The challenge: Model pitcher performance variability using MLB data.

Central question: Is a pitcher’s performance on any given night drawn from a fixed true talent, or does their “true ability” vary appearance-to-appearance?

What you’ll learn

• Modeling overdispersion in sports outcomes (Beta-Binomial models)
• Competing generative models: fixed talent vs. random game-by-game variation
• Model comparison using predictive performance (LOO, posterior predictive checks)
• Sequential Bayesian inference: updating beliefs in real time during games
• Ranking players under uncertainty

Hands-on: detect & model overdispersion; build two competing models of pitcher swinging-strike rates; compare models for ranking/evaluation/forecasting; generate stakeholder-ready visuals (calibration plots, rootograms, forest plots); perform in-game updates for current outing performance.

Exercises: Build a variety of Bayesian models on provided MLB data.

The core problem: When should you pool data across groups vs. treat each group separately?

What you’ll learn

• Why simple averages fail: the pooling vs. unpooling tradeoff
• Partial pooling: borrowing strength across groups intelligently
• When hierarchical models shine: nested data, small samples, extreme observations
• Regularization to the mean: extraordinary claims require extraordinary evidence

Hands-on: build your first hierarchical model from scratch in Bambi and PyMC; compare pooled, unpooled, and hierarchical approaches; choose centered vs. non-centered parameterization; posterior analysis and visualization with ArviZ; warm-up with biological data, then transition to sports thinking.

Exercises: Turn Session 1’s sports model into hierarchical variants.