A Correlation Heatmap: Which Team Stats Move Together

Hand me a table with six numeric columns and my first question is always the same: which of these move together? A correlation matrix answers it for every pair at once, and a heatmap turns that grid of numbers into something you can read in a glance — warm where stats rise together, cool where one rises as the other falls. Run it on NBA team ratings and the picture makes it obvious which number actually tracks winning.

This builds on Summary Statistics and Distributions. The data is the bundled nba_ratings.csv (per-100-possession team ratings, Basketball-Reference), so it runs offline.

1. One line builds the matrix

   .corr() computes the Pearson correlation between every pair of numeric columns — a value from −1 (perfect opposite) through 0 (no linear relationship) to +1 (perfect agreement).

   import pandas as pd
   
   df = pd.read_csv("nba_ratings.csv")
   cols = ["W", "ORtg", "DRtg", "NRtg"]
   corr = df[cols].corr().round(2)
   print(corr.to_string())

   The correlation matrix

            W  ORtg  DRtg  NRtg
   W     1.00  0.87 -0.75  0.98
   ORtg  0.87  1.00 -0.39  0.89
   DRtg -0.75 -0.39  1.00 -0.77
   NRtg  0.98  0.89 -0.77  1.00

   Read down the W (wins) column. Net rating correlates with wins at 0.98 — almost perfectly, as you'd hope from a stat built to summarize team quality. Offensive rating sits at 0.87. Defensive rating is −0.75: negative because a lower defensive rating is better, so allowing fewer points per 100 goes with winning more. The diagonal is all 1.00 — every column correlates perfectly with itself.

2. Turn the grid into a heatmap

   imshow draws the matrix as colored cells. A diverging colormap centered at zero is the right choice, so positive and negative correlations read as opposite colors; we annotate each cell so the exact value is there too.

   import matplotlib.pyplot as plt
   
   fig, ax = plt.subplots(figsize=(6.5, 5.5))
   im = ax.imshow(corr.values, cmap="RdBu_r", vmin=-1, vmax=1)
   ax.set_xticks(range(len(cols))); ax.set_xticklabels(cols)
   ax.set_yticks(range(len(cols))); ax.set_yticklabels(cols)
   for i in range(len(cols)):
       for j in range(len(cols)):
           ax.text(j, i, f"{corr.values[i, j]:.2f}", ha="center", va="center")
   fig.colorbar(im, ax=ax)
   fig.savefig("corr_heatmap.png", dpi=144, bbox_inches="tight")

   

   Setting vmin=-1, vmax=1 pins the color scale so zero is always the neutral midpoint — without it, matplotlib would stretch the colors to the data's range and exaggerate weak correlations. The deep-red wins/net-rating cell and the blue defensive-rating row tell the whole story at a glance.

3. Read it honestly

   Two cautions. First, correlation measures only a linear relationship, and it is not causation — net rating correlates with wins because it's essentially a restatement of them, not because it causes them. Second, a near-zero correlation means no linear link, not "no relationship" (a U-shaped pattern can hide at zero). A heatmap is a fast way to find leads worth investigating, not a verdict. For quantifying a single relationship properly, fit a line — see correlation and regression.

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