Bayesian A/B Testing Calculator

Compare two variants with practical Bayesian evidence today. Review lift, loss, risk, and intervals clearly. Export cleaner decisions for marketing, product, and growth teams.

Calculator

Example Data Table

Variant Visitors Conversions Prior Alpha Prior Beta Revenue Per Conversion
Control 10,000 820 1 1 $75
Variant B 9,800 890 1 1 $75

Formula Used

The calculator uses a beta-binomial Bayesian model for conversion data.

Posterior alpha: prior alpha + conversions.

Posterior beta: prior beta + visitors - conversions.

Posterior mean: posterior alpha / (posterior alpha + posterior beta).

Probability B beats A: simulated count where B rate exceeds A rate, divided by all simulations.

Expected loss choosing B: average value of max(A rate - B rate, 0).

Expected lift: (posterior mean B - posterior mean A) / posterior mean A.

Future revenue impact: future visitors × rate difference × revenue per conversion.

How to Use This Calculator

  1. Enter visitors and conversions for both variants.
  2. Keep alpha and beta as one for a flat prior.
  3. Change priors only when earlier evidence is reliable.
  4. Enter your decision threshold and practical lift.
  5. Add revenue per conversion for money impact.
  6. Press the calculate button.
  7. Review probability, lift, intervals, and expected loss.
  8. Download the result as CSV or PDF.

Understanding Bayesian A/B Testing

Bayesian A/B testing treats each conversion rate as an unknown value. It updates belief as real observations arrive. The method starts with a prior beta distribution. The prior can be flat, cautious, or based on past campaigns. After visits and conversions are entered, the calculator builds posterior beta distributions for both variants. These posteriors describe many likely true rates, not only one point estimate.

Why Posterior Probability Matters

Traditional tests often focus on a p value. Bayesian analysis asks a more direct question. It estimates the chance that variant B is better than variant A. It can also estimate the chance that A is better. This is useful for marketing pages, emails, pricing tests, product flows, and signup funnels. Teams can judge evidence in business terms. They can compare probability, lift, and possible regret before choosing a winner.

Risk, Loss, and Practical Lift

A variant may have a high probability of winning, yet still create small value. That is why practical lift matters. The calculator lets you enter a minimum useful lift. It also estimates expected loss per visitor. Expected loss shows the average penalty from choosing a weaker variant. Revenue per conversion turns rate differences into money. This helps teams avoid overreacting to tiny gains or noisy traffic.

Using Priors Responsibly

Priors should reflect honest knowledge. A flat prior, such as one and one, is common for new tests. Stronger priors may help when many similar tests already exist. However, very strong priors can hide new evidence. Use equal priors for fair comparisons unless you have a clear reason. Check sample size, traffic balance, and conversion tracking before trusting any result. Bayesian results are easy to read, but data quality still matters.

Decision Guidance

Use the recommendation as a guide, not an automatic rule. Launch a winner when posterior probability is high, loss is low, and lift is meaningful. Keep testing when the result is uncertain. Stop early only when the business risk is acceptable. Good decisions combine statistics, product judgment, and customer impact.

Document each test rule before launch. Record the prior choice, decision threshold, stopping plan, and main metric. This makes later reviews cleaner and reduces biased interpretation during analysis afterward.

FAQs

What is a Bayesian A/B test?

It is a test that updates belief about each variant after observing data. It gives probabilities for each conversion rate and compares them directly.

What prior should I use?

Use alpha one and beta one for a flat prior. Use stronger priors only when past tests are similar and trustworthy.

What does probability B beats A mean?

It means the estimated chance that Variant B has a higher true conversion rate than Variant A, based on the posterior distributions.

What is expected loss?

Expected loss is the average penalty from choosing a variant that may be worse. Lower expected loss means lower decision risk.

Why use practical lift?

Practical lift avoids decisions based on tiny gains. A variant should improve results enough to matter for the business.

Can I use this for revenue tests?

Yes, enter revenue per conversion. The calculator estimates future revenue impact from the posterior rate difference.

How many simulations should I run?

Thirty thousand iterations are enough for most page tests. Increase iterations when results are close or high precision is needed.

Can this replace business judgment?

No. Use it with tracking checks, customer impact, rollout risk, and product context. Statistics support decisions, but do not own them.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.