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.

 

 

How to read this cost-benefit chart, and why it is so confusing

Long-time reader Antonio R. found today's chart hard to follow, and he isn't alone. It took two of us multiple emails and some Web searching before we think we "got it".

 

Antonio first encountered the chart in a book review (link) of Hal Harvey et. al, Designing Climate Solutions. It addresses the general topic of costs and benefits of various programs to abate CO2 emissions. The reviewer praised the "wealth of graphics [in the book] which present complex information in visually effective formats." He presented the above chart as evidence, and described its function as:

policy-makers can focus on the areas which make the most difference in emissions, while also being mindful of the cost issues that can be so important in getting political buy-in.

(This description is much more informative than the original chart title, which states "The policy cost curve shows the cost-effectiveness and emission reduction potential of different policies.")

Spend a little time with the chart now before you read the discussion below.

Warning: this is a long read but well worth it.

 

***

 

If your experience is anything like ours, scraps of information flew at you from different parts of the chart, and you had a hard time piecing together a story.

What are the reasons why this data graphic is so confusing?

Everyone recognizes that this is a column chart. For a column chart, we interpret the heights of the columns so we look first at the vertical axis. The axis title informs us that the height represents "cost effectiveness" measured in dollars per million metric tons of CO2. In a cost-benefit sense, that appears to mean the cost to society of obtaining the benefit of reducing CO2 by a given amount.

That's how far I went before hitting the first roadblock.

For environmental policies, opponents frequently object to the high price of implementation. For example, we can't have higher fuel efficiency in cars because it would raise the price of gasoline too much. Asking about cost-effectiveness makes sense: a cost-benefit trade-off analysis encapsulates the something-for-something principle. What doesn't follow is that the vertical scale sinks far into the negative. The chart depicts the majority of the emissions abatement programs as having negative cost effectiveness.

What does it mean to be negatively cost-effective? Does it mean society saves money (makes a profit) while also reducing CO2 emissions? Wouldn't those policies - more than half of the programs shown - be slam dunks? Who can object to programs that improve the environment at no cost?

I tabled that thought, and proceeded to the horizontal axis.

I noticed that this isn't a standard column chart, in which the width of the columns is fixed and uneventful. Here, the widths of the columns are varying.

***

In the meantime, my eyes are distracted by the constellation of text labels. The viewing area of this column chart is occupied - at least 50% - by text. These labels tell me that each column represents a program to reduce CO2 emissions.

The dominance of text labels is a feature of this design. For a conventional column chart, the labels are situated below each column. Since the width does not usually carry any data, we tend to keep the columns narrow - Tufte, ever the minimalist, has even advocated reducing columns to vertical lines. That leaves insufficient room for long labels. Have you noticed that government programs hold long titles? It's tough to capture even the outline of a program with fewer than three big words, e.g. "Renewable Portfolio Standard" (what?).

The design solution here is to let the column labels run horizontally. So the graphical element for each program is a vertical column coupled with a horizontal label that invades the territories of the next few programs. Like this:

The horror of this design constraint is fully realized in the following chart, a similar design produced for the state of Oregon (lifted from the Plan Washington webpage listed as a resource below):

In a re-design, horizontal labeling should be a priority.

 

***

Realizing that I've been distracted by the text labels, back to the horizontal axis I went.

This is where I encountered the next roadblock.

The axis title says "Average Annual Emissions Abatement" measured in millions metric tons. The unit matches the second part of the vertical scale, which is comforting. But how does one reconcile the widths of columns with a continuous scale? I was expecting each program to have a projected annual abatement benefit, and those would fall as dots on a line, like this:

Instead, we have line segments sitting on a line, like this:

Think of these bars as the bottom edges of the columns. These line segments can be better compared to each other if structured as a bar chart:

Instead, the design arranges these lines end-to-end.

To unravel this mystery, we go back to the objective of the chart, as announced by the book reviewer. Here it is again:

policy-makers can focus on the areas which make the most difference in emissions, while also being mindful of the cost issues that can be so important in getting political buy-in.

The primary goal of the chart is a decision-making tool for policy-makers who are evaluating programs. Each program has a cost and also a benefit. The cost is shown on the vertical axis and the benefit is shown on the horizontal. The decision-maker will select some subset of these programs based on the cost-benefit analysis. That subset of programs will have a projected total expected benefit (CO2 abatement) and a projected total cost.

By stacking the line segments end to end on top of the horizontal axis, the chart designer elevates the task of computing the total benefits of a subset of programs, relative to the task of learning the benefits of any individual program. Thus, the horizontal axis is better labeled "Cumulative annual emissions abatement".

 

Look at that axis again. Imagine you are required to learn the specific benefit of program titled "Fuel Economy Standards: Cars & SUVs".  

This is impossible to do without pulling out a ruler and a calculator. What the axis labels do tell us is that if all the programs to the left of Fuel Economy Standards: Cars & SUVs were adopted, the cumulative benefits would be 285 million metric tons of CO2 per year. And if Fuel Economy Standards: Cars & SUVs were also implemented, the cumulative benefits would rise to 375 million metric tons.

***

At long last, we have arrived at a reasonable interpretation of the cost-benefit chart.

Policy-makers are considering throwing their support behind specific programs aimed at abating CO2 emissions. Different organizations have come up with different ways to achieve this goal. This goal may even have specific benchmarks; the government may have committed to an international agreement, for example, to reduce emissions by some set amount by 2030. Each candidate abatement program is evaluated on both cost and benefit dimensions. Benefit is given by the amount of CO2 abated. Cost is measured as a "marginal cost," the amount of dollars required to achieve each million metric ton of abatement.

This "marginal abatement cost curve" aids the decision-making. It lines up the programs from the most cost-effective to the least cost-effective. The decision-maker is presumed to prefer a more cost-effective program than a less cost-effective program. The chart answers the following question: for any given subset of programs (so long as we select them left to right contiguously), we can read off the cumulative amount of CO2 abated.

***

There are still more limitations of the chart design.

• We can't directly read off the cumulative cost of the selected subset of programs because the vertical axis is not cumulative. The cumulative cost turns out to be the total area of all the columns that correspond to the selected programs. (Area is height x width, which is cost per benefit multiplied by benefit, which leaves us with the cost.) Unfortunately, it takes rulers and calculators to compute this total area.
  
  
• We have presumed that policy-makers will make the Go-No-go decision based on cost effectiveness alone. This point of view has already been contradicted. Remember the mystery around negatively cost-effective programs - their existence shows that some programs are stalled even when they reduce emissions in addition to making money!
  
  
• Since many, if not most, programs have negative cost-effectiveness (by the way they measured it), I'd flip the metric over and call it profitability (or return on investment). Doing so removes another barrier to our understanding. With the current cost-effectiveness metric, policy-makers are selecting the "negative" programs before the "positive" programs. It makes more sense to select the "positive" programs before the "negative" ones!

***

In a Trifecta Checkup (guide), I rate this chart Type V. The chart has a great purpose, and the design reveals a keen sense of the decision-making process. It's not a data dump for sure. In addition, an impressive amount of data gathering and analysis - and synthesis - went into preparing the two data series required to construct the chart. (Sure, for something so subjective and speculative, the analysis methodology will inevitably be challenged by wonks.) Those two data series are reasonable measures for the stated purpose of the chart.

The chart form, though, has various shortcomings, as shown here.  

***

In our email exchange, Antonio and I found the Plan Washington website useful. This is where we learned that this chart is called the marginal abatement cost curve.

Also, the consulting firm McKinsey is responsible for popularizing this chart form. They have published this long report that explains even more of the analysis behind constructing this chart, for those who want further details.

Who is a millennial? An example of handling uncertainty

I found this fascinating chart from CNBC, which attempts to nail down the definition of a millennial.

It turns out everyone defines "millennials" differently. They found 23 different definitions. Some media outlets apply different definitions in different items.

I appreciate this effort a lot. The design is thoughtful. In making this chart, the designer added the following guides:

• The text draws attention to the definition with the shortest range of birth years, and the one with the largest range.
• The dashed gray gridlines help with reading the endpoints of each bar.
• The yellow band illustrates the so-called average range. It appears that this average range is formed by taking the average of the beginning years and the average of the ending years. This indicates a desire to allow comparisons between each definition and the average range.
• The bars are ordered by the ending birth year (right edge).

The underlying issue is how to display uncertainty. The interest here is not just to feature the "average" definition of a millennial but to show the range of definitions.

***

In making my chart, I apply a different way to find the "average" range. Given any year, say 1990, what is the chance that it is included in any of the definitions? In other words, what proportion of the definitions include that year? In the following chart, the darker the color, the more likely that year is included by the "average" opinion.

I ordered the bars from shortest to the longest so there is no need to annotate them. Based on this analysis, 90 percent (or higher) of the sources list 19651985 to 1993 as part of the range while 70 percent (or higher) list 19611981 to 1996 as part of the range.

 

 

Tennis greats at the top of their game

The following chart of world No. 1 tennis players looks pretty but the payoff of spending time to understand it isn't high enough. The light colors against the tennis net backdrop don't work as intended. The annotation is well done, and it's always neat to tug a legend inside the text.

The original is found at Tableau Public (link).

The topic of the analysis appears to be the ages at which tennis players attained world #1 ranking. Here are the male players visualized differently:

Some players like Jimmy Connors and Federer have second springs after dominating the game in their late twenties. It's relatively rare for players to get to #1 after 30.

This Wimbledon beauty will be ageless

This Financial Times chart paints the picture of the emerging trend in Wimbledon men’s tennis: the average age of players has been rising, and hits 30 years old for the first time ever in 2019.

The chart works brilliantly. Let's look at the design decisions that contributed to its success.

The chart contains a good amount of data and the presentation is carefully layered, with the layers nicely tied to some visual cues.

Readers are drawn immediately to the average line, which conveys the key statistical finding. The blue dot  reinforces the key message, aided by the dotted line drawn at 30 years old. The single data label that shows a number also highlights the message.

Next, readers may notice the large font that is applied to selected players. This device draws attention to the human stories behind the dry data. Knowledgable fans may recall fondly when Borg, Becker and Chang burst onto the scene as teenagers.

 

Then, readers may pick up on the ticker-tape data that display the spread of ages of Wimbledon players in any given year. There is some shading involved, not clearly explained, but we surmise that it illustrates the range of ages of most of the contestants. In a sense, the range of probable ages and the average age tell the same story. The current trend of rising ages began around 2005.

 

Finally, a key data processing decision is disclosed in chart header and sub-header. The chart only plots the players who reached the fourth round (16). Like most decisions involved in data analysis, this choice has both desirable and undesirable effects. I like it because it thins out the data. The chart would have appeared more cluttered otherwise, in a negative way.

The removal of players eliminated in the early rounds limits the conclusion that one can draw from the chart. We are tempted to generalize the finding, saying that the average men’s player has increased in age – that was what I said in the first paragraph. Thinking about that for a second, I am not so sure the general statement is valid.

The overall field might have gone younger or not grown older, even as the older players assert their presence in the tournament. (This article provides side evidence that the conjecture might be true: the author looked at the average age of players in the top 100 ATP ranking versus top 1000, and learned that the average age of the top 1000 has barely shifted while the top 100 players have definitely grown older.)

So kudos to these reporters for writing a careful headline that stays true to the analysis.

I also found this video at FT that discussed the chart.

***

This chart about Wimbledon players hits the Trifecta. It has an interesting – to some, surprising – message (Q). It demonstrates thoughtful processing and analysis of the data (D). And the visual design fits well with its intended message (V). (For a comprehensive guide to the Trifecta Checkup, see here.)

Too much of a good thing

Several of us discussed this data visualization over twitter last week. The dataviz by Aero Data Lab is called “A Bird’s Eye View of Pharmaceutical Research and Development”. There is a separate discussion on STAT News.

Here is the top section of the chart:

We faced a number of hurdles in understanding this chart as there is so much going on. The size of the shapes is perhaps the first thing readers notice, followed by where the shapes are located along the horizontal (time) axis. After that, readers may see the color of the shapes, and finally, the different shapes (circles, triangles,...).

It would help to have a legend explaining the sizes, shapes and colors. These were explained within the text. The size encodes the number of test subjects in the clinical trials. The color encodes pharmaceutical companies, of which the graphic focuses on 10 major ones. Circles represent completed trials, crosses inside circles represent terminated trials, triangles represent trials that are still active and recruiting, and squares for other statuses.

The vertical axis presents another challenge. It shows the disease conditions being investigated. As a lay-person, I cannot comprehend the logic of the order. With over 800 conditions, it became impossible to find a particular condition. The search function on my browser skipped over the entire graphic. I believe the order is based on some established taxonomy.

***

In creating the alternative shown below, I stayed close to the original intent of the dataviz, retaining all the dimensions of the dataset. Instead of the fancy dot plot, I used an enhanced data table. The encoding methods reflect what I’d like my readers to notice first. The color shading reflects the size of each clinical trial. The pharmaceutical companies are represented by their first initials. The status of the trial is shown by a dot, a cross or a square.

Here is a sketch of this concept showing just the top 10 rows.

Certain conditions attracted much more investment. Certain pharmas are placing bets on cures for certain conditions. For example, Novartis is heavily into research on Meningnitis, meningococcal while GSK has spent quite a bit on researching "bacterial infections."

What is a bad chart?

In the recent issue of Madolyn Smith’s Conversations with Data newsletter hosted by DataJournalism.com, she discusses “bad charts,” featuring submissions from several dataviz bloggers, including myself.

What is a “bad chart”? Based on this collection of curated "bad charts", it is not easy to nail down “bad-ness”. The common theme is the mismatch between the message intended by the designer and the message received by the reader, a classic error of communication. How such mismatch arises depends on the specific example. I am able to divide the “bad charts” into two groups: charts that are misinterpreted, and charts that are misleading.

 

Charts that are misinterpreted

The Causes of Death entry, submitted by Alberto Cairo, is a “well-designed” chart that requires “reading the story where it is inserted and the numerous caveats.” So readers may misinterpret the chart if they do not also partake the story at Our World in Data which runs over 1,500 words not including the appendix.

The map of Canada, submitted by Highsoft, highlights in green the provinces where the majority of residents are members of the First Nations. The “bad” is that readers may incorrectly “infer that a sizable part of the Canadian population is First Nations.”

In these two examples, the graphic is considered adequate and yet the reader fails to glean the message intended by the designer.

 

Charts that are misleading

Two fellow bloggers, Cole Knaflic and Jon Schwabish, offer the advice to start bars at zero (here's my take on this rule). The “bad” is the distortion introduced when encoding the data into the visual elements.

The Color-blindness pictogram, submitted by Severino Ribecca, commits a similar faux pas. To compare the rates among men and women, the pictograms should use the same baseline.

In these examples, readers who correctly read the charts nonetheless leave with the wrong message. (We assume the designer does not intend to distort the data.) The readers misinterpret the data without misinterpreting the graphics.

 

Using the Trifecta Checkup

In the Trifecta Checkup framework, these problems are second-level problems, represented by the green arrows linking up the three corners. (Click here to learn more about using the Trifecta Checkup.)

The visual design of the Causes of Death chart is not under question, and the intended message of the author is clearly articulated in the text. Our concern is that the reader must go outside the graphic to learn the full message. This suggests a problem related to the syncing between the visual design and the message (the QV edge).

By contrast, in the Color Blindness graphic, the data are not under question, nor is the use of pictograms. Our concern is how the data got turned into figurines. This suggests a problem related to the syncing between the data and the visual (the DV edge).

***

When you complain about a misleading chart, or a chart being misinterpreted, what do you really mean? Is it a visual design problem? a data problem? Or is it a syncing problem between two components?

Tightening the bond between the message and the visual: hello stats-cats

The editors of ASA's Amstat News certainly got my attention, in a recent article on school counselling. A research team asked two questions. The first was HOW ARE YOU FELINE?

Stats and cats. The pun got my attention and presumably also made others stop and wonder. The second question was HOW DO YOU REMEMBER FEELING while you were taking a college statistics course? Well, it's hard to imagine the average response to that question would be positive.

What also drew me to the article was this pair of charts:

Surely, ASA can do better. (I'm happy to volunteer my time!)

Rotate the chart, clean up the colors, remove the decimals, put the chart titles up top, etc.

***

The above remedies fall into the V corner of my Trifecta checkup.

The key to fixing this chart is to tighten the bond between the message and the visual. This means working that green link between the Q and V corners.

This much became clear after reading the article. The following paragraphs are central to the research (bolding is mine):

Responses indicated the majority of school counselors recalled experiences of studying statistics in college that they described with words associated with more unpleasant affect (i.e., alarm, anger, distress, fear, misery, gloom, depression, sadness, and tiredness; n = 93; 66%). By contrast, a majority of counselors reported same-day (i.e., current) emotions that appeared to be associated with more pleasant affect (i.e., pleasure, happiness, excitement, astonishment, sleepiness, satisfaction, and calm; n = 123; 88%).

Both recalled emotive experiences and current emotional states appeared approximately balanced on dimensions of arousal: recalled experiences associated with lower arousal (i.e., pleasure, misery, gloom, depression, sadness, tiredness, sleepiness, satisfaction, and calm, n = 65, 46%); recalled experiences associated with higher arousal (i.e., happiness, excitement, astonishment, alarm, anger, distress, fear, n = 70, 50%); current emotions associated with lower arousal (n = 60, 43%); current experiences associated with higher arousal (i.e., n = 79, 56%).

These paragraphs convey two crucial pieces of information: the structure of the analysis, and its insights.

The two survey questions measure two states of experiences, described as current versus recalled. Then the individual affects (of which there were 16 plus an option of "other") are scored on two dimensions, pleasure and arousal. Each affect maps to high or low pleasure, and separately to high or low arousal.

The research insight is that current experience was noticably higher than recalled experience on the pleasure dimension but both experiences were similar on the arousal dimension.

Any visualization of this research must bring out this insight.

***

Here is an attempt to illustrate those paragraphs:

The primary conclusion can be read from the four simple pie charts in the middle of the page. The color scheme shines light on which affects are coded as high or low for each dimension. For example, "distressed" is scored as showing low pleasure and high arousal.

A successful data visualization for this situation has to bring out the conclusion drawn at the aggregated level, while explaining the connection between individual affects and their aggregates.

Book review: Visualizing Baseball

I requested a copy of Jim Albert’s Visualizing Baseball book, which is part of the ASA-CRC series on Statistical Reasoning in Science and Society that has the explicit goal of reaching a mass audience.

The best feature of Albert’s new volume is its brevity. For someone with a decent background in statistics (and grasp of basic baseball jargon), it’s a book that can be consumed within one week, after which one receives a good overview of baseball analytics, otherwise known as sabermetrics.

Within fewer than 200 pages, Albert outlines approaches to a variety of problems, including:

• Comparing baseball players by key hitting (or pitching) metrics
• Tracking a player’s career
• Estimating the value of different plays, such as a single, a triple or a walk
• Predicting expected runs in an inning from the current state of play
• Analyzing pitches and swings using PitchFX data
• Describing the effect of ballparks on home runs
• Estimating the effect of particular plays on the outcome of a game
• Simulating “fake” games and seasons in order to produce probabilistic forecasts such as X% chance that team Y will win the World Series
• Examining whether a hitter is “streaky” or not

Most of the analyses are descriptive in nature, e.g. describing the number and types of pitches thrown by a particular pitcher, or the change in on-base percentage over the career of a particular hitter. A lesser number of pages are devoted to predictive analytics. This structure is acceptable in a short introductory book. In practice, decision-makers require more sophisticated work on top of these descriptive analyses. For example, what’s the value of telling a coach that the home run was the pivotal moment in a 1-0 game that has played out?

To appreciate the practical implications of the analyses included in this volume, I’d recommend reading Moneyball by Michael Lewis, or the more recent Astroball by Ben Reiter.

For the more serious student of sabermetrics, key omitted details will need to be gleaned from other sources, including other books by the same author – for years, I have recommended Curve Ball by Albert and Bennett to my students.

***

In the final chapters, Albert introduced the simulation of “fake” seasons that underlies predictions. An inquiring reader should investigate how the process is tied back to the reality of what actually happened; otherwise, the simulation will have a life of its own. Further, if one simulates 1,000 seasons of 2018 baseball, a large number of these fake seasons would crown some team other than the Red Sox as the 2018 World Series winner. Think about it: that’s how it is possible to make the prediction that the Red Sox has a say 60 percent chance of winning the World Series in 2018! A key to understanding the statistical way of thinking is to accept the logic of this fake simulated world. It is not the stated goal of Albert to convince readers of the statistical way of thinking – but you’re not going to be convinced unless you think about why we do it this way.

***

While there are plenty of charts included in the book, a more appropriate title for “Visualizing Baseball” would have been “Fast Intro to Baseball Analytics”. With several exceptions, the charts are not essential to understanding the analyses. The dominant form of exposition is first describe the analytical conclusion, then introduce a chart to illustrate that conclusion. The inverse would be: Start with the chart, and use the chart to explain the analysis.

The visualizations are generally of good quality, emphasizing clarity over prettiness. The choice of sticking to one software, ggplot2 in R, without post-production, constrains the visual designer to the preferences of the software designer. Such limitations are evident in chart elements like legends and titles. Here is one example (Chapter 5, Figure 5.8):

By default, the software prints the names of data columns in the titles. Imagine if the plot titles were Changeup, Fastball and Slider instead of CU, FF and SL. Or that the axis labels were “horizontal location” and “vertical location” (check) instead of px and pz. [Note: The chart above was taken from the book's github site; in the  Figure 5.8 in the printed book, the chart titles were edited as suggested.]

The chart analyzes the location relative to the strike zone of pitches that were missed versus pitches that were hit (not missed). By default, the software takes the name of the binary variable (“Miss”) as the legend title, and lists the values of the variable (“True” and “False”) as the labels of the two colors. Imagine if True appeared as “Miss” and False as “Hit” .

Finally, the chart exhibits over-plotting, making it tough to know how many blue or gray dots are present. Smaller dot size might help, or else some form of aggregation.

***

Visualizing Baseball is not the book for readers who learn by running code as no code is included in the book. A github page by the author hosts the code, but only the R/ggplot2 code for generating the data visualization. Each script begins after the analysis or modeling has been completed. If you already know R and ggplot2, the github is worth a visit. In any case, I don’t recommend learning coding from copying and pasting clean code.

All in all, I can recommend this short book to any baseball enthusiast who’s beginning to look at baseball data. It may expand your appreciation of what can be done. For details, and practical implications, look elsewhere.