Wilson Confidence Interval
The Wilson Score Interval is a confidence interval for a binomial proportion that remains accurate even when N is small or the true proportion is near 0 or 1.
The math
CI = [p̃ ± (z²/2n ± z√(p̂(1−p̂)/n + z²/(4n²))) / (1 + z²/n)]p̂ = observed win rate, n = trade count, z = z-score for desired confidence level (1.96 for 95%).
Why it matters
The naive normal-approximation interval (p̂ ± 1.96√(p̂(1−p̂)/n)) breaks down at small N or extreme proportions — it can produce intervals outside [0, 1]. Wilson's 1927 formula avoids this by "centering" the interval differently. Pancake uses Wilson CI for win-rate confidence intervals on every receipt.
Wilson CI assumes each trade outcome is independent and identically distributed — a strong assumption for strategies trading in related markets. It also produces an asymmetric interval (wider on one side when p̂ is not 0.5), which is correct but sometimes surprising.
Published source
Wilson, E. B. (1927). "Probable Inference, the Law of Succession, and Statistical Inference." Journal of the American Statistical Association, 22(158), 209–212.