Cite the lower bound,
not the point estimate.
The audit-defensible reporting standard for any model win-rate claim is the 95% Beta-Binomial credible interval, with the lower bound as the planning figure. Enter sample size and observed wins; this tool returns the posterior, the credible interval, and the gap to a configurable break-even bar.
Independent betting decisions, not Monte Carlo realizations.
Count of wins among the 226 trials above.
52.4% is the standard ATS break-even at -110. Adjust for your market.
Questions,
answered.
What is a Beta-Binomial credible interval?
The Beta-Binomial credible interval is the 95% probability range for an underlying win rate, given an observed count of wins out of trials. Under a uniform Beta(1,1) prior, the posterior on the win probability is Beta(wins + 1, trials − wins + 1); the credible interval is the [2.5th, 97.5th] percentile of that posterior. The lower bound is the figure that any audit-defensible win-rate claim should cite.
Why is the lower bound the planning figure?
The lower bound is the win rate that, given the observed sample, has a 97.5% posterior probability of being below the true rate. Sizing and planning against the lower bound builds in a margin against the single-season variance that point estimates conceal. A 65% point estimate on n=20 has a lower bound near coin-flip; a 65% point estimate on n=300 has a lower bound near 60%. The two claims are different and should not be reported the same way.
What's the break-even threshold for ATS betting?
At standard -110 odds (1.909 decimal), a bettor needs to win 52.4% of bets to break even after the bookmaker's vig. The default break-even bar on this calculator is 52.4% to match. Adjust if your market has different juice.
How is this different from a frequentist confidence interval?
A frequentist Wald or Wilson interval is computed under a fixed-true-rate, sample-the-data framing; a Bayesian credible interval is the posterior probability range over the underlying rate given the observed data. For small samples and edge cases (zero wins, all wins), the Bayesian formulation stays well-defined while frequentist Wald collapses. For the question 'what's the 95% range on the true win rate', the Bayesian credible interval is the direct answer.
How much sample do I need to push the lower bound above a break-even bar?
The interval width scales roughly as 1/sqrt(n). For a 60% point estimate, pushing the 95% CI lower bound above 52.4% typically requires several hundred independent samples; for a 55% point estimate, it requires thousands. The calculator reports the gap between the lower bound and the break-even bar so you can see how much room you have.
Beta-Binomial credible intervals are one of the eight rules in VAR's published validation discipline. See /methodology/protocol for the full spec, or the glossary entry for a longer-form explanation.