Calculator Inputs
Example Data Table
This example shows how coefficients and values combine into a score (z) and then a probability.
| Scenario | b₀ | β₁·x₁ | β₂·x₂ | β₃·x₃ | z | Probability (logistic) |
|---|---|---|---|---|---|---|
| A | -0.60 | 0.80 | 0.00 | 0.50 | 0.70 | 0.6682 |
| B | -0.60 | 0.00 | -0.40 | 0.75 | -0.25 | 0.4378 |
| C | 0.10 | 0.80 | -0.40 | 0.25 | 0.75 | 0.6792 |
| D | 0.10 | 1.60 | 0.00 | 0.00 | 1.70 | 0.8455 |
| E | -1.20 | 0.80 | -0.80 | 1.00 | -0.20 | 0.4502 |
Formula Used
First compute the score: z = b₀ + Σ(βᵢ · xᵢ)
Logistic Probability
p = 1 / (1 + e^(−z))
Interpretable via odds: odds = p/(1−p). A one-unit increase in z multiplies odds by e.
Probit Probability
p = Φ(z) where Φ is the normal CDF.
Probit can fit better when latent noise is Gaussian. Use the same score equation; only the probability mapping changes.
How to Use This Calculator
- Select the model type that matches your scoring method.
- Enter the intercept and each feature’s coefficient.
- Provide feature values for the case you’re evaluating.
- Set a decision threshold for class prediction.
- Click Calculate to view probability, odds, and contributions.
Binary Decisions Need Probabilities
Binary outcome probabilities support practical decisions where only two results exist, such as churn versus retain, fraud versus legitimate, or click versus no click. This calculator converts a linear score into an event probability, helping analysts compare cases on a common scale. By entering coefficients and feature values, you can reproduce a model’s scoring logic, validate pipelines, and communicate risk in business terms rather than raw scores.
Scores, Odds, And Contributions
Models often output a score z that is not yet intuitive. The calculator reports probability, odds, and log-odds to strengthen interpretation. Odds express how many times more likely the event is than the non-event, while log-odds add linearly with each feature contribution. Reviewing the contribution table reveals which variables drive the score, supports feature debugging, and highlights when a single extreme input dominates the prediction.
Logistic Versus Probit Mapping
Logistic and probit mappings both transform the score into a 0–1 probability, but they assume different error structures. Logistic uses the sigmoid function and yields straightforward odds ratios, which is useful for reporting and policy rules. Probit uses the normal cumulative distribution, which can align with latent Gaussian noise assumptions in some scientific settings. Comparing both mappings on the same inputs can reveal sensitivity around the center of the curve.
Thresholds Shape Operational Outcomes
Operational decisions require a threshold, not just a probability. This tool lets you set the cutoff and returns a predicted class, enabling what-if analysis. Lower thresholds increase recall of positives but raise false positives; higher thresholds reduce false alarms but miss more events. Pair threshold testing with cost estimates, prevalence, and capacity constraints to choose a policy that matches your objectives, not a generic 0.50 default.
Calibration, Drift, And Governance
Reliable probabilities depend on clean inputs and stable relationships over time. Standardize feature definitions, handle missing values consistently, and document coefficient versions so outputs remain comparable. Monitor calibration by comparing predicted probabilities with observed rates in recent data, especially after product changes or seasonality shifts. When drift appears, retrain or recalibrate, then update coefficients in this calculator to keep stakeholders aligned with the current model.
FAQs
What does the score z represent?
z is the linear combination of the intercept and feature contributions: z=b0+Σ(βi·xi). It is the model’s raw score before mapping into a probability. Larger z increases probability under both logistic and probit mappings.
When should I choose the probit option?
Use probit when your workflow, research domain, or historical models expect a normal CDF link. It can behave slightly differently near the center and tails. Logistic is often preferred when you want direct odds and odds-ratio interpretation.
How should I pick a decision threshold?
Start from the business cost of false positives versus false negatives. Then test thresholds on validation data and review precision, recall, and capacity limits. Choose a cutoff that meets operational constraints, not an arbitrary 0.50.
Do I need standardized or scaled features?
Only if your coefficients were trained on standardized inputs. If a model used z-scores, apply the same mean and standard deviation before entering values. Using unscaled values with scaled coefficients can distort the score and probability.
How do I interpret the odds shown?
Odds equal p/(1−p). Odds of 3 mean the event is three times as likely as the non-event. In logistic models, a one-unit increase in z multiplies odds by e, holding inputs constant.
Why might predicted probabilities drift over time?
Data distributions and relationships can change due to seasonality, product updates, or population shifts. Monitor calibration by comparing predicted probabilities with observed outcome rates. If drift appears, retrain or recalibrate the model and update coefficients.