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Module 2 · Bayesian series tracker

Beta–Binomial conjugate updating

Pick a matchup. The prior on p = P(A wins a single game) is centred at the Bradley–Terry win probability, with effective sample size α₀ + β₀. Each game appended to the series increments α (A win) or β (B win), and the posterior tightens around the in-series win rate as more games are played. The shaded band is the 95% equal-tailed credible interval, which is a probability statement about p, not a long-run coverage claim about a procedure.

where the prior comes fromthe conjugate updatecredible vs. confidence