Binning Continuous Data into Categories with pd.cut()

Raw numbers are precise but hard to talk about. "A +143 run differential" means less to most readers than "elite." So we bin. Binning turns a continuous column into labeled categories, and pd.cut() is the tool: you hand it the bin edges and it sorts every value into a band. Here's the part people trip over — cut() is the equal-width sibling of qcut() (equal counts), and knowing which one you actually want is the whole lesson.

This builds on Percentile Ranks and Tiers, where qcut() first appeared. The data is the bundled sample_standings.csv (real 2023 MLB standings), so it runs offline.

1. You define the edges

   Pass bins= a list of cut points and labels= a name for each resulting band. Here, six equal-width 100-run bands span the realistic range of run differential.

   import pandas as pd
   
   df = pd.read_csv("sample_standings.csv")
   edges  = [-300, -200, -100, 0, 100, 200, 300]
   labels = ["-300 to -200", "-200 to -100", "-100 to 0",
             "0 to +100", "+100 to +200", "+200 to +300"]
   df["RD_band"] = pd.cut(df["RunDiff"], bins=edges, labels=labels)

   Every team now carries an RD_band label. Note there are six labels for seven edges — n bins always need n+1 edges, the single most common cut mistake.

2. Count the bands in order

   value_counts() tallies each band, and sort=False keeps them in their natural low-to-high order instead of sorting by frequency — essential when the categories have a meaningful sequence.

   counts = df["RD_band"].value_counts(sort=False)
   print(counts.to_string())

   Teams per equal-width band

   Teams per run-differential band:
   RD_band
   -300 to -200     2
   -200 to -100     3
   -100 to 0       11
   0 to +100        5
   +100 to +200     6
   +200 to +300     2
   
   Widest band holds 11 teams; unlike qcut, equal-width bins can be uneven.

   This is the key contrast with qcut: equal-width bins come out uneven. The middle "-100 to 0" band is crowded because most teams cluster near average, while the extreme bands hold only a couple of teams each. qcut would have forced roughly equal counts by moving the edges; cut keeps the widths fixed and lets the counts fall where they may.

3. Chart the distribution

   A bar of the counts is effectively a histogram with bins you chose by hand — useful when the boundaries carry real meaning (a winning record, a playoff cutoff) rather than arbitrary auto-bins.

   import matplotlib.pyplot as plt
   
   fig, ax = plt.subplots(figsize=(9, 5.5))
   ax.bar(range(len(counts)), counts.values, color="#B23A3A")
   ax.set_xticks(range(len(counts)))
   ax.set_xticklabels(counts.index, rotation=30, ha="right")
   ax.set_ylabel("number of teams")
   fig.savefig("cut_bands.png", dpi=144, bbox_inches="tight")

   

   The tall middle and short tails are the signature of a roughly bell-shaped distribution. Because you controlled the edges, the chart answers a specific question — "how many teams were within 100 runs of average?" — that auto-binning can't target.

Troubleshooting