Beware the Radar Chart!

Along with the explosion of interest in visualizing data over the past few years has been an excessive focus on how attractive the graph is at the expense of how useful it is. Don't get me wrong...I believe that a colorful, modern graph comes across better than a black-and-white, pixelated one. Unfortunately, however, all the talk seems to be about the attractiveness and not the value of the information presented.

Although perhaps not the most egregious example, one that sticks out to me is the radar chart (also known as the spider chart). The web site Mock Draftable provides radar charts for every prospect in the NFL draft. For example, here is their radar chart for defensive end Dadi Nicolas of Virginia Tech:

This chart uses Dadi's percentiles among other defensive-end prospects on some body measurements and physical tests completed at the combine. It attempts to convey:

1. How well Dadi measures against the other prospects in each measurement, by providing a point on the axis pertaining to that measurement.
2. How good Dadi is overall, by connecting the dots and enclosing a polygon that has an area that increases as individual measurements increase.
3. How "well rounded" Dadi is by looking at how rounded the polygon is...more round indicates a more balanced player, and one with more peaks indicates a less balanced player.

There is no question that what the eye is immediately drawn to is the area covered by the shaded polygon. This is a very misleading graph because of that and I'll explain why. For starters, the order of the categories as you read each axis on the chart is arbitrary. In this example it begins with physical attributes and continues through physical tests in no meaningful order. Allow me to provide four examples of radar charts for Dadi Nicolas that plot the exact same information but change the order of the categories:

If I didn't tell you these were all the same player, you would have to carefully inspect the axes and specific numbers to figure it out. But more broadly, you could draw contradictory conclusions as you look through them:

1. These certainly give different impressions of how well-rounded Dadi is. Charts 1 and 4 appear to show a player that is exceptional in some categories and not very good at all in others. Charts 2 and 3 appear to show a much more balanced player.
2. The area of the polygon on the charts varied wildly and gives completely different impression of the overall skill of the player. Chart 4 covers 20% of the available area while chart 3 covers 40%...using the same information.

I could go into the mathematical details on why the area differs so much but I think the pictures above are worth 1000 words.

If I were asked to chart Dadi's statistics, I could quite easily use Minitab to provide one that conveys the information in a better format. To start, I would use an Individual Value Plot so that I can asses where the player lies on the distribution of prospects, rather than looking at the percentile. I would then create a grouping variable to highlight Nicolas' data on the graph. Then I would place the categories in order of importance—I'm obviously not an NFL scout, but I did a quick correlation on these stats for the 2015 prospects and their draft position to come up with a rough order.

With more work I might come up with some even better ideas, but the point here is to illustrate how quickly a more informative graph could be produced. My graph looks like this (after some editing for looks...that still matters, after all!):

Now I can quickly make the following assessments without being mislead:

1. Dadi is roughly average when all characteristics are combined, but not impressive on two of the three most important categories—40-yard sprint and weight.
2. By plotting the raw values and not just percentile, we see that Dadi not only had the highest vertical jump, but was well above all others. In fact, the gap from Dadi to the 2nd-highest equals the gap from 2nd to 10th.
3. Nicolas is in fact unique and not balanced.

Of course, instead of using an Individual Value Plot, you could also just watch a freshman Dadi Nicolas chase down future NFL wide receiver Brandon Coleman:

Just don't use a radar chart!