Most scatterplots end the same way: a cloud of dots, a mean, maybe an ellipse around everything. It looks rigorous. But sometimes, it hides the most interesting part of the data.
I realized this through golf.
I had a long break from the sport, but have recently started playing again, tracking my shots on a launch monitor. For months, I mostly looked at averages and spreads. Then I plotted one session properly and noticed something: the average described a shot I almost never hit.
The dataset is just 17 golf shots. You don't need to know anything about golf to see the problem. The same thing can happen with almost any scatterplot that gets reduced to a single summary.
A cloud of 17 points
I hit 17 shots with the same 7-iron, a mid-length golf club, at the same target. The launch monitor recorded two things about where each shot landed: its carry distance, or how far the ball travelled through the air before landing, and how far left or right it finished from the target line, the straight line between me and where I was aiming.
That gives me two variables to plot: carry distance on the y-axis and distance from the target line on the x-axis. The shots landed anywhere from 16 meters left to 8.5 meters right, with carry distance between 149 and 160 meters.
One small design choice matters here: both axes use the same scale. One meter left is the same visual distance as one meter forward. If you stretch one axis, you change the shape of the scatter without changing the data.
Figure 1. The 17 shots as dots, with equal scales on both axes. The mean is marked with a small cross.
The average tells a different story
The mean of the 17 shots is only 0.6 meters left of the target. That sounds pretty good.
If I only looked at the average, I might conclude that I'm consistently hitting close to where I'm aiming. But only 4 of the 17 shots landed within 2 meters of the target.
The mean isn't wrong. It just isn't telling me what I actually want to know. In this case, it describes a location, not a typical shot.
In fact, the mean lands in a part of the chart where very few shots actually exist. An ellipse doesn't solve the problem either. It wraps the entire cloud into one smooth shape and makes the distribution look like it gradually spreads out from the centre.
The misses have a pattern
The launch monitor records more than where the ball lands. It also tells me where the ball started and the direction the clubface—the part of the club that hits the ball—was pointing at impact. So I colored the shots by where they started.
Suddenly, the scatter made a lot more sense.
There are three groups:
Stock shot: 9 shots. This is my normal, intended shot: it starts slightly left and curves back toward the target.
Push: 6 shots. A push is a shot that starts right of the target and stays there. These finish 5-8.5 meters right.
Pull-hook: 2 shots. These start sharply left of the target and then curve even farther left. In golf, that's called a pull-hook. These finish 9 and 16 meters left.
The original cloud wasn't random. It was three different patterns sitting on top of each other. And that changes what the mean means.
The average is sitting between the stock shots and the pushes, with the two extreme hooks pulling it slightly left. It is an average of three different processes, but it doesn't really represent any of them.
This is the part I find most interesting.
The variable that explains a scatterplot might not be on either axis. Before summarizing a cloud, look at what else you recorded about each point. There may be a variable sitting in the background that explains why the cloud looks the way it does.
Figure 2. The same 17 shots, now colored by the three shot types. Each group is labelled directly rather than through a legend. The overall mean remains visible, showing how it falls in relatively sparse space.
A few design choices matter here:
Keep the categories limited. Three groups are easy to read. More would start adding noise.
Don't force an ellipse onto every group. With only 2–9 points per group, a fitted shape can suggest more certainty than the data supports.
Label the groups directly. There is no reason to make the reader bounce between the chart and a legend.
The pattern matters when there is something to lose
The scatter becomes even more useful when you put it against the thing you're actually trying to avoid. In golf, that might be a hazard or other trouble around the hole.
Imagine there's a hazard or other trouble along the left side. If I center my whole pattern on the target, most of my shots are fine. But the two pull-hooks reach the hazard.
Now shift the entire pattern 4 meters to the right. The stock shots finish slightly right of the target. The pushes go farther right, but they're still safe. Even the worst hook stays short of the hazard.
The average wouldn't have told me to do this.
In golf, you don't always aim directly at the final target. You can deliberately aim to give your typical shot, and especially your worst miss more room. Looking at the groups, and especially the group with the biggest consequence, gives me a much better way to make that decision.
Figure 3. A simplified top-down target with a hazard on the left. The shot pattern is shown once with the original aim point and once with the aim point shifted 4 meters right. The shift keeps every shot outside the hazard.
The same idea applies outside golf. Think about delivery times relative to a deadline. Sensor readings relative to a safety threshold. Forecasts relative to a budget.
Don't just show the distribution. Show what happens when the distribution meets the thing that matters.
Here’s a little swing sequence from one of my practice sessions.
