Bayesian Methods for Sports Analytics

Bayesian Thinking in Sports Analytics

Bayesian methods are particularly powerful in sports analytics because they allow us to combine prior knowledge with observed data. This is crucial when dealing with small sample sizes, new players, or uncertain information.

Core Concepts

• Prior: What we believe before seeing data (e.g., league average)
• Likelihood: How likely is the observed data given parameters
• Posterior: Updated belief after seeing data
• Credible Interval: Range containing true value with X% probability

Sports Applications

Beta-Binomial Model

Perfect for rate statistics (batting average, FG%, save percentage):

• Prior: Beta(α, β) where α/(α+β) = expected rate
• After n trials with k successes: Beta(α+k, β+n-k)
• Posterior mean: (α+k)/(α+β+n)

Key Takeaways

• Bayesian methods naturally handle uncertainty
• Priors should be based on real domain knowledge
• Results are interpretable as probabilities
• Hierarchical models share information across players
• Great for small sample sizes common in sports