Randomness, Inference & Simulation

The hardest question in sports analytics isn't computing a number — it's deciding whether the number means anything. Ten tutorials on exactly that: simulate a season to see how much of a standings table is luck, bootstrap a confidence interval instead of pretending you have one, test a difference by shuffling, measure how many games that test needs before it can find anything, correct a whole screen of tests instead of cherry-picking its smallest p-value, update a belief the Bayesian way, watch extreme records regress to the mean on schedule, and finish by turning a single-game edge into exact best-of-seven odds.

Everything is built from scratch with numpy — no scipy black boxes — so when a p-value comes out, you watched it being made.

What you'll be able to do

• Simulate seasons with Monte Carlo and read the spread honestly
• Attach uncertainty to any stat with the bootstrap
• Test claims with permutation and chi-square tests you wrote yourself
• Measure a test's power by simulation and size a sample honestly
• Correct a family of tests with Bonferroni and the false discovery rate
• Update estimates as evidence arrives with Beta-Binomial updating
• Shrink an extreme early record toward the mean before forecasting with it
• Turn a single-game win probability into exact playoff-series odds

Download the course bundle - every script + dataset, one ZIP

The bundle contains each part's finished script, the shared helpers, and the sample data they read, with a README listing the run order - the whole course works offline.

The syllabus

Pace: Strictly in order - each part leans on the one before. Ten sittings.

1. 1Monte Carlo: How Much Does Luck Move a Season's Record?Intermediate · ~5 minBefore trusting any standings gap, see how much a coin-flip league produces.
2. 2Bootstrap a Confidence Interval: Is Home-Court Advantage Real or Luck?Intermediate · ~9 minError bars from resampling - no formula memorization required.
3. 3Is the Difference Real? A Permutation TestIntermediate · ~5 minThe significance test you can explain to anyone: shuffle and count.
4. 4Statistical Power: How Many Games Until You Can Trust a Stat?Intermediate · ~10 minThe question before the test: how many games until a real edge can even show up?
5. 5Multiple Comparisons: What Survives a 30-Test ScreenIntermediate · ~18 minOne p-value is a finding; thirty at once is a lottery - correct the count or be fooled.
6. 6Crosstabs: Build a Contingency Table to Test Home AdvantageIntermediate · ~5 minCategories cross-tabulated - the table every count-based test starts from.
7. 7The Chi-Square Test from Scratch: Is an NBA Floor Left-Right Symmetric?Intermediate · ~5 minIs the imbalance real? The classic test, built by hand.
8. 8Bayesian Updating: Learn a Win Probability Game by GameIntermediate · ~6 minBeliefs that update as evidence arrives - shooting percentages done properly.
9. 9Regression to the Mean: Why Hot Starts Cool Off, on ScheduleIntermediate · ~12 minThe slope is not 1: why every hot start cools, and exactly how far to shrink it.
10. 10Best-of-Seven Math: Why Series Favor Favorites (and by How Much)Intermediate · ~11 minThe payoff: seven games amplify a single-game edge, and now you can say by exactly how much.

Check yourself

Five questions, graded on the page, nothing recorded anywhere - pick an answer and the explanation appears.

Where next: Machine Learning from Scratch.