Percentile Ranks and Tiers: Locate a Team in the Distribution

A raw rank tells you a team is 8th of 30. A percentile rank tells you it's at the 73rd percentile — and here's why that's better: a position from 0 to 1 means the same thing whether the pool is 30 teams or 300 players, so scouting reports and projection systems lean on it instead of raw ranks. To show the idea in action I'll score every 2023 team by run-differential percentile, then chop the field into four quartile tiers.

This builds on Summary Statistics and Distributions. The data is the bundled sample_standings.csv (real 2023 MLB standings), so it runs offline.

1. Percentile rank in one call

   rank(pct=True) returns each row's rank as a fraction of the field instead of an integer. Multiply by 100 to read it as a familiar percentile.

   import pandas as pd
   
   df = pd.read_csv("sample_standings.csv")
   df["RD_pct"] = df["RunDiff"].rank(pct=True)   # 0.0 (worst) to 1.0 (best)

   The best team lands at 1.0, the worst near 0.03 (1/30), and the median team at roughly 0.5. Unlike a raw rank, this number is comparable across seasons of different sizes or across leagues with different team counts — "90th percentile" is "90th percentile" everywhere.

2. Tiers with qcut()

   Where rank gives a continuous position, qcut chops the column into equal-count buckets. Four buckets give quartile tiers with about the same number of teams in each.

   tiers = ["Bottom", "Lower-mid", "Upper-mid", "Top"]
   df["Tier"] = pd.qcut(df["RunDiff"], 4, labels=tiers)
   
   out = df.sort_values("RD_pct", ascending=False)[["Team", "RunDiff", "RD_pct", "Tier"]]
   out["RD_pct"] = (out["RD_pct"] * 100).round().astype(int)
   print(out.head(10).to_string())
   print(df["Tier"].value_counts().reindex(tiers).to_string())

   Percentiles and tiers, best to worst

           Team  RunDiff  RD_pct       Tier
   0     Braves      231     100        Top
   2    Dodgers      207      97        Top
   3       Rays      195      93        Top
   7    Rangers      165      90        Top
   5     Astros      129      85        Top
   1    Orioles      129      85        Top
   10     Twins      119      80        Top
   14    Padres      104      77        Top
   9   Mariners       99      73  Upper-mid
   13      Cubs       96      70  Upper-mid
   
   teams per tier:
   Tier
   Bottom       8
   Lower-mid    7
   Upper-mid    7
   Top          8

   Note qcut splits by quantity of teams, not by value: each tier holds roughly a quarter of the league regardless of how lopsided the run-differential gaps are. That's the difference from cut, which would split the value range into equal-width bands and could leave a tier empty.

3. Color the bars by tier

   A horizontal bar of each team's percentile, colored by its tier, shows the continuous score and the discrete bands at once. Dashed lines at the 25th, 50th, and 75th percentiles mark where the tiers change hands.

   import matplotlib.pyplot as plt
   
   tier_color = {"Bottom": "#B23A3A", "Lower-mid": "#C56A1E",
                 "Upper-mid": "#6F8F5F", "Top": "#2E7D4F"}
   s = df.sort_values("RD_pct")
   
   fig, ax = plt.subplots(figsize=(8, 9))
   ax.barh(s["Abbr"], s["RD_pct"] * 100, color=[tier_color[t] for t in s["Tier"]])
   for q in (25, 50, 75):
       ax.axvline(q, color="#9A8F79", lw=0.8, ls="--")
   ax.set_xlabel("run-differential percentile")
   fig.savefig("percentile_bars.png", dpi=144, bbox_inches="tight")

   

   Because the bars are sorted, the color bands stack cleanly and the dashed lines fall right where one color gives way to the next — a visual confirmation that the percentile and the tier tell the same story two ways.

Troubleshooting