Crosstabs: Build a Contingency Table to Test Home Advantage

"Teams win more at home" is a hunch. A contingency table turns it into numbers. pd.crosstab() counts how often two categorical variables occur together — here, who won (home or away) against how decisive the game was — and one keyword flips those counts into the rates that tell the story. We'll find that home advantage isn't flat: it barely exists in tight games and balloons in blowouts.

This builds on Group, Pivot, and Reshape. The data is the bundled nba_home_results.csv (real 2023-24 NBA game results), so it runs offline.

1. Make two categorical columns

   A crosstab needs two category columns. We derive both from the score: who won, and which margin band the game fell into. pd.cut bins the absolute margin into labeled tiers.

   import pandas as pd
   
   games = pd.read_csv("nba_home_results.csv")
   games["winner"] = (games["home_pts"] > games["away_pts"]).map({True: "Home", False: "Away"})
   games["abs_margin"] = (games["home_pts"] - games["away_pts"]).abs()
   games["margin_tier"] = pd.cut(games["abs_margin"], bins=[0, 5, 10, 20, 100],
                                 labels=["1-5", "6-10", "11-20", "21+"])

   That gives every game a winner (Home/Away) and a margin_tier — exactly the two axes of the table we want.

2. crosstab counts the pairs

   Pass the two columns and crosstab returns a grid: rows are margin tiers, columns are winners, cells are how many games fall in each combination. Add normalize="index" and each row becomes proportions that sum to 1.

   counts = pd.crosstab(games["margin_tier"], games["winner"])
   rates  = pd.crosstab(games["margin_tier"], games["winner"], normalize="index").round(3)
   print(counts.to_string())
   print(rates.to_string())
   print("Overall home win rate:", round((games["winner"] == "Home").mean(), 3))

   Counts, then home/away share within each tier

   Counts:
   winner       Away  Home
   margin_tier            
   1-5           132   155
   6-10          173   173
   11-20         184   196
   21+            73   145
   
   Row-normalized (home/away share within each margin tier):
   winner        Away   Home
   margin_tier              
   1-5          0.460  0.540
   6-10         0.500  0.500
   11-20        0.484  0.516
   21+          0.335  0.665
   
   Overall home win rate: 0.543

   Read the bottom row: in games decided by 21+ points, the home team won about two-thirds of the time, versus a near-even split in 6-10 point games. The overall home win rate (~0.54) hides that structure — the crosstab is what exposes it.

3. Chart the row you care about

   The normalized table already holds the answer; a bar of the home-win share per tier makes the trend impossible to miss. A reference line at 50% marks "no advantage".

   import matplotlib.pyplot as plt
   
   home_share = rates["Home"] * 100
   fig, ax = plt.subplots(figsize=(8, 5.5))
   ax.bar(home_share.index.astype(str), home_share.values, color="#C56A1E")
   ax.axhline(50, color="#20242B", lw=1, ls="--")   # 50% = no home advantage
   ax.set_xlabel("final margin (points)"); ax.set_ylabel("home share of wins (%)")
   fig.savefig("home_advantage_crosstab.png", dpi=144, bbox_inches="tight")

   

   A natural reading is that home advantage shows up most when games get away from a team — close games are coin-flips, but lopsided ones tilt home. The crosstab doesn't explain why; it just gives you the clean, countable pattern to reason about.

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