan although I like that they add a festive note to the presentation. The large snowflake isn't randomly positioned but placed exactly where it causes the least interference with the bar chart.