Enter your number of successes (S) and total trials (T), then select a confidence level to compute four point estimates at once: Maximum Likelihood (MLE), Laplace, Jeffrey, and Wilson. The best estimate is highlighted so you can immediately see the most reliable approximation of your unknown population parameter.
Best Point Estimate
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Maximum Likelihood Estimate (MLE)
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Laplace Estimate
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Jeffrey Estimate
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Wilson Estimate
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A point estimate is a single value used as a best guess for an unknown population parameter, such as a probability or proportion. It is derived from sample data and represents the most likely value of the parameter based on the observations collected.
The MLE is the simplest point estimate: divide the number of successes (S) by the total number of trials (T). Formula: MLE = S / T. It represents the proportion of successes in your sample and is the most commonly used estimate when sample sizes are large.
The Laplace estimate adds 1 to the successes and 2 to the trials before dividing: Laplace = (S + 1) / (T + 2). This smoothing technique prevents extreme estimates of 0 or 1 when successes are at the boundaries, making it more robust for small samples.
The Jeffrey estimate uses a Bayesian approach with a non-informative prior: Jeffrey = (S + 0.5) / (T + 1). It applies a smaller correction than Laplace and is considered a good compromise between pure MLE and more aggressive smoothing methods.
The Wilson estimate incorporates the z-score from your chosen confidence level: Wilson = (S + z²/2) / (T + z²), where z is the z-score corresponding to the confidence level (e.g., z ≈ 1.96 for 95%). It is especially reliable for small samples or extreme proportions near 0 or 1.
No single formula is universally best. For large samples, MLE performs very well. For small samples or when the proportion is near 0 or 1, Wilson or Jeffrey estimates tend to be more reliable. Many statisticians favor the Wilson estimate for its strong theoretical properties across all sample sizes.
A point estimate gives a single best-guess value for a parameter, while an interval estimate (or confidence interval) provides a range of plausible values with a stated level of confidence. Point estimates are simpler but carry no information about uncertainty; interval estimates convey the precision of the estimate.
Use this calculator whenever you have sample data from a series of trials — such as survey responses, clinical tests, or quality control checks — and you want to estimate the true underlying probability or proportion of success in the broader population.