Posterior win rates
Shaded area under each curve is the credible interval. Hover or drag across the chart to read off probabilities.
Head to head
vsHow this works
For a deck with k successes in n trials (wins in games, or conversions in entries), the likelihood is binomial. With the Jeffreys prior Beta(½, ½) the posterior is Beta(k + ½, n − k + ½). This prior is the standard “uninformative” choice for a proportion: it’s invariant under reparameterisation and adds the weight of just one pseudo-observation.
The head-to-head treats the two decks as independent, so the joint posterior is the product of the two marginals. P(B > A) is computed by numerically integrating that joint density over the region above the diagonal; the difference B − A is summarised from 100,000 posterior draws.
Caveats: the model assumes every game is an independent trial with the same win probability. Real tournament data violates this (pilot skill, pod composition, the meta at each event), so the true uncertainty is wider than shown. In 4-player pods, a 25% win rate is the fair-share baseline.