Over at Daring Fireball, John Gruber makes a passing observation about the Apple Sports app:

I’ve got some gripes about certain specific aspects of Apple Sports. Like, where does one even start to explain how much is wrong with their zero-sum visualization of team stats? Has anyone ever even seen a presentation like that before? Anyone?

That “Anyone” link lands over here. Hi everyone! The team stats image is quite confusing. It’s a summary of a game between the San Antonio Spurs and the Oklahoma City Thunder. I don’t know much about basketball, but I do know a bit about data visualization and in a pleasing coincidence my former student Josh Fink is the A-VP of Basketball Data Science for the Spurs. Here is the image that John objected to:

I just finished driving a very long way up the side of the country, so I’m kind of tired. But even allowing for that, boy, this way of representing things really is quite confusing. Not being an Apple Sports user I had to look at it for a bit to understand what was happening. But, now that it has given me a headache, I can kind of see why whoever designed this ended up in the undoubtedly bad place they did.

Before I get to why I have some sympathy for the designer, why did I find this representation of these numbers so disorienting? It’s not just just because I’ve been driving for nine hours. John is right to call the picture a “Zero Sum” representation. The design strongly suggests to the viewer that, within each row, we’re looking at each team’s share of a total. Each pair of black and blue lines seem to be vying for control of their whole row, with the longest line being the “winner” in each case.

This sort of representation would make perfect sense for a measure that really was zero sum. Take an example from a properly good sport, like rugby. There, like in basketball, to a first approximation a team either has the ball or it doesn’t.¹ But there’s no shot clock in rugby, and possession routinely gets turned over without the game stopping. So, knowing that Team A had 65% possession is not only informative, it also immediately entails that Team B had 35%. You could show that with a representation like one of the rows above.

Literally none of the measures in the Basketball data above are zero-sum in this way. Both teams could shoot 100% from the free throw line, or zero percent. But because the first three measures shown are percentages, this reinforces the zero-sum impression given by the lines. It certainly did that in my case. But then, starting with Assists, the remaining rows are just absolute numbers. When I started looking at the absolute numbers, I got confused a second time by the length of the lines. “Oh so it’s not a share, it’s the value” I thought—but no, they do correspond in terms of relative proportions to the teams share within each row. But they’re not really shares they’re just magnitudes. But they have to be shown in a fixed space and we want to make them relatively comparable somehow so … Argh.

It would be nice if there were One Weird Trick to fully fix this figure. But I’m not sure that there is. For example, at a minimum we could redraw these numbers to reflect the fact that they’re not zero-sum. Keep each measure as a row (i.e. on the y-axis) but have the lines, or columns, be side by side within each category instead of facing off. Like this:

This view at least lets you immediately see who “won” each measure. The viewer can just directly compare the length of the bars in each category. People are really good at doing that accurately. In that sense it’s much less confusing than the original. But there’s still a lot wrong with it. The core problem is that when we draw a graph like this, we’re usually putting the same kind of thing (e.g. countries, or religious groups, or sports teams) on the y-axis, and then seeing how different their scores are on some single measure (e.g. GDP, or number of adherents, or average points scored per game), which we put on the x-axis. Maybe we use color to break things out by some third measure as well.² In this case, I’ve just labeled the x-axis as generically as possible. “Value” covers the range of all the measures. The lowest value is 5, in Largest Lead. The highest is 88, in Free Throw %. But these numbers are not meaningfully comparable. The graph encourages us to compare across as well as within categories. But while within-category comparisons are meaningful, the between-category ones are not. There were way more Bench Points than Blocks in the game. But that is not a useful thing to know.

Knowing who won each measure isn’t nothing. It can be informative about how the game went, maybe especially when a team won the game but “lost” on a number of the measures. If you really wanted to lean in to that aspect, you could sort of justify the zero-sum view, and maybe look for a way to sort and order by “how much” a team “won” each category. But again, what’s the right denominator for those measures? For instance, do we care about a team’s share of all Defensive Rebounds in the game? Or do we care about the share of Defensive Rebounds a team won relative to every opportunity it had to make a Defensive Rebound? How meaningful is ordering our rows by those kinds of shares? Even worse, some measures (notably Fouls) are bad to “win”, so we’d have to do something about those.

Our fundamental problem is that we just have two cases (the teams) and fifteen different measures, or variables. Each variable, except for the three percentages, is in effect on its own scale. There’s no direct way to make comparisons across them. Sure, some of these measures are probably going to be associated with one another—e.g. Turnovers and Points Off Turnovers—but the numeric values aren’t directly comparable in general. If you know a lot about basketball you might have some informative rules of thumb about each one of these measures, or some of them in combination. But at that point the lines in this particular graph are not going to be doing any work for you; you’ll just end up looking directly at the numbers. If we had data on all these measures for every NBA game for a whole season then we could of course do much more with them, because then each measure would have a distribution across all games and across all teams.

As it is, the purpose of the “Stats” screen in Apple Sports is just to summarize information from a single game. The other thing I could think of to do with the numbers as kind of graph is something like this:

This is marginally more helpful than the one before just because, again, it gets rid of the unhelpful zero-sum look of the original. As I hope you can immediately see, it creates many other difficulties. It also doesn’t do away with the core problem. That problem is principally one of information design rather than data visualization. What I mean is that what we’re trying to organize is, in effect, fifteen pairs of related but fundamentally distinct numbers. If we had fifteen cases and two variables things would be simple. But with fifteen variables and two cases … well, this is not the kind of thing you can make a single effective and non-confusing graph out of. That’s why I kind of sympathize with the designer. In a constrained space they have to show thirty numbers (thirty two, including the score). Lots of information. A straight table seems like it would be boring. Surely there’s some way to thematically integrate the numbers in a visually appealing manner that brings out some of the relationships across the rows. That’s what graphs do; it seems like the right thing to reach for. But at its heart this information is not a graph. It just sort of looks like one, and that ends up confusing people.