Bayesian Test Duration Calculator

Predict experiment duration using Bayesian evidence and traffic assumptions. Compare variants, priors, and conversion goals. Make faster launch decisions with practical probability based planning.

Calculator Inputs

Example Data Table

Scenario Baseline Rate Expected Lift Daily Visitors Split Posterior Target Prior Strength Estimated Days
Recommendation model update 8.00% 12.00% 5000 50 / 50 95.00% 100 About 7 to 14 days
Prompt variant test 4.20% 8.00% 18000 60 / 40 97.50% 80 About 6 to 12 days
Ranking change on low traffic page 2.10% 5.00% 2400 50 / 50 95.00% 50 About 30 to 60 days

Formula Used

This tool uses a practical Bayesian planning approximation for two variants.

1. Baseline rate: p0 = baseline_rate / 100

2. Variant rate: p1 = p0 × (1 + expected_lift / 100)

3. Prior for each arm: Beta(1 + m × p0, 1 + m × (1 - p0)), where m is prior strength.

4. Posterior mean for each arm: alpha / (alpha + beta)

5. Posterior variance for each arm: (alpha × beta) / (((alpha + beta)^2) × (alpha + beta + 1))

6. Difference model: diff = mean_variant - mean_control

7. Probability variant beats control is approximated from a normal model on the posterior difference.

8. Duration equals the first evaluation day where sample, conversion, and posterior targets are all satisfied.

How to Use This Calculator

  1. Enter the current baseline conversion rate.
  2. Enter the relative lift you believe the new variant can achieve.
  3. Provide daily visitors and the control and variant traffic allocation.
  4. Set prior strength based on how much trusted historical data you have.
  5. Choose the posterior probability threshold needed for a decision.
  6. Define minimum sample size, minimum conversions, and the first day you allow review.
  7. Set the evaluation interval and the maximum runtime window.
  8. Adjust the traffic realization factor when actual traffic may be lower than forecast.
  9. Click the calculate button to see projected runtime, posterior metrics, and export options.

Bayesian Test Duration Calculator for AI and Machine Learning

Why test duration matters

A Bayesian test duration calculator helps teams estimate how long an experiment should run. That matters in AI and Machine Learning work. Product teams test ranking models, prompts, onboarding flows, and recommendation systems. Ending too early increases risk. Running too long wastes traffic, time, and engineering effort.

What this calculator estimates

This calculator combines baseline conversion rate, expected lift, traffic split, and prior strength. It then estimates the sample needed per variant. Next, it converts that sample into days. It also checks minimum samples, minimum conversions, and a target posterior probability. The result gives a practical runtime estimate for a two variant Bayesian experiment.

Why Bayesian planning is useful

Bayesian planning is useful because it matches real decision making. Teams often ask, “What is the probability the new version is better?” That is a Bayesian question. Instead of focusing only on fixed horizon significance, Bayesian testing uses priors and posterior updates. This makes the framework flexible for product optimization and model iteration.

Inputs that strongly affect duration

Low baseline conversion rates usually extend the test. Small expected lifts also extend the test. Higher posterior certainty targets need more evidence. Uneven traffic splits slow one arm and can delay completion. Stronger priors can shorten the estimate when prior information is trustworthy. Lower real traffic also increases total days.

Where AI teams use it

AI teams use Bayesian experiments in many places. They compare chatbot prompts. They test model assisted search. They evaluate recommendation policies. They monitor checkout ranking, fraud rules, and retention flows. A duration estimate helps teams plan launch calendars, stakeholder reviews, and experiment queues with less guesswork.

Use the estimate correctly

This tool gives an informed estimate, not a guarantee. Real results still depend on actual behavior, seasonality, tracking quality, and data drift. Use it before launch. Recheck assumptions when traffic changes. Pair it with sound metrics and clear stop rules. That creates faster, safer, and more reliable experiment decisions. It is helpful when experiment portfolios are large and each week affects revenue, learning speed, planning quality, and confidence.

FAQs

1. What does this calculator estimate?

It estimates how many days a Bayesian A/B test may need before the variant has enough evidence to beat control under your chosen rules.

2. Why do low conversion rates increase test duration?

Low rates create fewer conversions per day. That means weaker evidence builds more slowly, so the model needs more time or more traffic.

3. Does a stronger prior always reduce the duration?

No. A stronger prior only helps when it is credible and aligned with reality. Weak or biased prior assumptions can distort planning.

4. Can I use this for prompt testing or model ranking tests?

Yes. Use it when your success metric is a rate or binary outcome, such as click, conversion, accept, or win rate.

5. Why are minimum samples and minimum conversions included?

They prevent decisions based on very early noise. They also make the runtime estimate more realistic for production experiments.

6. Is this the same as a frequentist sample size calculator?

No. This tool plans around posterior probability and priors. Frequentist tools plan around significance, alpha, and power targets.

7. Should I stop the test as soon as the threshold is reached?

Only if that stop rule was defined before launch. Predefined rules reduce bias and make your decision process more consistent.

8. What should I do if traffic drops during the test?

Update the traffic realization factor and rerun the estimate. Lower traffic often lengthens runtime and may change planning decisions.