Conversion Probability Tool Calculator

Calculator

Pick a method, provide inputs, then submit.

Responsive form: 3/2/1 columns

Method

Switch methods to reveal relevant inputs.

Confidence level

Used for intervals in each method.

Decision threshold

Used to label the prediction as likely or unlikely.

Feature-based model inputs

Compute p = 1 / (1 + e^-z) where z = b0 + Σ(bi·xi).

Intercept (b0)

Baseline log-odds when all features are zero.

Score standard error (optional)

If provided, interval uses z ± z*SE.

Notes

Keep values on consistent scales. Use 0/1 for binary indicators.

Feature 1 name

Coefficient b1

Value x1

Feature 2 name

Coefficient b2

Value x2

Feature 3 name

Coefficient b3

Value x3

Feature 4 name

Coefficient b4

Value x4

Feature 5 name

Coefficient b5

Value x5

Reset

How to use this calculator

Select a method based on the data you have.
Enter inputs using consistent units and scales.
Set a confidence level and, if relevant, targets.
Press Submit to view results below the header.
Download CSV or PDF for sharing and records.

Formula used

Logistic prediction

Score: z = b0 + Σ(bi·xi)

Probability: p = 1 / (1 + e^{-z})

Optional interval uses z ± z*SE then transforms back to p.

Bayesian update from counts

Prior: p ~ Beta(α, β)

Posterior: Beta(α + k, β + n − k) where k conversions in n visits.

Credible interval comes from posterior quantiles.

Wilson interval for observed rate

Observed: p̂ = k/n

Wilson CI uses a score-based adjustment for stability.

Useful when you only have visits and conversions.

Example data table

Sample rows you can mirror in your own dataset.

Session	Intent	Engagement	Returning	Pred. probability	Converted
101	0.90	0.70	1	42.00%	1
102	0.40	0.20	0	18.00%	0
103	0.65	0.55	0	31.00%	0
104	0.80	0.30	1	36.00%	1
105	0.25	0.60	0	22.00%	0
106	0.95	0.85	1	55.00%	1
107	0.55	0.10	0	19.00%	0
108	0.70	0.40	1	34.00%	1

These probabilities are illustrative, not fitted from the example.

What the probability score represents

The calculator outputs a probability between 0 and 1 that summarizes conversion likelihood for a session, lead, or cohort. In the feature-based mode, the probability comes from a logistic transformation of the score z (log-odds). Odds follow p/(1−p), so p=0.70 implies odds near 2.33. Use the score to rank prospects and compare scenarios across segments.

Choosing the right modeling mode

Use the feature-based model when you have coefficients from a fitted model and want scenario analysis. Use the evidence-based mode when you only have counts and want to blend past belief with new data. For example, 80 conversions in 1,000 visits is an 8.0% observed rate; with a Beta(2,8) prior, the posterior mean becomes 82/1010 = 8.12%. The sample-based mode reports a stable interval when you prefer classical summaries.

Interpreting uncertainty with intervals

Intervals quantify how much the estimate can vary with sampling noise. With count-only data, Wilson intervals remain stable even when rates are low. For k=4 conversions out of n=50 visits at 95% confidence, the interval is roughly 3.2% to 18.8%, showing meaningful uncertainty. In feature mode, providing the score standard error enables an interval on z that is transformed back to probability.

Thresholding for operational decisions

A threshold turns a probability into an action label. Choose it from cost and value rather than intuition. If an intervention costs $1 per user and the expected value of a conversion is $20, a break-even probability is 1/20 = 0.05. Higher thresholds reduce volume but increase precision, while lower thresholds increase reach at the cost of efficiency.

Sharing results for analysis workflows

Exports support audit trails and team alignment. The CSV captures inputs and outputs for reproducible analysis, while the PDF creates a lightweight report for stakeholders. Pair the exported probability with observed outcomes to monitor calibration, track drift, and refresh coefficients when performance changes in new traffic sources. Keep definitions consistent across dashboards and cohorts. For forecasting, multiply selected probability by planned traffic to estimate expected conversions and workload weekly, reliably, internally.

FAQs

Which method should I start with?

If you have trained coefficients and feature values, use the feature-based mode. If you only know visits and conversions, use the sample-based mode. Use the evidence-based mode when you want priors to stabilize early data.

What does the score z mean in feature mode?

z is the log-odds: z = b0 + Σ(bi·xi). Each unit increase in z multiplies odds by e. The probability is then p = 1/(1+e^{-z}).

How do I choose a reasonable prior?

Convert prior belief into pseudo-counts. A Beta(α,β) prior behaves like α−1 prior conversions and β−1 prior non-conversions. Start weak, such as α=1.5 and β=18.5, then update as evidence grows.

Why use Wilson intervals instead of a normal interval?

Wilson intervals avoid negative bounds and stay accurate when rates are near 0 or 1, or when sample sizes are small. They are generally tighter and better behaved than the simple p̂ ± z·SE approximation.

Can I set thresholds for different segments?

Yes. Different segments often have different values, costs, and base rates. Export results, evaluate precision and lift by segment, then set separate thresholds that meet capacity and ROI constraints.

How should I validate the calculator output?

Compare predicted probabilities with observed outcomes in bins (calibration), track AUC for ranking, and monitor drift in feature distributions. Refit coefficients or revise priors when performance drops across recent traffic windows.