I downloaded 2026 MLB OPS data through the end of August to create the following figures. I always start with Stem-and-Leaf Plots when I begin a study. This short post is not about the distribution of OPS in Major League Baseball; I simply want to illustrate the difference between Stem-and-Leaf Plots and Histograms. Why? I think it is a useful exercise, especially for aspiring scientists or anyone curious about how to approach data.
A histogram and a stem-and-leaf plot can look remarkably similar. Both are designed to reveal the distribution of a numerical variable. Both can show where observations cluster, where the tails extend, and whether the distribution appears symmetric or skewed.
But they do not show the data in quite the same way.
Consider the OPS values for the 142 players in this dataset. The values range from .542 to 1.035, with a mean of .756 and a median of .747. When those values are placed in a histogram, the overall shape of the distribution becomes immediately visible.
The histogram excels at this.
Grouping OPS values into intervals provides a quick visual summary of where most players are concentrated. We can see the center of the distribution, its spread, and the relatively small number of players occupying the extreme upper and lower ends. If the primary question is “What does this distribution look like?”, the histogram is difficult to beat.
There is a cost, however. The individual observations disappear.
Suppose a histogram bar represents OPS values between .750 and .775. We know how many players fall within that interval, but we cannot see their actual OPS values. A player with a .751 OPS and another with a .774 OPS are simply members of the same bin.
The stem-and-leaf plot preserves that information.
Using a key such as
0.7 | 5 = .75 OPS
we can still see the shape of the distribution, but the leaves retain the underlying observations. A cluster of leaves tells us that many players occupy a particular region, while the individual digits allow us to reconstruct their approximate OPS values.
The split-stem version offers an especially useful compromise. Each tenth is divided into two rows, with leaves 0 through 4 on one row and 5 through 9 on the next. It creates more visual separation than the highly condensed stem-and-leaf plot, without producing the very long display that results from using hundredths as individual stems.
This highlights an important distinction between the two techniques.
A histogram emphasizes shape.
A stem-and-leaf plot emphasizes shape while preserving the data.
That makes the histogram particularly effective for larger datasets and quick visual comparisons. The stem-and-leaf plot is often more revealing with small or moderate datasets because it allows us to move back and forth between the distribution and the observations that created it.
Neither graph is inherently better.
They answer slightly different questions.
The histogram asks us to look at the forest. The stem-and-leaf plot lets us see the forest while still being able to identify many of the trees.
For exploratory data analysis, there is considerable value in looking at both.
POSTSCRIPT
I took a closer look at the two plots from above. The most interesting thing about them is the extreme outlier evident at the higher end. This is exactly what Exploratory Data Analysis is for. The outlier is Yordan Alvarez of the Houston Astros. Take a look at the Box Plot I created based on the same data as the Stem-and-Leaf Plot and Histogram.
The small circle on the right-hand side represents Alvarez. He is having an exceptional season; his OPS is a bit of an anomaly. His performance is far above what everyone else in the league has achieved. In this instance, the Box Plot is my favorite visualization. It clearly shows how unusual Alvarez has been this year.
