The problem with slope charts

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tl;dr: Slope charts and other common ways of showing “before and after” data are almost always misleading. Using a “merged arrow chart” eliminates the risk of misleading readers.

A video version of this post is available if you prefer to watch rather than read.

We often need to visualize how a set of values changed between a “before” period and an “after” period. For example, maybe our company has recently implemented a new sales strategy and we want to see which country’s sales team improved the most after the new strategy was implemented. Probably the most common ways to visualize this kind of data are side-by-side pie charts or clustered bar charts:

While these are probably the most common ways to visualize “before and after” data, they’re virtually never the most effective ways. Many posts that have been written on this topic, virtually all of which mention slope charts as a better alternative:

Those posts generally do a good job of explaining why slope charts and are more effective than side-by-side pies or clustered bars in “before and after” situations, but you can probably see the reasons for yourself. For example, in the slope chart above, it’s much clearer that France’s sales increased the most because we notice right away that its line has a steeper slope than the others.

Hold the proverbial phone, though. The title of that chart isn’t “Which country’s sales increased the most?”, it’s “Which country improved its sales performance the most?” If that’s the question that we’re trying to answer, it’s the relative change (i.e., the % change) that matters, not the absolute change (i.e., the change in euros). When we look at relative change, though, a quite different picture emerges:

As it turns out, the French sales team isn’t the hero in this story, the Belgian sales team is. By a wide margin, in fact (52% improvement versus 35%). Indeed, the French team doesn’t even come in second (Austria also improved more). That sure isn’t what the slope chart seemed to say, though.

This isn’t a rare, straw-man problem because slope charts always make relative changes among small values look smaller than they really are. This is why I think that slope charts can be—and often are—misleading, and why I tend not to use them much anymore.

Another option for showing before-and-after scenarios is an arrow chart, which looks like this:

Unfortunately, though, these charts also suffer from the same perceptual problem as slope charts, i.e., France’s performance still looks like it improved far more than Belgium’s when, in reality, it improved less.

Is there a way to avoid misleading readers when visualizing before-and-after values, then? Well, the solution that I recommend in my Practical Charts course is what I call a “merged arrow chart”:

By showing relative changes (%) alongside absolute values (euros), readers get accurate answers to both “absolute” questions like “Which country had the highest sales after the change?” and “relative” questions such as “Which country improved their sales performance the most?” Yes, this is a busier chart but, if we don’t show the “relative change” values alongside the absolute values, the risk isn’t that readers will miss out on important insights, it’s that they’ll get completely wrong insights, which is obviously a much bigger problem.

Even when the relative changes among smaller values are less dramatic, it’s still necessary to show them alongside the absolute values. For example, in the chart below, the arrow chart on the left makes it look like Zuckerberg increased his wealth considerably more than other billionaires during the pandemic (ugh):

The “Change in %” chart on the right clarifies that, in reality, the relative increases in wealth were actually quite similar for all the billionaires in this list. Without the “Change in %” chart, many readers would conclude that Zuckerberg experienced a greater relative increase in wealth than the others even though, in fact, his wealth actually increased a bit less than most of the others, in relative terms.

If we don’t include the relative changes, at best, readers will wonder which values changed the least or most. At worst, it won’t even occur to readers to wonder that in the first place, and they’ll come away with a fundamentally incorrect understanding of the data. This is why, IMHO, showing relative changes on before-and-after charts isn’t just useful, it’s essential. Yes, technically, we only need to show relative changes when they’re relevant to the insights that the chart was designed to convey, but they’re almost always relevant in before-and-after situations. Even if the story that we want to tell is solely about absolute values, there’s still a high risk that readers will make incorrect relative inferences if we only show them a standard slope or arrow chart.

[Oct. 27, 2020 update: After this post was originally published, several people commented in this great Twitter thread that slope charts can be appropriate in situations when only the absolute change is relevant. This comment makes several implicit assumptions, though:

1. Most audiences understand the difference between relative change and absolute change.
2. Most audiences understand that the slopes of lines in slope charts only represent absolute change, not relative change.

I’ve seen even quite sophisticated audiences make mistake #2, though, and several data viz pros commented or DM’ed that they hadn’t really noticed this problem until reading this post. I think that these are far from safe assumptions, then (unfortunately).

If presented with the slope chart in my example and asked which country grew the most, I suspect that very few people would answer “Well, in absolute terms, France grew the most but, in relative terms, it’s unclear which country grew the most.” Most would just answer “France”. This is a problem because relative change is relevant more often than absolute change. The CEO ends up giving the “most improved” award to France when she should be giving it to Belgium.

Yes, sometimes relative change is truly irrelevant to a situation, and sometimes absolute change is truly irrelevant. The problem is that, with slope, arrow, and comet charts specifically, audiences tend to mash the two types of change together, perceiving absolute change as relative change. With other chart types, such as regular bar charts, this is less of an issue (though these have other important limitations in before-and-after situations).

Others commented that a best practice should be to ALWAYS show both relative and absolute values, but I wouldn’t go that far. The problem that I’m pointing out is specific to situations in which we’re comparing two sets of quantities and doesn’t apply to, say, showing absolute and percentage breakdowns of a total, or showing absolute and relative changes in rank (as opposed to changes in quantity).]

[Feb. 2, 2021 update: Astute readers, including Dan Zvinca and James Thomson, pointed out that slope charts would be a better choice than arrow charts in situations when we want to feature changes in rank, as opposed to changes in quantity. I agree with them since, in those particular situations, relative changes in quantity are truly unimportant and slope charts make changes in rank more visually obvious. Thanks guys!]

Finally, I want to flag an important caveat that applies to all of the charts in this post, which is that insights that are based on comparing just two time periods should be taken with a boulder of salt, which I discuss in this post.

What do you think? Agree? Disagree? Let me know in the comments.

By the way…

If you’re interested in attending my Practical Charts or Practical Dashboards course, here’s a list of my upcoming open-registration workshops.