scipy.stats — significance, distributions, intervals

Level 3 · Lesson 7

Hook

“Is this real, or is it noise?” comes up the moment you start making situational calls. scipy.stats is a small library that answers it: significance tests, distributions, confidence intervals, correlation. You don’t need a stats degree — you need the right test for the question.

Concept

Four tests handle most football questions:

Question shape	Test
”Are two groups’ averages different?”	`ttest_ind` (independent t-test)
“Is a frequency split different from chance?”	`chi2_contingency`
”Do these two metrics move together?”	`pearsonr` (linear) or `spearmanr` (rank)
“What’s a reasonable range for this average?”	`bootstrap` for a confidence interval

Common pattern:

from scipy import stats

# Goff's passing yards in wins vs losses — is the gap real or noise?
wins   = df.loc[df['result'] == 'W', 'passing_yards']
losses = df.loc[df['result'] == 'L', 'passing_yards']

t, p = stats.ttest_ind(wins, losses, equal_var=False)
print(f"t = {t:.2f}, p = {p:.3f}")

A p near 0.05 or below is the loose convention for “probably real.” Don’t over-claim with small samples — 17 games is not a lot of data.

Lions example

Bootstrap a 95% confidence interval for Lions points-per-game in 2024:

import numpy as np
import pandas as pd
from scipy import stats
from sqlalchemy import create_engine

eng = create_engine("postgresql+psycopg://onepride:lions@localhost:5432/onepride")

points = pd.read_sql(
    """
    SELECT CASE WHEN home_team = 'DET' THEN home_score ELSE away_score END AS pts
    FROM schedules
    WHERE season = 2024 AND game_type = 'REG'
      AND (home_team = 'DET' OR away_team = 'DET')
    """,
    eng,
)['pts'].to_numpy()

res = stats.bootstrap(
    (points,),
    statistic=np.mean,
    confidence_level=0.95,
    n_resamples=10_000,
    random_state=42,
)

print(f"Mean PPG: {points.mean():.1f}")
print(f"95% CI:   [{res.confidence_interval.low:.1f}, "
      f"{res.confidence_interval.high:.1f}]")

You’ll get a confidence interval that’s noticeably wide because the sample is small. That’s the data telling you “I’m not certain.” Respect it.

Try it

Test whether Lions rushing attempts are significantly higher in wins vs losses across the 2022-2024 regular seasons. (Pool three seasons — the 2024 split alone has just 2 losses, which makes the t-test essentially undefined.) Split by result, run an independent t-test, report t and p.

Common mistakes

equal_var=True by default. Don’t trust it — use equal_var=False (Welch’s t-test) unless you’ve confirmed equal variances. It’s the safer default.
Treating p < 0.05 as gospel. With 17 games per season, you’re often underpowered. Report the effect size and the interval, not just the p-value.
Pearson on non-linear data. pearsonr measures linear correlation. For rank-order relationships, spearmanr.
bootstrap without random_state. Pin the seed for reproducible results. Otherwise your “95% CI” jiggles every time you run the notebook.

Quick check

Which scipy test answers “are these two groups’ means different?”
Why use Welch’s t-test (equal_var=False) as the default?
What does n_resamples=10_000 control in stats.bootstrap?